Zeta Lab: Research Timeline

[Qualified] [ordinary mathematical derivation] paid_surplus_obstruction: At N=144 the rational vector 20(c_1,...,c_12)=(20,-20,-20,0,-20,-13,7,6,0,0,0,13) has harmonic balance, coverage through q=5, mass 119/20, and zero positive surplus at every prime power, so the fully saturated paid cost is exactly psi(144).

Mon, 14 Sep 2026 00:02:06 -0500

Outcome: At N=144 the rational vector 20(c_1,...,c_12)=(20,-20,-20,0,-20,-13,7,6,0,0,0,13) has harmonic balance, coverage through q=5, mass 119/20, and zero positive surplus at every prime power, so the fully saturated paid cost is exactly psi(144).

Question: Can balanced rational coefficients supported through 12 and covering q through 5 eliminate paid surplus at N=144?

Method: Exact rational substitution checked W_d <= 1 at all 47 prime powers through 144, and both interval backends at 35 and 70 digits priced the old endpoint surplus 4.414404 against the new surplus of zero.

Disposition: qualified | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: Disposition is qualified because the case log records independent challenge pending. The independent test implementation is by the same producer, not an independent reviewer. This does not supply a scale-dependent family or a uniform bound. Zero of 47 prime powers have positive surplus; eight have strict deficits, including a negative row at d=23 that must be retained in the repair cost.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [ordinary mathematical derivation] paid_shortfall_scaling: The perfect-power cap saving for old fixed-seed square-root-support lifts is at most order N^{1/4} log N, and an explicit balanced Mobius-prefix family at N=36864 lowers full excess over N from 877.252193 to 220.982190 by excluding composites witnessed by 2, 3, 5, 7, with coefficients unchanged; the uniform N+O(sqrt(N) log(N)^2) target remains unproved.

Sun, 13 Sep 2026 19:31:01 -0500

Outcome: The perfect-power cap saving for old fixed-seed square-root-support lifts is at most order N^{1/4} log N, and an explicit balanced Mobius-prefix family at N=36864 lowers full excess over N from 877.252193 to 220.982190 by excluding composites witnessed by 2, 3, 5, 7, with coefficients unchanged; the uniform N+O(sqrt(N) log(N)^2) target remains unproved.

Question: Can scale-dependent balanced coefficients lower the complete paid excess, and how much can perfect-power caps contribute?

Method: An exact signed factorial-sum identity prices the perfect-power cap, a Mobius-prefix family is given with mass at most 2y-1, and five fixed cutoffs were checked with two interval implementations at two precisions.

Disposition: partly settled | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: Disposition is partly settled because the finite identities and the N=36864 improvement are recorded, while the uniform complete-cost target is explicitly unproved. No extrapolated exponent, RH claim, or novelty claim.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] paid_shortfall_saturation: For the five fixed selected-prefix cutoffs N=144, 576, 2304, 9216, 36864, every ordinary composite in the local repair interval is exposed by primes through floor(sqrt(X)) while every prime power remains, and the saturated local cap equals the exact Mangoldt weight, with zero remaining local cap surplus.

Sun, 13 Sep 2026 23:10:55 -0500

Outcome: For the five fixed selected-prefix cutoffs N=144, 576, 2304, 9216, 36864, every ordinary composite in the local repair interval is exposed by primes through floor(sqrt(X)) while every prime power remains, and the saturated local cap equals the exact Mangoldt weight, with zero remaining local cap surplus.

Question: Does full trial division through floor(sqrt(floor(N/y))) make the local repair cap equal the Mangoldt weight for the five fixed selected-prefix cases?

Method: Unchanged selected prefixes were saturated by trial division through floor(sqrt(X)) at supports 12, 18, 48, 95, 192, with exact prime-log vectors and both python-flint and mpmath.iv interval routes overlapping at 35 and 70 digits.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: No RESULTS.md at the pin. Headline filled from the case log and RUNS.md. Ordinary-composite retention failures, prime-power retention failures, and cap-equality failures were all zero. Global positive surplus S remains nonzero; only the local repair cap saturates. No general rate claim. Enclosure-supported applies to the two-backend log pricing of the exact vectors, not to a new analytic bound.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] paid_shortfall: An early-truncated finite balanced lift has a complete paid-tail bound of order sqrt(N) log N at square-root support, but the leading constant stays above one so excess over N is still linear, while at N=14 with support at most three, perfect-power caps remove the optimal raw excess log(2)/2.

Sun, 13 Sep 2026 18:47:57 -0500

Outcome: An early-truncated finite balanced lift has a complete paid-tail bound of order sqrt(N) log N at square-root support, but the leading constant stays above one so excess over N is still linear, while at N=14 with support at most three, perfect-power caps remove the optimal raw excess log(2)/2.

Question: Can an early-truncated explicit factorial lift have a proved full paid-shortfall budget at square-root support?

Method: An explicit early-truncation lemma charges every remainder, and the durable run passed 768 truncation cases and 3072 inequalities on both interval backends at 35 and 70 digits, including the exact N=14 primal and dual identities.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: No Lean proof or external review. The all-N bound rests on the displayed derivation, not on the size of the finite domain. The base-6 seed has leading constant (4 log 2 + 3 log 3)/5 > 1. No RH or novelty claim.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Open] [measured] lambda_dh_exact: Open, theory phase only: the hunt is entitled to say nothing about Lambda_DH, the pre-registered crowding mechanism was never scored after the 2026-08-18 evaluation runs died on API 529 errors, and the one height-1e6 float-grade zero (y0=0.3583) is shallower than hunt #4's height-240 pair.

Sat, 12 Sep 2026 22:52:48 +0000

Outcome: Open, theory phase only: the hunt is entitled to say nothing about Lambda_DH, the pre-registered crowding mechanism was never scored after the 2026-08-18 evaluation runs died on API 529 errors, and the one height-1e6 float-grade zero (y0=0.3583) is shallower than hunt #4's height-240 pair.

Question: Does the crowding shave vanish along a sequence of Davenport-Heilbronn zeros whose depth approaches Delta, so that sup t* = Delta^2/2 and the bracket 0.0576 < Lambda_DH <= 0.19242481458 collapses to a point, or does the shave stay bounded away from zero so the gap is real?

Method: A crowding model calibrated on hunt #4's nine landings (rms 0.54 percent) was left unadjudicated, a float64 Euler-Maclaurin screen at height 10^6 located one off-line zero, and an argument-principle control nested flagged windows as the inner abscissa moved from 0.85 to 0.55.

Disposition: open | Evidence: measured | Role: primary investigation

Notes: RESULTS.md exists to say there is no result. Artifacts are measured, unadjudicated, and unreviewed: the height-1e6 zero is float grade, the screen is not exhaustive, and the model extrapolation to depths near Delta remains an extrapolation from y0 <= 0.37. None of the five kill conditions was evaluated. Renumbered from #52 to #119 on 2026-09-12. Hunt #61's bracket is unchanged.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] quotient_certificate: Requiring the factorial ceiling only at floor(N/d) reduces the earlier all-cell excess by 34.4 percent, 29.9 percent, and 41.9 percent at N=1000, 10000, and 100000, and an exact N=27, y=9 example with eight prime-looking cells has minimum excess log(2), refuting the earlier dimension-count argument for zero excess.

Mon, 07 Sep 2026 11:22:02 -0500

Outcome: Requiring the factorial ceiling only at floor(N/d) reduces the earlier all-cell excess by 34.4 percent, 29.9 percent, and 41.9 percent at N=1000, 10000, and 100000, and an exact N=27, y=9 example with eight prime-looking cells has minimum excess log(2), refuting the earlier dimension-count argument for zero excess.

Question: How much excess does positivity on unattainable cells force in the finite factorial-certificate LP?

Method: The attainable-quotient LP at square-root support retained 889 constraints checked in exact integer arithmetic, and an exact rank-seven row relation at N=27 produced a feasible vector attaining excess log(2).

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Status is finite improvement and correction, no asymptotic result; mapped to completed for the finite work. The N=27 counterexample is an ordinary exact argument; the percentage reductions are measured LP ceilings, so the composite grade is measured. Input is the factorial LP at main d393e1a under prime_pair_error/frontier.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] prime_pair_error: Chou-Haag-Huryn-Ledoan Table 1 reproduces at all eleven rows after truncation, E(N)/(N^2 log^2 N) keeps rising to 0.244 at 10^7, odd separations carry nothing, and on even k the error is S(k)[R(N)+R(N-k)-R(k)], a k-resolved refinement of Korevaar and te Riele's Approximation 2.1 that explains 1 to 3 percent of E(N).

Sun, 06 Sep 2026 01:30:13 -0500

Outcome: Chou-Haag-Huryn-Ledoan Table 1 reproduces at all eleven rows after truncation, E(N)/(N^2 log^2 N) keeps rising to 0.244 at 10^7, odd separations carry nothing, and on even k the error is S(k)[R(N)+R(N-k)-R(k)], a k-resolved refinement of Korevaar and te Riele's Approximation 2.1 that explains 1 to 3 percent of E(N).

Question: Which separations k carry the Chou-Haag-Huryn-Ledoan error E(N), and is there one compact relationship, with the Hardy-Littlewood prediction held fixed, that accounts for a measurable part of psi_2(N, k) - S(k)(N - k)?

Method: FFT autocorrelation of Lambda through N=10^7 was cross-checked against pure-Python and direct pair sums, with a three-profile fit discovered on N<=10^6 and tested at the held-out cutoffs 3e6 and 1e7.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is settled as a reproduction plus one measured relationship, not new; mapped to completed. k divisible by 3 is one sixth of the separations and about half of the error. The directory at the pin later accumulated residue, wronskian, upper-bound, and factorial-certificate-frontier files; this row records the case-log reproduction, not those later arms. Nothing bears on RH.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] outband_certificate: Kill condition 2 fires at prose grade: the out-of-band positivity is worth zero to any certificate whose positivity input is Weil's Hermitian form, because a positive-definite kernel has nonnegative transform so bandwidth one is forced, and what hunt #110 priced was the RH-conditional class.

Sun, 06 Sep 2026 00:21:59 -0500

Outcome: Kill condition 2 fires at prose grade: the out-of-band positivity is worth zero to any certificate whose positivity input is Weil's Hermitian form, because a positive-definite kernel has nonnegative transform so bandwidth one is forced, and what hunt #110 priced was the RH-conditional class.

Question: Is there an inertia or isolation argument, valid for a kernel signed only on alpha in (1, 1.5], that lets a finite certificate spend the BGSTB out-of-band positivity, and what unconditional simple-zero proportion does it deliver; or is 0.6725007 a ceiling for every certificate reading only that positivity?

Method: Dual kernels of the configuration LP were read off at matched grids, an edge lemma for real even spectral factors was proved, and a signed-window candidate died because an even autocorrelation is strictly positive just inside its support edge.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: RESULTS.md grades the edge lemma and dichotomy as proved, the paper-compression structure as read, and the LP numbers as measured; nothing is kernel-checked. The composite headline is the ceiling, so the row grade is ordinary mathematical derivation. A strip of width 0.05 is inside method error; the wide strip from hunt #110 stays established at 3.5 times that error. Renumbered from #111 to #118 on 2026-09-06.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [measured] four_point_pressure: Exact substitution of n=4, c=2330/1000000, p=2500, m=432 produces the candidate (14400000*H - 17240)/14366681 about 0.6728603588, above the registered 0.6728470198, but GitHub Actions run 33987435968 canceled during the dependency build and every candidate proof step was skipped, so no new proved bound is claimed.

Sat, 05 Sep 2026 21:13:47 +0000

Outcome: Exact substitution of n=4, c=2330/1000000, p=2500, m=432 produces the candidate (14400000*H - 17240)/14366681 about 0.6728603588, above the registered 0.6728470198, but GitHub Actions run 33987435968 canceled during the dependency build and every candidate proof step was skipped, so no new proved bound is claimed.

Question: Can joint pressure and floor tuning improve the four-point bound with a manageable exact proof tree?

Method: The candidate was substituted exactly into the existing bridge, an emitted-source preflight reported 1516 cell lemmas and 11863 leaves with zero problems, and the complete Lean workflow at d28df5f992479cd32751cb90c8c88551550582a3 was canceled at 2026-09-05T19:42:20Z before FourPoint.Base ran.

Disposition: qualified | Evidence: measured | Role: artifact preservation

Notes: No RESULTS.md or HANDBACK at the pin. Question filled from the HuntSpec. Case log records closed exploratory record, complete Lean check canceled. Disposition is qualified rather than completed because the candidate proof was canceled during the dependency build and no new proved constant was established. Role is artifact preservation because MISSION.md exists to preserve arithmetic and terminal status without importing the candidate.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] cycle_moments: Finite concave spectral counting inequalities and an exact counting distinction are established, including eight Lean files with AXLE receipts under standard axioms, but second and third moments alone cannot force a gain, and no stronger zeta proportion is asserted.

Sat, 05 Sep 2026 12:51:19 -0700

Outcome: Finite concave spectral counting inequalities and an exact counting distinction are established, including eight Lean files with AXLE receipts under standard axioms, but second and third moments alone cannot force a gain, and no stronger zeta proportion is asserted.

Question: Can joint cycle moments strengthen simple-real counting beyond its quadratic bound?

Method: Eight standalone Lean 4.33.0 files were checked via AXLE with printed axioms restricted to propext, Classical.choice, and Quot.sound, beside exact finite examples, 160-bit interval sign checks, and Haar-unitary probes that do not establish a population gain.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No explicit Status field in the root case-log entry; disposition is completed from RESULTS.md bounded outcome. Evidence grade is measured under ALIGNMENT weakest-step discipline: while eight individual Lean declarations have AXLE kernel-check receipts, the moment scans, mixed inequalities, and absence of an asymptotic zeta proportion gain are measured and unproved, so the composite row grade is measured rather than kernel-checked.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] outband_intake: The BGSTB out-of-band positivity is worth about +0.005 to +0.009 at the measure level, landing the configuration class in [0.679, 0.682], but no known certificate can spend it: a kernel with ghat <= 0 outside [-1,1] is not a Gram matrix, so the inertia lemma's positivity half fails.

Mon, 31 Aug 2026 18:22:01 -0500

Outcome: The BGSTB out-of-band positivity is worth about +0.005 to +0.009 at the measure level, landing the configuration class in [0.679, 0.682], but no known certificate can spend it: a kernel with ghat <= 0 outside [-1,1] is not a Gram matrix, so the inertia lemma's positivity half fails.

Question: Is there a diagonal-isolation argument valid for a kernel with ghat <= 0 outside [-1,1], and what unconditional proportion does the resulting certificate deliver for the simple on-line zeros of zeta?

Method: Two matched LP ladders of five rungs priced the out-of-band constraint against an in-band control whose known limit is the record 0.6725007036794116, calibrating method error at about +0.0018, while a 2-by-2 witness with indefinite S refuted the inertia half for a signed kernel.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is probe, complete, GAP, not a barrier; mapped to completed because the measurement finished and the kill condition did not fire. The coincidence with CGdL's RH-conditional 0.6792 is withdrawn in RESULTS.md, as is the ratio test. Gate #3 fires: the drop is prime-blind. Row_range is 0-indexed as in batch 1, so these eleven rows are hunt-list rows 88 through 98.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [ordinary mathematical derivation] support_78c499b4: A targeted literature search across arXiv and web sources found the Cohn-Elkies LP certificate route untouched and live for one-dimensional pair sums with positive-part targets, but standard bibliographic databases (MathSciNet, zbMATH, Google Scholar, ontology/knownness.py) were omitted, and in dimension 1 the equidistant lattice ground-state property is not guaranteed outside completely monotone potentials.

Tue, 25 Aug 2026 08:46:55 -0500

Outcome: A targeted literature search across arXiv and web sources found the Cohn-Elkies LP certificate route untouched and live for one-dimensional pair sums with positive-part targets, but standard bibliographic databases (MathSciNet, zbMATH, Google Scholar, ontology/knownness.py) were omitted, and in dimension 1 the equidistant lattice ground-state property is not guaranteed outside completely monotone potentials.

Question: Has a Cohn-Elkies / Delsarte linear-programming certificate been applied to a one-dimensional pair sum with positive-part band-limited shape, and does a published theorem settle whether the LP value equals the lattice value in dimension 1?

Method: Executed nine targeted web queries and resolved 14 arXiv preprints via Atom API without querying MathSciNet, zbMATH, Google Scholar, or ontology/knownness.py, identifying Rupert Li discrete-reduction dual bounds as the relevant transfer method.

Disposition: qualified | Evidence: ordinary mathematical derivation | Role: support work

Notes: Case-log status is settled as far as a literature question can be settled in one search pass; disposition is qualified to reflect search scope boundaries (MathSciNet, zbMATH, Google Scholar, and ontology/knownness.py were not searched). Evidence grade is ordinary mathematical derivation for the structural deductions; no computation or measurement was performed in this directory.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_5418c63e: Depth-1 damage windows do not drift: the first correction to D(1,s) is odd so it translates the window rather than widening it, D(1, 2 pi d) > 0 for every integer d >= 1 by an exact cubic with no d_max, and a 0.002 scan of [1e-6, 1e5] finds 31830 sign changes with all 15915 lattice points inside a window.

Tue, 25 Aug 2026 08:46:52 -0500

Outcome: Depth-1 damage windows do not drift: the first correction to D(1,s) is odd so it translates the window rather than widening it, D(1, 2 pi d) > 0 for every integer d >= 1 by an exact cubic with no d_max, and a 0.002 scan of [1e-6, 1e5] finds 31830 sign changes with all 15915 lattice points inside a window.

Question: Do the windows of D(1, s) > 0 track 2 pi asymptotically or drift, and does every multiple of 2 pi lie inside a depth-1 window for all d >= 1?

Method: ghat was put over the common denominator z^2+2 to an exact one-term form, D restricted to 2 pi Z reduced to a cubic P(u) with one nonnegative root below (2 pi)^2, and a 0.002 scan plus bisection on [1e-6, 1e5] was checked against mpmath dps=60 edge locations.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HANDBACK at the pin. Question filled from the bounded question in MISSION.md. Raw RESULTS H1 is only a title; the headline is taken from the RESULTS status paragraph and the case log. Evidence grade is ordinary mathematical derivation for D(1, 2 pi d) > 0 for all d >= 1; the scan is measured confirmation. d = 0 is the one exception (D(1,0) = -0.9116) and never arises in P because the sum is over p != q. One expansion error (expanding 1/S at 2 pi d instead of keeping the x term) was caught before the number was written down. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Artifact-only] [unreviewed] support_4019e8e5: Artifact only, no write-up and no results: oracles.py and t1lp.py from ARM A-PRIME of the r_c7f779 fan-out were rescued from an uncommitted fulcrum worktree, and the code has never been run in this tree.

Tue, 25 Aug 2026 08:46:57 -0500

Outcome: Artifact only, no write-up and no results: oracles.py and t1lp.py from ARM A-PRIME of the r_c7f779 fan-out were rescued from an uncommitted fulcrum worktree, and the code has never been run in this tree.

Question: Can a Cohn-Elkies-style certificate LP for T1 be implemented with independent oracles for f, sharing one implementation of f between the probe and the a-posteriori verifier?

Method: No method ran in this tree; t1lp.py is shared machinery for the T1 certificate LP and oracles.py checks f against gram_form and against quadrature, both committed so they survive git clean.

Disposition: artifact-only | Evidence: unreviewed | Role: artifact preservation

Notes: No MISSION.md, HANDBACK, RESULTS.md, or results file at the pin. Question filled from the t1lp.py and oracles.py module docstrings. Disposition is artifact-only as specified for this pair. Case log: it has never been run in this tree.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Artifact-only] [unreviewed] support_17a0f787: Artifact only, no write-up: probe.py and results_quick.json from ARM C of the r_c7f779 fan-out were rescued from an uncommitted fulcrum worktree, and the JSON carries a planted-control ladder with firing scales that this entry does not claim shows anything.

Tue, 25 Aug 2026 08:46:49 -0500

Outcome: Artifact only, no write-up: probe.py and results_quick.json from ARM C of the r_c7f779 fan-out were rescued from an uncommitted fulcrum worktree, and the JSON carries a planted-control ladder with firing scales that this entry does not claim shows anything.

Question: At several depths 2y, is the ratio row(y)/Shq(y) maximised at y = 1/2, is the maximiser still the uniform 2*pi lattice, and where does the optimal base spacing sit?

Method: No method was written up in this tree; probe.py is ARM C of r_c7f779, a finer periodic-occupancy search plus a planted-fault control, and results_quick.json is the only committed output.

Disposition: artifact-only | Evidence: unreviewed | Role: artifact preservation

Notes: No MISSION.md, HANDBACK, or RESULTS.md at the pin. Question filled from the probe.py module docstring, which names the bounded question put by run 872d7dce. Disposition is artifact-only as specified for this pair. The case log forbids citing the JSON as a result. The run is recorded stopped in fulcrum.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_4166b0: Every soundcalc parameter that could be re-derived from a vendor's own source re-derived exactly, 51 of 51 numeric fields across RISC0, Miden, OpenVM and SP1, and soundcalc at its pin reproduces its own reports byte-for-byte, while the failures are all in provenance: two of eight cited pins do not resolve, and four units ship no reproduction path.

Tue, 25 Aug 2026 11:21:58 -0500

Outcome: Every soundcalc parameter that could be re-derived from a vendor's own source re-derived exactly, 51 of 51 numeric fields across RISC0, Miden, OpenVM and SP1, and soundcalc at its pin reproduces its own reports byte-for-byte, while the failures are all in provenance: two of eight cited pins do not resolve, and four units ship no reproduction path.

Question: Do the ten zkVM soundness figures published by ethereum/soundcalc reproduce to the bit from the vendors' own trees at the versions the TOMLs name, and do the same TOMLs still describe the vendors' current releases?

Method: Each unit received two unmerged verdicts, REPRODUCTION and FRESHNESS, by regenerating parameters from the named vendor tree and rerunning soundcalc at pin d9078d64c9c3, with six planted faults each turning the verdict they should.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled for the units where a source existed; four units have no reproduction path and that is a property of the artifacts, not of the budget. Disposition maps to completed because the missing paths are findings, not unfinished work. SP1 is scoped: 30 of 42 numeric fields from source constants, 12 from machine.shape() at runtime, which needs a Rust build this run did not do. FRESHNESS unchanged for RISC0 means only that the cited September 2024 notebook is byte-identical, not that the vendor's prover is unchanged. Question filled from the HuntSpec. Paired with r_0dfb8d as the other transfer test outside mathematics.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [ordinary mathematical derivation] support_f3ab3e34: Erdos #126 reduces in four elementary lines to a unit-equation solution count: g(k) <= 2 + N(k+1) where N(r) bounds solutions of x+y=1 in a rank-r subgroup of Q*, so N(r)=exp(o(r)) implies the conjecture, and the known N(r) <= 2^{8r+8} is the same exponential wall the 1934 theorem sits at.

Mon, 24 Aug 2026 20:58:22 -0500

Outcome: Erdos #126 reduces in four elementary lines to a unit-equation solution count: g(k) <= 2 + N(k+1) where N(r) bounds solutions of x+y=1 in a rank-r subgroup of Q*, so N(r)=exp(o(r)) implies the conjecture, and the known N(r) <= 2^{8r+8} is the same exponential wall the 1934 theorem sits at.

Question: Ignoring the earlier brief's three lanes, what proof program does Erdos #126 admit from the statement, and which first unproved step is strongest?

Method: The injectivity map c |-> ((a1+c)/D, -(a2+c)/D) into X+Y=1 was written out and machine-checked on a witness as exact rationals, then four chains were ranked by the strength of their first unproved step.

Disposition: qualified | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HuntSpec.question field; question filled from the bounded question in MISSION.md. Handback status is not-settled; case log says not settled, and the program is named. Disposition is qualified because the reduction is a program, not a settlement, and is not claimed as new. Literature rows come from search summaries and arXiv:2602.07545 because erdosproblems.com/126 returned HTTP 403; treat them as cited, not verified at source.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_eccd5f5e: The Erdos #126 scout's mathematics survives adversarial audit: the inverse g(k) reformulation, the positivity equivalence, the Fekete/composition refutation and the whole finite table are correct and the table reproduces under an independently written search, while the omitted-prime loose thread is false and the no-progress-beyond-1934 framing hides three relevant papers the scout cites none of.

Mon, 24 Aug 2026 20:58:08 -0500

Outcome: The Erdos #126 scout's mathematics survives adversarial audit: the inverse g(k) reformulation, the positivity equivalence, the Fekete/composition refutation and the whole finite table are correct and the table reproduces under an independently written search, while the omitted-prime loose thread is false and the no-progress-beyond-1934 framing hides three relevant papers the scout cites none of.

Question: Does the Erdos #126 scout's mathematics in r_186989 survive adversarial audit?

Method: Every claim in r_186989/RESULTS.md was re-proved or independently recomputed, and a second search written from the problem statement reproduced all seven table rows 2, 4, 5, 6, 8, 10, 11 exactly.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: audit

Notes: No HuntSpec.question field; question filled from MISSION.md. Disposition maps settled (audit) to completed. Literature constants (1/8+eps, exp(c sqrt(s)/log s)) rest on erdosproblems.com plus web-search summaries of Gyory-Stewart-Tijdeman 1986 and Erdos-Stewart-Tijdeman 1988 whose abstracts were not read at source. The S-unit reduction in section 7 is proved; the counting step built on it is explicitly not.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [ordinary mathematical derivation] support_d5d5ccae: The S-unit arm has a sound two-line injectivity lemma, so g(k) <= 2 + max_d N_S(d), but Evertse's 37^{d+2s} gives g(k) <= 2 + 37^{2k+3} ~ 1029*49^k, weaker than the 1934 bound by a factor about 24.5^k, and at k=7 the quantity Evertse bounds by 7.0e14 has measured value 96 against the elementary ceiling 128.

Mon, 24 Aug 2026 20:57:54 -0500

Outcome: The S-unit arm has a sound two-line injectivity lemma, so g(k) <= 2 + max_d N_S(d), but Evertse's 3*7^{d+2s} gives g(k) <= 2 + 3*7^{2k+3} ~ 1029*49^k, weaker than the 1934 bound by a factor about 24.5^k, and at k=7 the quantity Evertse bounds by 7.0e14 has measured value 96 against the elementary ceiling 128.

Question: Does the two-variable S-unit equation route, with injectivity from fixed base elements, produce a bound on g(k) better than the classical 2^k, or is it provably too weak?

Method: The injectivity lemma was written in two lines, Evertse 1984 and Beukers-Schlickewei were read off the Beukers-Schlickewei paper, and S-smooth differences were counted to 10^14, reproducing Lehmer's Stormer table exactly for k=1..8.

Disposition: qualified | Evidence: ordinary mathematical derivation | Role: support work

Notes: Question filled from the HuntSpec. Handback status is not-settled; case log returns the too-weak verdict the brief allowed. Disposition is qualified rather than completed because the route is not refuted, it is starved: box-truncated counts are lower bounds only, and eight points cannot separate polynomial from exponential growth. The lemma is not claimed as new.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_baf4cde6: The entropy/signature lane is closed by proof: for every prime bound P, arbitrarily large sets satisfy every constraint S-summability imposes at primes below P (Theorem B), so no entropy, VC, container, DRC or forbidden-pattern argument over prime-valuation signatures can bound |A| at all, let alone beat 2^k.

Mon, 24 Aug 2026 20:57:40 -0500

Outcome: The entropy/signature lane is closed by proof: for every prime bound P, arbitrarily large sets satisfy every constraint S-summability imposes at primes below P (Theorem B), so no entropy, VC, container, DRC or forbidden-pattern argument over prime-valuation signatures can bound |A| at all, let alone beat 2^k.

Question: Can prime-valuation signatures plus entropy, VC, containers, dependent random choice, or forbidden patterns show that an S-summable set has subexponential size?

Method: Theorem B was proved by taking A = {1+iM} with M the product of odd primes <= P outside S, checked at P=60 with |A|=200 and zero violations, and Lemma A was witnessed by A={1,3,7,13}, S={2,5,7} re-verified by trial division.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps lane closed, by proof rather than by a failed attempt to completed. Theorem B kills arguments whose input is p-adic data at a fixed finite prime set; it does not kill an argument that uses the archimedean ordering or the cofinite condition. ESS unit-equation numbers are recalled from literature.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_95bb5cb7: The size dichotomy cannot close: the controlled-interval horn delivers log g(k) = o(k) if and only if max(A) = rad(S)^{o(1)}, pinned from both sides by Rankin above and simplex volume below, and the other horn cannot supply that because after gcd-normalization the height of a primitive admissible set of sub-extremal size is unbounded.

Mon, 24 Aug 2026 20:55:56 -0500

Outcome: The size dichotomy cannot close: the controlled-interval horn delivers log g(k) = o(k) if and only if max(A) = rad(S)^{o(1)}, pinned from both sides by Rankin above and simplex volume below, and the other horn cannot supply that because after gcd-normalization the height of a primitive admissible set of sub-extremal size is unbounded.

Question: Does a size dichotomy (large-gap descent vs smooth-number counting in a controlled interval) yield log g(k) = o(k) for Erdos 126, and if not, where exactly does it fail?

Method: The counting horn was pinned from both sides (Rankin upper, simplex-volume lower), and height witnesses for primitive admissible triples were enumerated by full trial division up to 5.6e14 for k=2, |A|=3.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: Question filled from the HuntSpec. Disposition maps the arm is settled negative; the conjecture is untouched to completed for the arm, not for Erdos #126. The arity paragraph cites Evertse-Schlickewei-Schmidt and Erdos-Stewart-Tijdeman from literature and was not re-derived here. The audit correction that r_186989's 'every optimal witness has elements < 50' fails is reported here and was not edited into r_186989.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_8ea74995: The equivalences r_186989 used are correct and are now proved in full, and its arm-3 finding is right but understated: any amplification law g(k+C) >= lambda*g(k) with C and lambda>1 constant refutes Erdos #126, not just supermultiplicativity; the load-bearing new statement is that #126 is a forall-S forall-A claim while every enumeration produces exists-S exists-A, so the computational arm can only refute.

Mon, 24 Aug 2026 20:57:24 -0500

Outcome: The equivalences r_186989 used are correct and are now proved in full, and its arm-3 finding is right but understated: any amplification law g(k+C) >= lambda*g(k) with C and lambda>1 constant refutes Erdos #126, not just supermultiplicativity; the load-bearing new statement is that #126 is a forall-S forall-A claim while every enumeration produces exists-S exists-A, so the computational arm can only refute.

Question: Are the equivalent formulations r_186989 used correct, and what is the exact implication direction of construction, composition, and pruning statements for Erdos #126?

Method: The inverse relation was proved as a Galois connection, five asymptotic equivalences were written out, the omitted-prime thread was refuted by A congruent to 1 mod p, and the amplification direction was proved by induction from g(1)=2 rather than by Fekete.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps settled, for the bounded question it was given to completed. Evertse and Erdos-Stewart-Tijdeman counts are literature, not verified here. The Erdos-Turan bound 3*2^(k-1) is used as published.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_7ddfee4b: Omitting an odd prime p from S caps occupied residue classes mod p, not |A|, and only p = 2 caps |A|, at 2; a descent g*(k) <= 2^k exists for primitive A and is tight at k = 1, 2, but its per-prime loss cannot go below 2 because the residue relaxation that parity, residue classes, prime deletion and the power-of-2 lemma all factor through has optimum exactly 2^k.

Mon, 24 Aug 2026 20:57:10 -0500

Outcome: Omitting an odd prime p from S caps occupied residue classes mod p, not |A|, and only p = 2 caps |A|, at 2; a descent g*(k) <= 2^k exists for primitive A and is tight at k = 1, 2, but its per-prime loss cannot go below 2 because the residue relaxation that parity, residue classes, prime deletion and the power-of-2 lemma all factor through has optimum exactly 2^k.

Question: Is there a descent recurrence for g(k) whose per-prime loss tends to 1 rather than 2, and does omitting a small prime from S cap |A|?

Method: The omission claim was refuted by explicit A inside 1 + pZ at p = 3, 5, 7, 11, re-verified by trial division, and the loss-2 wall was proved by exhibiting a relaxation whose optimum is exactly 2^k.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps settled, in both directions to completed. Theorem 4 covers primitive sets only; the divisible part A_p escapes the descent. Nothing here improves the classical 3*2^(k-1).

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_60982bf6: Ranging over all k-subsets of the first nine primes for k <= 5 does not beat the first k primes, so r_186989's flagged door with genuine trade shape is slack; the sweep produced a proved normalization (admissible sets are exactly the S-smooth dilates of primitive ones) and a refutation of the residue lemma |A| <= p-1 for p not in S, which is false for every odd p.

Mon, 24 Aug 2026 20:56:42 -0500

Outcome: Ranging over all k-subsets of the first nine primes for k <= 5 does not beat the first k primes, so r_186989's flagged door with genuine trade shape is slack; the sweep produced a proved normalization (admissible sets are exactly the S-smooth dilates of primitive ones) and a refutation of the residue lemma |A| <= p-1 for p not in S, which is false for every odd p.

Question: Does ranging over choices of S, instead of freezing the first k primes, beat r_186989's table, and which structural lemmas does that computation discover or falsify?

Method: A solver that builds edges from S-smooth sums rather than scanning O(N^2) pairs ran exhaustively over all binom(9,k) subsets for k <= 5 (381 searches), and the residue lemma was killed by trial-division witnesses at p = 3, 5, 7 including A={1,3,7,13}, S={2,5,7} from r_186989's own table.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps settled, as a support answer to completed. 'First k primes are not beaten' is exhaustive over the stated subsets and boxes only, and is a claim about a maximum, which this machinery cannot refute. The height conjecture is not leaned on.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] support_517b887f: The Erdos-Turan factor 2 per prime cannot be improved to (2-delta) by joint or reordered prime processing: the architecture reduces entirely to c(A), the largest subset whose pairwise sums are powers of 2, which satisfies c(A) in {1,2} and is defined order-blind, so the selection lemma with phi(k)=(2-delta)^k is logically equivalent to the target bound rather than a refinement of the 1934 bookkeeping.

Mon, 24 Aug 2026 20:56:27 -0500

Outcome: The Erdos-Turan factor 2 per prime cannot be improved to (2-delta) by joint or reordered prime processing: the architecture reduces entirely to c(A), the largest subset whose pairwise sums are powers of 2, which satisfies c(A) in {1,2} and is defined order-blind, so the selection lemma with phi(k)=(2-delta)^k is logically equivalent to the target bound rather than a refinement of the 1934 bookkeeping.

Question: Can the Erdos-Turan 1934 factor of 2 per prime be replaced by (2-delta)^k by processing primes jointly, retaining valuation information, or changing the order?

Method: The 1934 proof was reconstructed into a base case c(A) <= 2 plus one binary residue choice per odd prime, then two sketch defects were witnessed by exact integer sets re-verified by trial division, with a 104183-set sweep kept as bounded-box evidence only.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: support work

Notes: No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps settled, negatively to completed. The two defect witnesses are about the literature sketch, not about the theorem, which stands. The exhaustive sweep is not a proof of the repaired lemma.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Open] [unreviewed] r_c7f779: Opened 2026-08-24 and still in progress at the pin: the Cohn-Elkies-style certificate LP for T1 is being re-solved between the achievability floor 0.05716502 and the budget 0.06750841, with no RESULTS.md or handback recorded.

Mon, 24 Aug 2026 23:11:23 -0500

Outcome: Opened 2026-08-24 and still in progress at the pin: the Cohn-Elkies-style certificate LP for T1 is being re-solved between the achievability floor 0.05716502 and the budget 0.06750841, with no RESULTS.md or handback recorded.

Question: Does the Cohn-Elkies-style certificate LP for T1 have value below Shq(1/2) = 0.06750841, above it, or is it unresolvable at this cost?

Method: The hunt was opened from r_b9552d run 37fb06a9 loose thread 2, with certificate.py and lp.py present at the pin and the case log stating the entry will be rewritten when the run closes.

Disposition: open | Evidence: unreviewed | Role: primary investigation

Notes: No HANDBACK or RESULTS.md at the pin. Question filled from the HuntSpec. Headline filled from the case-log in-progress status. Support arms 17a0f787 (ARM C), 4019e8e5 (ARM A-PRIME), 5418c63e (ARM B), and 78c499b4 (ARM E, literature review on Cohn-Elkies LP bounds) were launched from this fan-out; only 5418c63e and 78c499b4 have write-ups. Evidence is unreviewed because nothing was measured in this directory.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_2969b0: Penman and Wells, INTEGERS 13 (2013) A57, Theorem 21, state DeepMind Problem 42's quantity character for character and reach sup g = ln(32/5)/ln(26/5) = 1.125944426, above the AlphaEvolve value which re-counts exactly to 1.1219357375 on 309 integers, and their Q_36, a 197-element set published thirteen years earlier, already beats it at g = 1.1219505699.

Mon, 24 Aug 2026 04:03:39 -0500

Outcome: Penman and Wells, INTEGERS 13 (2013) A57, Theorem 21, state DeepMind Problem 42's quantity character for character and reach sup g = ln(32/5)/ln(26/5) = 1.125944426, above the AlphaEvolve value which re-counts exactly to 1.1219357375 on 309 integers, and their Q_36, a 197-element set published thirteen years earlier, already beats it at g = 1.1219505699.

Question: Does Penman-Wells (2013) reach a higher value of DeepMind Problem 42's quantity than the AlphaEvolve construction?

Method: Both constructions were counted by exact integer enumeration from the primary sources, the decisive inequality was decided at 120 decimal digits, and Corollary 13's four counting formulas reproduced at 64 values of j with zero mismatches.

Disposition: completed | Evidence: measured | Role: audit

Notes: Disposition maps settled to completed. The safe statement is that the 2013 result beats the AlphaEvolve value, not that it is the current record: Staps (2015) and intervening literature were taken from the issue and not read here. The paper's abstract quantity f = ln|A+A|/ln|A-A| ranks the two sets the other way and is handled explicitly in RESULTS.md, kept out of the one-sentence headline. Question filled from the HuntSpec.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [ordinary mathematical derivation] r_186989: Erdos #126 is not settleable at scout cost and the scout died on a preregistered kill condition (suggestive finite data, no iterable lemma, no exp(o(k)) reduction); two things survive: f(n-1) <= f0(n) <= f(n), so the Formal Conjectures Finset Nat statement is faithful for the limit and wrong for pinned finite values, and a rigorous composition law would refute the conjecture rather than prove it, since g(1)=2 plus supermultiplicativity gives g(k) >= 2^k by Fekete.

Mon, 24 Aug 2026 21:29:51 -0500

Outcome: Erdos #126 is not settleable at scout cost and the scout died on a preregistered kill condition (suggestive finite data, no iterable lemma, no exp(o(k)) reduction); two things survive: f(n-1) <= f0(n) <= f(n), so the Formal Conjectures Finset Nat statement is faithful for the limit and wrong for pinned finite values, and a rigorous composition law would refute the conjecture rather than prove it, since g(1)=2 plus supermultiplicativity gives g(k) >= 2^k by Fekete.

Question: Does bounded reconnaissance on Erdos 126 find an iterable lemma, an exp(o(k)) reduction, or a rigorous composition law strong enough to promote the pair-sum prime-support problem to a funded lane?

Method: The problem was inverted to g(k) before any search, then exact branch-and-bound clique search on the S-smooth pair-sum graph produced lower bounds g(k) >= 2, 4, 5, 6, 8, 10, 11 for k = 1..7, with the positivity inequality and the Fekete direction written as short proofs.

Disposition: qualified | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: Handback status is not-settled; case log says not settled, scout killed on a preregistered kill condition. Disposition is qualified rather than completed because the conjecture is untouched and the table is lower bounds only. Evidence grade is ordinary mathematical derivation for the two survivors; the g(k) table is measured and is not an upper bound. Later support hunts refute the omitted-prime thread and the 'optima live below 50' reading; those corrections are recorded on the support rows and are not silently edited into this headline. Question filled from the HuntSpec. Hunt number in the brief was #90, already taken by amtopa_ceiling; the case log records this as Hunt #91.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [measured] r_0dfb8d: Five of six preregistered SWE-bench Verified entries recount to the integer from their own archived per-instance logs (265, 359, 384, 388, 396), agree on all twelve per-repository sub-counts, and show zero self-consistency failures across 2484 reports, while the sixth answers none of its 500 documented log keys and an archive-wide three-key probe finds 15 of 134 entries missing at the documented location.

Mon, 24 Aug 2026 20:58:53 -0500

Outcome: Five of six preregistered SWE-bench Verified entries recount to the integer from their own archived per-instance logs (265, 359, 384, 388, 396), agree on all twelve per-repository sub-counts, and show zero self-consistency failures across 2484 reports, while the sixth answers none of its 500 documented log keys and an archive-wide three-key probe finds 15 of 134 entries missing at the documented location.

Question: Do the resolved counts published in SWE-bench/experiments for six Verified leaderboard entries recount from the per-instance logs those entries archived, and does each per-instance verdict follow from the test results recorded in the same file?

Method: Logs were fetched by anonymous HTTPS GET from s3://swe-bench-submissions with recorded ETags and byte counts, recount arithmetic was cross-checked at 12-way per-repository grain, and four planted faults each turned the verdict they should and left the other alone.

Disposition: partly settled | Evidence: measured | Role: audit

Notes: Handback status is settled; case-log status is settled for the units run, with the archive-wide availability question open. Disposition is partly settled for that split, not completed. Absence means absent at the documented key: anonymous ListBucket returns 403, so the hunt never claims absence from the bucket. Question filled from the HuntSpec. Paired with r_4166b0 as the other transfer-test reproduction outside mathematics.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] field_audit: This laboratory's best simple-zero proportion 0.6730529829896288 ranks tenth of fifteen public claims, the leader AMTOPA/zeta-exact-pressure at 0.6734164909714992949 sits 0.001726 below Hunt #82's 0.675142509660254 barrier, and trmdy is outside that n-point pressure family on window and block profile.

Mon, 24 Aug 2026 06:34:29 -0500

Outcome: This laboratory's best simple-zero proportion 0.6730529829896288 ranks tenth of fifteen public claims, the leader AMTOPA/zeta-exact-pressure at 0.6734164909714992949 sits 0.001726 below Hunt #82's 0.675142509660254 barrier, and trmdy is outside that n-point pressure family on window and block profile.

Question: What is the true public state of the art for the simple-zero proportion, and does any public construction sit inside the n-point pressure family whose ceiling Hunt #82 fixed at 0.675142509660254?

Method: Fifteen public claims were ranked by exact decimal comparison in rank.py, trmdy/zeta-simple-zeros-673137 was replayed from a scratch clone against its own Arb binding including the 2168370-box seven-point run, and assembly_compare.py recomputed this laboratory's constants at 300-bit Arb.

Disposition: completed | Evidence: measured | Role: audit

Notes: No HANDBACK at the pin. Question filled from the HuntSpec. Raw RESULTS H1 is only a title; the headline is taken from RESULTS section 1 and the case log. Only trmdy was replayed; AMTOPA's leading claim is REPORTED, not VERIFIED, in this hunt. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Withdrawn] [measured] amtopa_ceiling: The +3.96e-06 improvement candidate is withdrawn: at verifier revision b3b7784 the leader's headline is accepted on 8 of 8 shards with the gate alive, while this hunt's candidate was refused on 4 of 8 and a descent at the candidate's own weights bottoms at 0.0078960, 1.5e-5 under the leader's floor, so the claimed pair-weight, pressure, and window headroom are withdrawn with it.

Mon, 24 Aug 2026 17:27:10 -0500

Outcome: The +3.96e-06 improvement candidate is withdrawn: at verifier revision b3b7784 the leader's headline is accepted on 8 of 8 shards with the gate alive, while this hunt's candidate was refused on 4 of 8 and a descent at the candidate's own weights bottoms at 0.0078960, 1.5e-5 under the leader's floor, so the claimed pair-weight, pressure, and window headroom are withdrawn with it.

Question: Holding the AMTOPA exact-pressure construction fixed (its 17-term cosine window family, its span-capacity-2 pair-weight polytope, its fixed-total position pressure, its scalar-Gram block assembly), what is the supremum of the proportion that family can produce, is 0.6734164909714992949 at that supremum, and which constraint is binding when it stops improving?

Method: AMTOPA's own table builder and verifier were run at pinned commit 7253fdc and at the candidate.json revision b3b7784, then this hunt's candidate was refused on 4 of 8 shards and a stronger cut oracle re-solved the pair-weight LP.

Disposition: withdrawn | Evidence: measured | Role: primary investigation

Notes: No HANDBACK at the pin. Question filled from the HuntSpec, with the two hyphen-clause asides rewritten as parentheses. RESULTS.md section 1 still prints the +3.96e-06 sentence as written, then marks it WITHDRAWN 2026-09-06; the headline follows the correction, not the uncorrected H1 title. The separate tip-replay finding (INCONCLUSIVE at HEAD because the convexity gate fires zero times) is retained in RESULTS.md and the case log and is not treated as a second disposition. Every constant inherits the unreviewed analytic bridge named in the mission.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] r_a7c12f: 637/1000 survives at depth 1: an Arb pass at 96 bits over s in [37.0135, 400] bounds sup Dam(1,s)*(s^2-2) by 0.6317735, margin +0.0052 against the constant, and the 0.6636 in K2-TWO-SPECIES.md is a range mismatch because it is a sup over s in [8, 400] while 637/1000 is only asserted for s >= 37.0135.

Sun, 23 Aug 2026 00:27:25 -0500

Outcome: 637/1000 survives at depth 1: an Arb pass at 96 bits over s in [37.0135, 400] bounds sup Dam(1,s)*(s^2-2) by 0.6317735, margin +0.0052 against the constant, and the 0.6636 in K2-TWO-SPECIES.md is a range mismatch because it is a sup over s in [8, 400] while 637/1000 is only asserted for s >= 37.0135.

Question: Does the far-field constant 637/1000 survive at depth 1, given that K2-TWO-SPECIES.md section 2 measures 0.6636 there?

Method: An Arb pass at 96 bits through hunts/r_a97060/ball_field.py, adaptive cells, 45030 evaluations, enclosed the asserted range s >= 37.0135, and an independent float scan sat under that enclosure at cost 1.00005.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: Case-log status is settled, the recorded correction is withdrawn, which withdraws the K2-TWO-SPECIES.md depth-1 failure rather than this hunt's claim. Disposition maps settled to completed. Evidence grade is enclosure-supported for the depth-1 bound on [37.0135, 400]; s > 400 is float-grade only and the break depths 1.0494 and 0.9727 are double-precision scans, so those caveats stay in the notes. Question filled from the HuntSpec.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_8539dc: The published verifier computes A = max(ff)/(int f)^2 while the November 2025 statement defined B = max|ff|/(int f)^2, so the n=400 witness reaches 1.4557 only under A (exact A = 1.45564279537..., B = 4.33404652438...); the mix-up was corrected in arXiv:2511.02864 v2, and the improvement survives against each functional.

Sun, 23 Aug 2026 22:53:04 -0500

Outcome: The published verifier computes A = max(f*f)/(int f)^2 while the November 2025 statement defined B = max|f*f|/(int f)^2, so the n=400 witness reaches 1.4557 only under A (exact A = 1.45564279537..., B = 4.33404652438...); the mix-up was corrected in arXiv:2511.02864 v2, and the improvement survives against each functional.

Question: Is the published bound 1.4557 attached to the functional the published verifier computes, and does the claimed improvement survive the inequality as written?

Method: Both functionals were evaluated in exact rational arithmetic on the published ten-place heights, the n=150 construction was used as the coinciding-functional check, and the v1/v2/v3 LaTeX sources plus the 2025-12-19 colab commit were read for the correction chronology.

Disposition: completed | Evidence: measured | Role: audit

Notes: The brief's premise that no correction had appeared is wrong. What remains broken is opposite labelling of the two problems across the two corrected artifacts, and problems/4.html was never given a sibling page. No new bound is claimed. The assignment of prior 1.45810 to the A-functional rests on the corrected paper's changed citation, not on reading Vinuesa's thesis.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [measured] r_828c8b: The upper-bound half reproduces as a primal rational C <= 9990167/26214400 = 0.381094627, 1.7e-4 above Haugland's 0.380926, with the m=32 stall being the solver rather than the family, while the convex-program half was not reproduced and the plain averaging skeleton caps four weights at 0.2526 or below.

Sun, 23 Aug 2026 17:11:56 -0500

Outcome: The upper-bound half reproduces as a primal rational C <= 9990167/26214400 = 0.381094627, 1.7e-4 above Haugland's 0.380926, with the m=32 stall being the solver rather than the family, while the convex-program half was not reproduced and the plain averaging skeleton caps four weights at 0.2526 or below.

Question: is the published minimum-overlap record the limit of its own parameterisation, or the point at which the search stopped

Method: The m-piece minimax was run at m = 4/8/16/32 and the accepted object was re-evaluated in exact rationals, while the lower side was probed with uniform and Fourier averaging skeletons and four explicit weight-profile witnesses.

Disposition: partly settled | Evidence: measured | Role: primary investigation

Notes: Handback status is not-settled; RESULTS status is partly settled. Disposition follows RESULTS. Do not read front B float local minima as optima. White's actual program was not read here; that is overlap_lower. A shift-enumeration guard caught 2 of 3 planted faults, with the third recorded as a known miss.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_6f0f63: The Delsarte LP for kissing numbers has no headroom in its degree (value stops moving by degree 14 in dimensions 3-24, rediscovering 6 and 10 for E8 and Leech), and the node-discretised sign condition is a relaxation sitting strictly below the true kissing number at every node count tested.

Sun, 23 Aug 2026 17:16:30 -0500

Outcome: The Delsarte LP for kissing numbers has no headroom in its degree (value stops moving by degree 14 in dimensions 3-24, rediscovering 6 and 10 for E8 and Leech), and the node-discretised sign condition is a relaxation sitting strictly below the true kissing number at every node count tested.

Question: Where is the ceiling of the Delsarte LP parameterisation for kissing numbers, and is the acceptance step of the standard node-discretised implementation sound?

Method: E8 and Leech certificates were rebuilt from contact structure rather than printed coefficients, five planted faults were fired first, then degree 1-30 was swept in dimensions 3-24 and the node-set discretisation was scored against the exact kissing numbers 240 and 196560.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is probe, complete; handback status is settled. Disposition maps to completed. Float grade throughout, no ball arithmetic. Cohn-Elkies SDP half was not attempted. Soundness number to lean on: 196505.76 at 600 nodes in dimension 24 against exact 196560.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [measured] overlap_lower: White's choice of R is already at his method's ceiling (simplified-program gain 2.9e-6 from R=20 to R=320), one exact dual point 0.37399241331 was accepted, and the full program was not reproduced to 0.379005 because the Parseval cone needs a conic solver this run did not have.

Sun, 23 Aug 2026 22:24:47 -0500

Outcome: White's choice of R is already at his method's ceiling (simplified-program gain 2.9e-6 from R=20 to R=320), one exact dual point 0.37399241331 was accepted, and the full program was not reproduced to 0.379005 because the Parseval cone needs a conic solver this run did not have.

Question: is the published lower bound on Erdos's minimum overlap constant the limit of its own convex program, or the point at which the search stopped

Method: White's simplified and full programs were reconstructed and swept in R, with one dual point accepted in exact directed-rounded rationals and four cutting-plane attempts failing to enforce the Parseval cone.

Disposition: partly settled | Evidence: measured | Role: primary investigation

Notes: Three opening-brief premises were wrong at the source: the lower bound has moved (Kim-Pilanci 0.37912, 2026-06-30 preprint), the catalogue entry has no asterisk, and 0.000059 of upper-bound movement is 2016 human minus 2026 AI, not twelve months of AI. White discretises M and never f, so the unsafe direction hunt r_828c8b worried about does not arise. No bound on C is claimed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] family_wall: The n-point pressure family saturates: lim Phi_n = H = 0.6725007036794116 and sup_n Phi_n <= 0.675142509660254, more than 0.0066 short of the configuration ceiling 0.6818286874638, which is 71.7% of the H-to-ceiling distance.

Sun, 23 Aug 2026 21:39:09 -0500

Outcome: The n-point pressure family saturates: lim Phi_n = H = 0.6725007036794116 and sup_n Phi_n <= 0.675142509660254, more than 0.0066 short of the configuration ceiling 0.6818286874638, which is 71.7% of the H-to-ceiling distance.

Question: Does the n-point pressure family converge to a limit strictly below the configuration ceiling 0.6818286874638, and to what value?

Method: The bound was reduced to Phi_n <= H(1+W) by cancelling the pressure term against a witness of length (n-1)/H, then an independent audit repaired two invalid chain steps and supplied a period-37 word that covers every n, verified here against famlib.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is probe, complete. BARRIER. Disposition maps to completed because the barrier is the recorded outcome. The audit broke two inequality steps as written and did not break the claim. inf F_7,3000 still has no global certificate. Nothing here is machine-checked.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] bloch_ceiling: The published Bloch verification reproduces, and the author's own verifier accepts sqrt(3)/4 + 0.0153040536, so the published 0.0153 left 4.05e-6 of its own near-branch certificate unclaimed and that data has no further room.

Sun, 23 Aug 2026 21:37:32 -0500

Outcome: The published Bloch verification reproduces, and the author's own verifier accepts sqrt(3)/4 + 0.0153040536, so the published 0.0153 left 4.05e-6 of its own near-branch certificate unclaimed and that data has no further room.

Question: How far above 0.0153 can the variable-radius dichotomy for Bloch's constant be pushed with the author's own cuts, grid and Arb verifier when ETA, LARGE_RAD and the point-certificate resolution are moved off their chosen values, and is the published verification sound as shipped?

Method: Archive bloch-computations-1.0.0.zip checksums were verified, the author's programs were reproduced locally and on Modal, and the unmodified certificate data were rerun at target 0.0153040536 across all 24 away sectors and 38,400 initial cells with zero refusals.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: The near branch is Arb-verified; the away floor and the moved-parameter ceiling near 0.015359 are INFERRED float search, so the composite grade stays measured. Sectors 0 and 1 at the published target match reference-run/logs to the integer (270,744 and 292,931). Cost 324 core-hours on GitHub Actions, billed zero. Nothing here bears on RH.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] ainta_seven_point: Ainta 19/5000 and Gohms 191/50000 reproduce, inf F6 is bracketed 0.003826 <= inf F6 <= 0.0038262312115073 so this certificate family ceilings near 0.673025 (about 5.6% of the room under the configuration ceiling), and a later Lean bridge states the bound for riemannZeta conditional on F6 >= c.

Sun, 23 Aug 2026 03:04:58 -0500

Outcome: Ainta 19/5000 and Gohms 191/50000 reproduce, inf F6 is bracketed 0.003826 <= inf F6 <= 0.0038262312115073 so this certificate family ceilings near 0.673025 (about 5.6% of the room under the configuration ceiling), and a later Lean bridge states the bound for riemannZeta conditional on F6 >= c.

Question: What is the largest value the seven-point certificate F6 >= c can reach, what configuration of six consecutive gaps attains the floor, and how much of the room between the 0.6725 window ceiling and the 0.6818287 configuration ceiling does this certificate family leave unreachable?

Method: The published verifier was rerun on pinned Ainta and Gohms certificates, a float minimiser was checked against the verifier's Arb table, and the map Phi(c,m,p) was reconstructed from the two published data points, with later days adding a sorry-free bridge conditional on F6 >= c.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is closed, bounded, in two halves, plus later Aristotle and Bridge days. Composite evidence stays measured because F6 >= c is an Arb run, not a Lean fact, even though seven_point_bound is sorry-free given that hypothesis. The laboratory had been quoting configuration ceiling 0.68185; the Lean development proves 0.6818286874638. Probe certificates at 1913/500000 are recorded as ceiling locators, not headlined as new records.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] zeta_temperament: In units theta = gamma ln2 / 2pi, Odlyzko's first 100,000 zeros avoid prime-power equal temperaments within 0.0012 of Landau's coefficient and ignore composites at 0.0000, with integer-temperament density 0.801 against 0.800 predicted, which is interesting structure and classical in substance.

Sat, 22 Aug 2026 20:02:11 -0500

Outcome: In units theta = gamma ln2 / 2pi, Odlyzko's first 100,000 zeros avoid prime-power equal temperaments within 0.0012 of Landau's coefficient and ignore composites at 0.0000, with integer-temperament density 0.801 against 0.800 predicted, which is interesting structure and classical in substance.

Question: In tuning units theta = gamma ln2 / 2pi, do the Riemann zeros avoid the equal temperaments that tune prime-power harmonics, with the deficit Landau's formula predicts, and ignore composite harmonics?

Method: Mod-1 Fourier coefficients of Odlyzko's first 100,000 zeros were computed at frequencies log2 n for n <= 32 and compared with -Lambda(n)/sqrt(n)/, with the lab's 2000 cached zeros as a second table and composites as the vanishing control.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No RESULTS.md or HANDBACK at the pin. Headline filled from the case-log verdict INTERESTING STRUCTURE, classical in substance. A 2026-08-22 correction notes that the composite control re-measures zeta.explicit.prime_spectrum, which this repository already exposed. Nothing here bears on RH.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_31b6c1: The Krenn-Gu 8x3 system has exactly 252 edge-weight variables; the H x S2 quotient reduces it to 8 variables and 70 equations, and sympy.groebner returns [1] in under 5 s after a 6x3 calibration that reproduces the known no-complex-witness verdict, ruling out any symmetric complex witness.

Sat, 22 Aug 2026 18:29:56 -0500

Outcome: The Krenn-Gu 8x3 system has exactly 252 edge-weight variables; the H x S2 quotient reduces it to 8 variables and 70 equations, and sympy.groebner returns [1] in under 5 s after a 6x3 calibration that reproduces the known no-complex-witness verdict, ruling out any symmetric complex witness.

Question: Can the Krenn-Gu 8x3 polynomial system be emitted over the orbit-reduced quotient and priced by Groebner elimination, after a 6x3 calibration that reproduces the known no-complex-witness verdict?

Method: The generator pipeline was calibrated on the 6x3 H x S2 quotient (Groebner [1] in 0.44 s), then applied to the 8x3 8-variable reduced ideal, where sympy.groebner finished in 4.37 s at 80.50 MB and returned [1].

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No HuntSpec question field at the pin; question filled from MISSION.md. The settled claim is absence of an H x S2-symmetric complex witness, not a full unrestricted 8x3 certificate. Variable count 252 is confirmed as 28 edges times 9 colourings.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [measured] r_044dd2: All 31 S8 x S3 target-matching branches have support survivors (76 to 132 active entries, median 118), so inherited support conditions close zero branches, and on the sparsest branch Support 7 avoids eight signed-Laurent cuts while cap-5 elimination hit fill-in before a membership decision.

Sat, 22 Aug 2026 11:21:53 -0500

Outcome: All 31 S8 x S3 target-matching branches have support survivors (76 to 132 active entries, median 118), so inherited support conditions close zero branches, and on the sparsest branch Support 7 avoids eight signed-Laurent cuts while cap-5 elimination hit fill-in before a membership decision.

Question: For each of the 31 S8 x S3 target-matching branches, does any support on the 252 aggregate edge entries survive target nonemptiness, non-target non-singleton cancellation, star-anchor, pair-pencil, and full-column necessities?

Method: A support optimizer returned 31 of 31 survivors and an independent replay checked 203,391 branch-colouring conditions with zero failures, then signed-Laurent certificates and fixed-degree spans were run on orbit-18 supports including Support 7.

Disposition: partly settled | Evidence: measured | Role: primary investigation

Notes: RESULTS status is exact support census settled; algebraic sieve open. Hunt #71's statement that the 31 orbits reduce the full polynomial system is withdrawn here. No branch is closed and no complex witness was found. Disposition is partly settled for that split.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] chroma_hue: A note-to-hue bijection makes hue distance a function of interval class only if it is affine, and over 21,772,800 canonical maps the circle of fifths is the unique Spearman argmax under three dissonance measures while the HSL wheel is not a metric 12-gon, so the correspondence is pretty but trivial.

Sat, 22 Aug 2026 18:54:21 -0500

Outcome: A note-to-hue bijection makes hue distance a function of interval class only if it is affine, and over 21,772,800 canonical maps the circle of fifths is the unique Spearman argmax under three dissonance measures while the HSL wheel is not a metric 12-gon, so the correspondence is pretty but trivial.

Question: Does any bijection from Z_12 to twelve hue classes preserve a relation, metric, symmetry or spectrum that is not already a consequence of Z_12 acting on a circle?

Method: Every canonical bijection with f(0) fixed was scored against Spearman(hue distance, dissonance) under a random-permutation null, and the colour side was checked as a metric 12-gon with CIEDE2000, OKLCH, and equal-tempered light-frequency steps.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No RESULTS.md or HANDBACK at the pin. Question is the HuntSpec scalar. Headline filled from the case-log verdict PRETTY BUT TRIVIAL plus the exhaustive-search numbers in results_consonance.json (evaluated 21772800, fifths 0.609 Sethares, chromatic -0.730). Nothing here bears on RH.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [measured] aimo2: The AIMO clear-cut protocol is reconstructed from public data as minority-robust, a legal model-identity prior beats the constant leave-one-problem-out (26/28 vs 19/28), the Small-track entry is the always-non-robust constant, and the learned-method GPU arm stays killed.

Sat, 22 Aug 2026 21:01:20 -0500

Outcome: The AIMO clear-cut protocol is reconstructed from public data as minority-robust, a legal model-identity prior beats the constant leave-one-problem-out (26/28 vs 19/28), the Small-track entry is the always-non-robust constant, and the learned-method GPU arm stays killed.

Question: Can we (a) reproduce, from public data alone, a validation-design finding about the AIMO sample worth a technical-report submission, and (b) build a legal Small/Main-track method that beats the better constant baseline out-of-fold under a preregistered leakage-controlled protocol?

Method: val-sample's 9 robust rows were matched to sample-full pairs with base accuracy 1.0 and zero detrimental perturbations, a per-model prior was scored leave-one-problem-out on public sets, and the official container path was replayed at starter e46be92.

Disposition: qualified | Evidence: measured | Role: primary investigation

Notes: Successor to r_662b12; the withdrawn +25 pp claim stays withdrawn and is re-measured here as a model-identity base rate. Status is report-ready with the learned arm killed, so disposition is qualified rather than completed. Grade is measured on public data. No GPU spent. Hidden-set model identifiers and the hidden robust fraction remain unsettled.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [unreviewed] rogue_frontier: No single campaign status exists at the root because the work lived on an unmerged branch: a deliberate subset (weil_trunc, sine_gram, window_opt, nyman_beurling) later landed on main, while fkappa was withheld for conflict with higher_xi.

Fri, 21 Aug 2026 14:28:00 -0500

Outcome: No single campaign status exists at the root because the work lived on an unmerged branch: a deliberate subset (weil_trunc, sine_gram, window_opt, nyman_beurling) later landed on main, while fkappa was withheld for conflict with higher_xi.

Question: Which RH-adjacent frontier admits the largest new mathematical advance this run can produce and defend, and what is that advance?

Method: The campaign ran on claude/riemann-hypothesis-research-ofds8s; Hunt r_f00e48 landed four arms from 7043621a and recorded the withheld fkappa arm in LANDING.md so the gaps would not read as loss.

Disposition: partly settled | Evidence: unreviewed | Role: primary investigation

Notes: No explicit status, HANDBACK, or root RESULTS.md at the pin; hunt-list records that metadata gap. Disposition is partly settled from LANDING.md, not from a missing case-log field. Date is the landing commit shared with r_f00e48, not the 2026-08-17 branch open. Evidence status is unreviewed as an archival landing and adjudication record, rather than an asserted physical measurement. fkappa is an adjudication, not a cherry-pick. Headline filled from LANDING.md rather than a missing handback.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_f00e48: Four rogue_frontier arms landed intact from origin/claude/riemann-hypothesis-research-ofds8s at 7043621 (1,717,013 bytes, fkappa held back), 29/29 checks pass including digit-for-digit Weil agreement with Hunt #45 at (c, N) = (31, 60), and REPRODUCE.md's headline RF-C003 command named a symbol that never existed.

Fri, 21 Aug 2026 14:28:00 -0500

Outcome: Four rogue_frontier arms landed intact from origin/claude/riemann-hypothesis-research-ofds8s at 7043621 (1,717,013 bytes, fkappa held back), 29/29 checks pass including digit-for-digit Weil agreement with Hunt #45 at (c, N) = (31, 60), and REPRODUCE.md's headline RF-C003 command named a symbol that never existed.

Question: Do the four unlanded rogue_frontier arms land intact on main, and does what they claim about themselves survive being checked in the tree they land in?

Method: probe.py ran 29 acceptance checks on the landed bytes, recomputed RF-C003's promoted rational from the landed source, and compared the salvaged DH failure cell to main's r_ac9ca3 enclosures digit for digit.

Disposition: completed | Evidence: measured | Role: artifact preservation

Notes: Re-running an arm's own code is not an independent check of its mathematics. RF-C003 was entered in the review ledger as lacking a blind attack. erdos_scan and matchings appeared on the branch after the specified sweep and are not this hunt's landed four.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [measured] r_662b12: The official all-False baseline is reproduced at 67.86% (19/28) with full coverage, but the reported 92.86% intervention is withdrawn: it is an in-sample model-name rule chosen after reading all 28 labels, the CV loops never fit inside training folds, and the scrambled-text surrogate keeps the same 92.86%.

Fri, 21 Aug 2026 23:30:47 -0500

Outcome: The official all-False baseline is reproduced at 67.86% (19/28) with full coverage, but the reported 92.86% intervention is withdrawn: it is an in-sample model-name rule chosen after reading all 28 labels, the CV loops never fit inside training folds, and the scrambled-text surrogate keeps the same 92.86%.

Question: AIMO Interpretability 2026: reproduce the official baseline and test one structure-matched robustness signal

Method: The public val-sample of 28 rows was inventoried and the all-False constant was scored through the official ingestion shape; an independent audit then showed the frontier rule hard-codes gpt-5.2 and glm-5.1 after seeing those labels, so LOOCV, LOPO, and 5-fold only rescore a frozen in-sample rule.

Disposition: partly settled | Evidence: measured | Role: primary investigation

Notes: STALE HANDBACK: HANDBACK.json still claims a +25 pp GO. RESULTS.md (correction 2026-08-22) and AUDIT.md reject the intervention. Only the 67.86% baseline and the 19/9 sample census stand. Prize disposition is NO-GO on this evidence. Disposition is partly settled, not completed, because the baseline is retained and the intervention is withdrawn.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_322dae: The 6x3 checksum of 15 matchings, 3375 triples, and 8 S6 x S3 orbits is verified, and the 8x3 frontier of 105 matchings and 1,157,625 triples partitions into exactly 31 S8 x S3 orbits with matching Burnside and orbit-stabilizer counts.

Fri, 21 Aug 2026 23:30:26 -0500

Outcome: The 6x3 checksum of 15 matchings, 3375 triples, and 8 S6 x S3 orbits is verified, and the 8x3 frontier of 105 matchings and 1,157,625 triples partitions into exactly 31 S8 x S3 orbits with matching Burnside and orbit-stabilizer counts.

Question: What is the exact orbit census and stabilizer decomposition of the 1157625 monochromatic matching triples in the Krenn-Gu 8x3 problem under S8 x S3 symmetry?

Method: The 31 orbits were obtained both by exhaustive disjoint partition of the 1,157,625 triples and by Burnside evaluation over S8 x S3 conjugacy classes, after a 6x3 calibration against the known 8-orbit checksum.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Later hunt r_044dd2 withdraws the claim that these 31 orbits quotient the full 252-variable polynomial system; they remain an exhaustive outer branch cover. That correction is not retrofitted into this row's headline. Evidence is combinatorial exactness, not a Lean kernel check.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] epp_herglotz: Euler-product positivity plus the functional equation does not force Re(xi'/xi) >= 0 on Re s > 1/2: the shifted product W_a(s) = zeta(s+a) zeta(s-a) at a = 1/4 carries every hypothesis in larger quantity than zeta and has zeros off its own critical line.

Fri, 21 Aug 2026 19:42:19 -0500

Outcome: Euler-product positivity plus the functional equation does not force Re(xi'/xi) >= 0 on Re s > 1/2: the shifted product W_a(s) = zeta(s+a) zeta(s-a) at a = 1/4 carries every hypothesis in larger quantity than zeta and has zeros off its own critical line.

Question: Does Euler-product positivity plus the functional equation force Re ξ'/ξ ≥ 0 on Re s > 1/2?

Method: The mechanism was written in MISSION.md in a commit containing nothing else, then attacked with the explicit rival W_a at a = 1/4, measuring the functional equation, Hardy-style Z, scalar Euler product, EPP coefficients, and off-line zeros in a committed box.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Status is settled, negative. Disposition maps to completed because the kill finished; the outcome is a negative result, not RH progress. No HANDBACK.json at the pin. Headline filled from RESULTS.md rather than the H1 title. The repaired mechanism needing square-root cancellation is recorded as the exact remaining step, not as a new attack.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_e2ee73: Compiler refinement verdicts rest on a hand-written Python model whose exposure is bounded by a 655,360-point zero-mismatch cross-check against Clang and full model power on the poison hazard, and true LLVM-native refinement remains absent because Alive2 is not installed.

Thu, 20 Aug 2026 09:49:31 -0500

Outcome: Compiler refinement verdicts rest on a hand-written Python model whose exposure is bounded by a 655,360-point zero-mismatch cross-check against Clang and full model power on the poison hazard, and true LLVM-native refinement remains absent because Alive2 is not installed.

Question: What are the exact epistemic bounds and scope caveats of compiler verdicts resting on a hand-written Python interpreter in the absence of Alive2?

Method: All 10 compiler fixtures were cross-checked against Apple Clang at -O0 and -O2 over 655,360 comparable points, and both detectors were run against the four planted lesions in compiler.catalog, including the poison nsw-flag case.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed. Alive2 absence is an environment fact at the pin, not a claim that rung-3 refinement is impossible in principle.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_dc6e6f: The guard scripts/make_context.py --check is 100% blind to additions and modifications under compiler/, because that package is omitted from the scanned directory targets; 0 of 17 curated compiler mutants and 0 of 37 public symbols were detected, while positive controls in scanned packages were 100% caught.

Thu, 20 Aug 2026 16:39:59 -0500

Outcome: The guard scripts/make_context.py --check is 100% blind to additions and modifications under compiler/, because that package is omitted from the scanned directory targets; 0 of 17 curated compiler mutants and 0 of 37 public symbols were detected, while positive controls in scanned packages were 100% caught.

Question: Does scripts/make_context.py --check detect public functions, classes, constants, or module additions under compiler/, and what is the exact boundary?

Method: Seventeen curated compiler mutants plus an exhaustive AST census of all 37 public symbols were applied under two-stage controls, clean baseline reproduction and post-mutant undo, with five positive controls in scanned packages.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_c35cd1: scripts/make_context.py --check does not detect test files whose names do not match test_.py, because test_counts() uses a shallow TESTS.glob('test_.py') and filters AST nodes strictly by def test_*; 0/20 out-of-pattern specimens were caught, while 3/3 in-scope test modifications were caught.

Thu, 20 Aug 2026 16:45:40 -0500

Outcome: scripts/make_context.py --check does not detect test files whose names do not match test_*.py, because test_counts() uses a shallow TESTS.glob('test_*.py') and filters AST nodes strictly by def test_*; 0/20 out-of-pattern specimens were caught, while 3/3 in-scope test modifications were caught.

Question: Does scripts/make_context.py --check detect test files whose names do not match test_*.py, and what is the exact boundary?

Method: A 25-specimen battery was run in an isolated sandbox with baseline and undo controls, checked against AST analysis of test_counts() and a census of 87 items in tests/ plus 79 historical git paths.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_7ad39f: make_context.py --check is structurally blind to length-neutral in-place helper renames across all 49 modules declaring all (0/299 unexported private symbols), because module_api filters strictly by all and line count is unchanged, while non-all modules and any edit that changes line count are 100% detected.

Thu, 20 Aug 2026 10:01:42 -0500

Outcome: make_context.py --check is structurally blind to length-neutral in-place helper renames across all 49 modules declaring __all__ (0/299 unexported private symbols), because module_api filters strictly by __all__ and line count is unchanged, while non-__all__ modules and any edit that changes line count are 100% detected.

Question: Does scripts/make_context.py --check detect in-place length-neutral private helper renames in modules with __all__, and what is the exact boundary?

Method: Twenty-five curated mutants and a 305-symbol exhaustive census were applied across all 67 scanned modules in an isolated sandbox with clean baseline and undo controls.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] r_2ac05f: hunts/higher_xi/C2_EXACT.json is the correct kappa=2 table: a fourth derivation importing neither disputant reproduces its eleven values and the published Farmer-Gonek kappa=1 row, while hunts/rogue_frontier/fkappa/ is wrong from i=2 because it carried Bian's Lemma 12 constant C_kappa,2 = -4 as an axiom.

Thu, 20 Aug 2026 23:21:49 -0500

Outcome: hunts/higher_xi/C2_EXACT.json is the correct kappa=2 table: a fourth derivation importing neither disputant reproduces its eleven values and the published Farmer-Gonek kappa=1 row, while hunts/rogue_frontier/fkappa/ is wrong from i=2 because it carried Bian's Lemma 12 constant C_kappa,2 = -4 as an axiom.

Question: Which of the two recorded kappa=2 form-factor coefficient tables, hunts/higher_xi/C2_EXACT.json or hunts/rogue_frontier/fkappa/coefficients.json (corrected mode), is the correct C_2,i?

Method: A fourth derivation in a formal Dirichlet word algebra, exact rationals throughout and importing neither hunt, was calibrated on the Farmer-Gonek kappa=1 row, with a planted Lemma-12 defect and a one-factorial pairing corruption as controls.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: Case-log status is settled. Disposition maps settled to completed. Evidence grade is ordinary mathematical derivation for the exact-rational identity; the Farmer-Gonek row is an external control, not a literature search of the kappa=2 table.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_2946de: scripts/make_context.py --check is completely blind to meta/, detecting 0 of 16 curated mutants and 0 of 32 public AST symbols, because the scanner hard-codes paths and omits meta/ entirely.

Thu, 20 Aug 2026 18:04:07 -0500

Outcome: scripts/make_context.py --check is completely blind to meta/, detecting 0 of 16 curated mutants and 0 of 32 public AST symbols, because the scanner hard-codes paths and omits meta/ entirely.

Question: Does scripts/make_context.py --check detect public functions added under meta/, and what is the exact boundary?

Method: Sixteen curated mutants and an exhaustive 32-symbol AST census were applied in isolated sandboxes with baseline and undo controls, against in-scope positive controls in scanned directories.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] prime_zeta_rightmost: The OEIS A107311 conjectures are false: zeros of the prime zeta function accumulate up to sigma_c = 1.77954465354699... rather than x* = 1.72864723899818..., but kill condition 2 fired because Belovas, Cepaityte and Sabaliauskas 2025 Theorem 1 already owns the threshold by the same argument.

Thu, 20 Aug 2026 21:25:57 -0500

Outcome: The OEIS A107311 conjectures are false: zeros of the prime zeta function accumulate up to sigma_c = 1.77954465354699... rather than x* = 1.72864723899818..., but kill condition 2 fired because Belovas, Cepaityte and Sabaliauskas 2025 Theorem 1 already owns the threshold by the same argument.

Question: Is x* = 1.7286... (root of zeta(x)=2) an upper bound for the real parts of the zeros of the prime zeta function and all prime-subset Dirichlet series, as OEIS A107311 conjectures, or is the true supremum sigma_c = 1.7795... (root of P(sigma) = 2^(1-sigma))?

Method: Both backends (python-flint at 350 bits and mpmath.iv at dps 40, with exact Fraction endpoint logic) decided sigma_c, x*, and the subset constant sigma_3, then a literature search fired MISSION.md kill condition 2 and reclassified the core as rediscovery.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: No HANDBACK.json at the pin. Headline filled from the rewritten RESULTS headline and the case log, not from the RESULTS H1 title. Case-log status is settled, kill condition 2 fired. Disposition maps settled to completed. The OEIS refutation and the tail-subset unboundedness corollary remain this hunt's own; the threshold theorem is rediscovery.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] lambda_dh_bounds: Two-sided bounds for Lambda_DH are 0.2304 < Lambda_DH <= 0.7696992583210755065522 in the wide frame and 0.0576 < Lambda_DH <= 0.19242481458026887663805 in the narrow frame, ratio 3.341, with Lambda_DH > Lambda_zeta unconditionally, and the 2026-08-18 hardening left the lower side unmoved in every digit.

Thu, 20 Aug 2026 21:25:57 -0500

Outcome: Two-sided bounds for Lambda_DH are 0.2304 < Lambda_DH <= 0.7696992583210755065522 in the wide frame and 0.0576 < Lambda_DH <= 0.19242481458026887663805 in the narrow frame, ratio 3.341, with Lambda_DH > Lambda_zeta unconditionally, and the 2026-08-18 hardening left the lower side unmoved in every digit.

Question: What are the first quantitative two-sided bounds for the de Bruijn-Newman constant Lambda_DH of the Davenport-Heilbronn function?

Method: The lower side is a ball-arithmetic winding count with a zero-shared-layer second witness; the upper side is a decided strip constant fed to de Bruijn 1950 Theorem 13, later sharpened in-tree by a phase obstruction that reaches Bombieri-Ghosh's abscissa on both backends.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: No HANDBACK.json at the pin. Headline filled from RESULTS section 0 and the case log, not from the RESULTS H1 title. Status is closed 2026-08-16, gate verdict publication candidate, hardened 2026-08-18 with verdict unchanged. Disposition maps closed to completed. A factor-of-4 frame error and a withdrawn sigma_0 originality claim are retained as corrections, not silently dropped. Nothing here is evidence about RH.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_c62e44: The guard test_no_two_docs_share_a_number detects duplicate leading numbers but does not detect a document renamed without its number changing when citations use bare references, and an exhaustive census finds zero tests that read document body content.

Wed, 19 Aug 2026 23:55:33 -0500

Outcome: The guard test_no_two_docs_share_a_number detects duplicate leading numbers but does not detect a document renamed without its number changing when citations use bare references, and an exhaustive census finds zero tests that read document body content.

Question: Does tests/test_docs_numbering.py::test_no_two_docs_share_a_number detect a document renamed without its number changing, and do any guards in the tree read doc content?

Method: A 20-mutant battery was run against a clean sandbox under baseline and per-mutant undo controls, together with a static census of all 37 test files mentioning docs/.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] r_ac9ca3: The first positivity failure of the truncated Weil form on Davenport-Heilbronn on the integer lattice is at (c, N) = (31, 60) with enclosure lambda_min = -1.8739e-31 < 0, while (31, 59) is strictly positive and the Riemann zeta control at (31, 60) remains positive, and the sign flip is accounted for by the first off-line pair.

Wed, 19 Aug 2026 07:43:25 -0500

Outcome: The first positivity failure of the truncated Weil form on Davenport-Heilbronn on the integer lattice is at (c, N) = (31, 60) with enclosure lambda_min = -1.8739e-31 < 0, while (31, 59) is strictly positive and the Riemann zeta control at (31, 60) remains positive, and the sign flip is accounted for by the first off-line pair.

Question: Truncated Weil form: first positivity failure on Davenport-Heilbronn is at (c, N) = (31, 60), tracking the off-line pair

Method: Integer-lattice Galerkin truncations were scanned for c in [6, 60] and N <= 128, with the (31, 60) sign decided by Arb ball LDL^T, a Rump verified eigenvalue enclosure, and an exact dyadic Rayleigh quotient, plus a dictionary decomposition attributing the negative contribution to the off-line quadruple.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: Case-log status is settled. Disposition maps settled to completed. Question is the HuntSpec scalar, which is a statement rather than an interrogative. Evidence is enclosure-supported; the dictionary attribution is the mechanism, not a separate grade.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_6f088d: The zeta23ext root load failure was caused by 17 colliding declarations, including Retention.Aconst and Retention.c2, across EForm, EForm2, and EForm3 in the un-scoped Retention namespace; sub-namespacing or importing only EForm3 resolves the collision, while mathematical duplication remains.

Wed, 19 Aug 2026 07:39:39 -0500

Outcome: The zeta23ext root load failure was caused by 17 colliding declarations, including Retention.Aconst and Retention.c2, across EForm, EForm2, and EForm3 in the un-scoped Retention namespace; sub-namespacing or importing only EForm3 resolves the collision, while mathematical duplication remains.

Question: What caused the root module load failure in zeta23ext for Retention.Aconst and c2 across arms, how was it scoped, and what symbol duplication remains?

Method: AST symbol parsing across 64 modules was combined with isolated Lean 4 compiler error reproduction of the environment collision.

Disposition: completed | Evidence: measured | Role: tooling/method work

Notes: Case-log status is settled. Disposition maps settled to completed. Role is tooling/method work because the finding is a namespace collision in a vendored Lean package, not a mathematical claim.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_365c6c: The guard test_no_hunt_claims_the_reserved_word explicitly whitelists only .py, .md, and .json, so every other file format is skipped and overclaims in those formats pass undetected.

Wed, 19 Aug 2026 23:41:07 -0500

Outcome: The guard test_no_hunt_claims_the_reserved_word explicitly whitelists only .py, .md, and .json, so every other file format is skipped and overclaims in those formats pass undetected.

Question: Does test_no_hunt_claims_the_reserved_word detect file types outside .py/.md/.json?

Method: The unmodified guard was executed via pytest against 40 file specimens across 12 format categories in an isolated sandbox, with empty-specimen and clean-baseline controls, plus a census of all 447 files under hunts/.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled. Disposition maps settled to completed. None of the 76 currently unscanned hunts/ files contain the reserved word; that is a census fact, not a claim that the gap is harmless.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Not settled] [measured] r_b9552d: Gap A of the lattice-extremality route is not a missing calculation: any single density-independent certificate proving J <= L at every density is pinned to ghat(0)=0, and the Fejer family that closed gap B reaches that constant only at a c the admissibility cap forbids by a factor 1.15554665, while the route remains alive with a first all-density bound J(T) <= 0.5715840116 = 4.99942 * L.

Tue, 18 Aug 2026 03:45:20 +0000

Outcome: Gap A of the lattice-extremality route is not a missing calculation: any single density-independent certificate proving J <= L at every density is pinned to ghat(0)=0, and the Fejer family that closed gap B reaches that constant only at a c the admissibility cap forbids by a factor 1.15554665, while the route remains alive with a first all-density bound J(T) <= 0.5715840116 = 4.99942 * L.

Question: does the centre-gas obligation T1 of the two-species split admit a bound with a strictly positive atom reserve rho, over all centre configurations rather than only lattices?

Method: The Fejer family was evaluated for the c that zeros the rho-slope, the admissibility cap was re-measured as a closed form, and sup f was scanned on (0,400] plus a 1/s^2 tail, with a planted 3.05x inflation of f as a detector control.

Disposition: not settled | Evidence: measured | Role: primary investigation

Notes: Two case-log entries share this directory: Hunt #46 and Hunt #64 are both negative attempts, both status not settled. Recorded_disposition is not settled per coordinator guidance. Run 1 artifacts are preserved under run-tagged names. The Paley-Wiener uniqueness claim in RESULTS section 3 is quoted, not proved here.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] r_8c3b94: The moment-method route to Erdos-Kac costs roughly 2400 to 3700 lines of Lean and every obligation is a thing somebody knows how to write down, while the characteristic-function route is blocked on the fundamental lemma of sieve theory, which Mathlib lacks and which has no Lean formalization.

Tue, 18 Aug 2026 03:47:34 +0000

Outcome: The moment-method route to Erdos-Kac costs roughly 2400 to 3700 lines of Lean and every obligation is a thing somebody knows how to write down, while the characteristic-function route is blocked on the fundamental lemma of sieve theory, which Mathlib lacks and which has no Lean formalization.

Question: What does each of the two standard routes to a formal Erdős–Kac cost in Lean, given Mathlib at mathlib4 rev 51e6992e (toolchain v4.33.0-rc2) and this tree's zero-sorry base?

Method: Every Mathlib claim was resolved by compiling Probe.lean against the pin, 43 declarations plus nine from this tree, with misses searched by name over the pinned source rather than remembered.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: tooling/method work

Notes: Case-log status is settled, a mapping run, not a proving run. Disposition maps settled to completed. Role is tooling/method work because the run priced two routes and walked neither. HuntSpec en-dash in Erdos-Kac is retained in the question; the headline uses ASCII Erdos-Kac.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [kernel-checked] r_88dc5e: Both halves landed with zero sorrys and standard axioms only: O9Seam.r_comp_mem and Retention.rIv_mem are retired at no reproof cost, and the two-mode arithmetic is proved and instantiated at a recorded kernel box after O9Bridge identified Phi2 with the retention integrals Qre and Qim.

Tue, 18 Aug 2026 03:42:24 +0000

Outcome: Both halves landed with zero sorrys and standard axioms only: O9Seam.r_comp_mem and Retention.rIv_mem are retired at no reproof cost, and the two-mode arithmetic is proved and instantiated at a recorded kernel box after O9Bridge identified Phi2 with the retention integrals Qre and Qim.

Question: Does the O9 checker's Bool verdict imply the real damage bound on the box it decided, and can the two dead-weight seam lemmas be retired without reproof?

Method: O9Bridge.lean proves Re Phi2 = Qre and Im Phi2 = -Qim for y != 0 by closed forms, O9Modes.lean turns the checker Bool into dam_le_of_box, and a re-run of the use-site survey deleted the two unused seam lemmas.

Disposition: completed | Evidence: kernel-checked | Role: primary investigation

Notes: Case-log status is settled. Disposition maps settled to completed. What this does not close is the remaining O9 soundness chain beyond the two-mode arithmetic at one recorded box.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] r_a97060: The k=2 equal-depth tau-table closes under ball-arithmetic enclosures over the same 6600 cells on [0,132], with 0 nonpositive cells in all three cap modes, worst margin +0.0677 signed and +0.0146 unsigned, and enclosure cost a factor 1.0000 to 1.0004 on the dominant near-field term.

Mon, 17 Aug 2026 02:05:32 +0000

Outcome: The k=2 equal-depth tau-table closes under ball-arithmetic enclosures over the same 6600 cells on [0,132], with 0 nonpositive cells in all three cap modes, worst margin +0.0677 signed and +0.0146 unsigned, and enclosure cost a factor 1.0000 to 1.0004 on the dominant near-field term.

Question: Does the k=2 equal-depth tau-table of k2_closure.py still close when every scan-grade supremum is replaced by a ball-arithmetic enclosure over the same 6600 cells?

Method: Every scan-grade supremum was replaced by an Arb complex-ball envelope at 96 bits, with mpmath.iv as a containing cross-check, and the open-interval centre-centre row was closed by a second-order bound that uses evenness of ghat rather than a y-grid.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: Case-log status is settled. Disposition maps settled to completed. Evidence is enclosure-supported for the table pass; the composite k=2 claim does not automatically inherit that grade, which RESULTS.md states. No HuntSpec Status line; the case log uses Question/Result form.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [kernel-checked] r_938ab4: The two numerator fields answer differently: reNum encloses Re num unconditionally, while imNumOverY encloses Im num / y only for y != 0 and encloses the removable limit at y = 0, and both identifications are proved with zero sorrys and instantiated at the first recorded o9boxes box.

Mon, 17 Aug 2026 22:19:08 +0000

Outcome: The two numerator fields answer differently: reNum encloses Re num unconditionally, while imNumOverY encloses Im num / y only for y != 0 and encloses the removable limit at y = 0, and both identifications are proved with zero sorrys and instantiated at the first recorded o9boxes box.

Question: Do the reals enclosed by reNum_mem and imNumOverY_mem equal Re num and Im num / y, and under what hypotheses?

Method: O9NumShape.lean identifies the computed interval shapes with Re num and Im num / y under the stated hypotheses, then qreIv_mem_phi2 and rIv_mem_phi2 read the compositions back against Phi2 itself.

Disposition: completed | Evidence: kernel-checked | Role: primary investigation

Notes: Case-log status is settled, and the two fields answer differently. Disposition maps settled to completed. The dead-weight retirement of r_comp_mem and rIv_mem is a verdict recorded here and executed in r_88dc5e.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_908de5: Setting beta := normLower makes the rung-3 grid site inequality true by construction and the cell obligation still holds at all 200 endpoints, but docs/25 4.3's prediction of at least 10x slack is wrong: the worst clearance is 1.3697x in ball arithmetic and 1.3566x in chained rect, moved under 1%.

Mon, 17 Aug 2026 01:55:17 +0000

Outcome: Setting beta := normLower makes the rung-3 grid site inequality true by construction and the cell obligation still holds at all 200 endpoints, but docs/25 4.3's prediction of at least 10x slack is wrong: the worst clearance is 1.3697x in ball arithmetic and 1.3566x in chained rect, moved under 1%.

Question: Does setting beta := normLower make the rung-3 grid obligation true by construction without breaking the cell condition that spends beta?

Method: Beta was read off the enclosure rather than predicted, then eps' + L*h/2 <= beta was evaluated in exact rationals over the committed plan at all 200 cell endpoints in both ball and chained-rect arithmetic.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is settled, and one prediction on main is refuted. Disposition maps settled to completed. The remedy is additionally contingent on porting scripts/60 emission to composite chains, because in the non-chain rect arithmetic it emits today the cell condition fails. No in-inventory hunt is a direct continuation of this grid-beta measurement.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [kernel-checked] r_6c7d6a: Six of seven boxParts fields already had zero-sorry enclosure lemmas; Retention.imNum_mem now supplies the seventh, so both O9 composition lemmas instantiate at a box, and discharging them exposed that O9Seam.r_comp_mem writes the wrong denominator and is vacuous at every box in the table.

Mon, 17 Aug 2026 01:43:38 +0000

Outcome: Six of seven boxParts fields already had zero-sorry enclosure lemmas; Retention.imNum_mem now supplies the seventh, so both O9 composition lemmas instantiate at a box, and discharging them exposed that O9Seam.r_comp_mem writes the wrong denominator and is vacuous at every box in the table.

Question: Can every numerator-side boxParts field of the O9 two-dimensional checker be given a zero-sorry enclosure lemma, so that the qreIv and rIv composition lemmas can be instantiated at a box?

Method: imNum_mem is the product of imNumOverY and Y with the component left abstract, then every hypothesis of qreIv_mem and rIv_mem is discharged at one box, which is what exposed the denAbs2 mismatch in r_comp_mem.

Disposition: completed | Evidence: kernel-checked | Role: primary investigation

Notes: Case-log status is settled, and one defect found on the way. Disposition maps settled to completed. The brief's premise that the numerator side was missing was stale: commit 6f81078 had already landed reNum_mem and imNumOverY_mem.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_401bbf: Re-solving all 13200 cell evaluations (6600 cells times two cap modes) with zone_trade's cuts removed moves no margin, max |delta| 8.3e-17 signed and 1.1e-16 unsigned, so the inner prune never understates the adversary's zone trade on the published k=2 table.

Mon, 17 Aug 2026 22:31:58 +0000

Outcome: Re-solving all 13200 cell evaluations (6600 cells times two cap modes) with zone_trade's cuts removed moves no margin, max |delta| 8.3e-17 signed and 1.1e-16 unsigned, so the inner prune never understates the adversary's zone trade on the published k=2 table.

Question: Does the inner prune in k2_closure.zone_trade ever understate the adversary's zone trade on any of the 6600 published k=2 tau-cells?

Method: The trade was re-solved on every cell by exhaustive enumeration over every multiplicity vector with sum m <= 10, with both of the search's cuts removed, and a planted negative-charge instance was used as a detector-power control.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is settled, outcome (a), on every cell rather than a sample. Disposition maps settled to completed. Headline numbers follow the handback; the case log quotes max |delta| 4.4e-16 on the same census. The prune is also argued sound for nonnegative pair charges, which are squares.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [kernel-checked] r_233abe: Both leftover threads closed with zero sorrys: omega is bridged to ArithmeticFunction.cardDistinctFactors by rfl, and the pointwise log log n form is proved from the density form by splitting (0,N] at the square root of N, consuming variance 275 and Mertens band 16 unchanged.

Mon, 17 Aug 2026 22:37:47 +0000

Outcome: Both leftover threads closed with zero sorrys: omega is bridged to ArithmeticFunction.cardDistinctFactors by rfl, and the pointwise log log n form is proved from the density form by splitting (0,N] at the square root of N, consuming variance 275 and Mertens band 16 unchanged.

Question: Can omega be bridged to ArithmeticFunction.cardDistinctFactors, and can the density-form Hardy-Ramanujan theorem be upgraded to the pointwise log log n form, both kernel-checked with zero sorrys against pinned Mathlib v4.33.0-rc2?

Method: The bridge is rfl between n.primeFactors.card and n.primeFactorsList.dedup.length, carried through to a Mathlib-vocabulary restatement, and the pointwise form splits (0,N] at sqrt(N) with delta fixed at 1/2 so no extra parameter is carried.

Disposition: completed | Evidence: kernel-checked | Role: primary investigation

Notes: Case-log status is settled. Disposition maps settled to completed. The bridge is a restated definition pinned by a theorem; the pointwise form is the classical statement, including that n below e^e sit in the exceptional set where log log n is negative.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_f7cd45: Issue #21's table is confirmed cell for cell: the functional equation, a real Hardy-style Z, and having zeros on the critical line are each shared by 3 of 3 RH-violating rivals, while multiplicative and completely multiplicative coefficients are shared by 0 of 3, and the sixth property remains vacuous and expensive because the Epstein completed function at t=85.5 needs dps 60 against battery's cap of 20.

Sun, 16 Aug 2026 09:23:48 -0500

Outcome: Issue #21's table is confirmed cell for cell: the functional equation, a real Hardy-style Z, and having zeros on the critical line are each shared by 3 of 3 RH-violating rivals, while multiplicative and completely multiplicative coefficients are shared by 0 of 3, and the sixth property remains vacuous and expensive because the Epstein completed function at t=85.5 needs dps 60 against battery's cap of 20.

Question: For each of six claimed structural properties of zeta, does the property distinguish zeta from the RH-violating look-alikes of gate #3, or is it shared with them?

Method: A probe ran the five unpublished issue #21 properties end to end against Davenport-Heilbronn and both discriminant -23 Epstein zetas, with zeta as a positive control, and independently reproduced property 6 on two boxes preregistered at 53c8cd1 before any winding number.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is settled for the five unpublished properties; the sixth was already settled by gate5_p6_a/b/c. Disposition maps to completed because the queued table is published and the price tag is measured. Grade is measured, not enclosure-supported: no enclosure carries any step.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [kernel-checked] r_4218d4: The Turan variance constant falls from 5855 to 275, a factor of 21.3, by tightening the Mertens band it inherits quadratically: mertens_first_theorem from log 4 + 16 to log 4 + 3 and mertens_second_theorem from 76 to 16, with every statement's shape preserved, no sorry, and an unchanged axiom audit.

Sun, 16 Aug 2026 21:38:04 +0000

Outcome: The Turan variance constant falls from 5855 to 275, a factor of 21.3, by tightening the Mertens band it inherits quadratically: mertens_first_theorem from log 4 + 16 to log 4 + 3 and mertens_second_theorem from 76 to 16, with every statement's shape preserved, no sorry, and an unchanged axiom audit.

Question: Can the Turan variance constant 5855 be lowered by tightening the Mertens band it inherits quadratically, without weakening any statement?

Method: Three local slack steps were tightened in Mertensstheorems.lean using log t <= t/e, the two halves of Mertens I were kept apart, then mertens_second_theorem and sum_sq_dev_le were re-derived as 16^2 + 16 + 3, with lake build green against Mathlib v4.33.0-rc2.

Disposition: completed | Evidence: kernel-checked | Role: primary investigation

Notes: Case-log status is settled. Disposition maps settled to completed. Evidence is kernel-checked for the three edited modules; the remaining-slack arithmetic in probe.py is float bookkeeping and is not the grade. Classical constants 2 and 4 are not claimed to be close.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [measured] r_065f29: The white-box attack does not withdraw URMS2-051: the load-bearing new step saturates to four significant figures as W/U grows from 1.3 to 9.9, but the record's falsification control violates the hypothesis of the step it supports, gate 6's independent route shares its entire numerical substrate, and the four recorded margins do not select 51/100.

Sun, 16 Aug 2026 14:11:30 -0500

Outcome: The white-box attack does not withdraw URMS2-051: the load-bearing new step saturates to four significant figures as W/U grows from 1.3 to 9.9, but the record's falsification control violates the hypothesis of the step it supports, gate 6's independent route shares its entire numerical substrate, and the four recorded margins do not select 51/100.

Question: does a white-box attack on the URMS2-051 claim, seeing the author's reasoning and hunting the recorded checklist, find a fault that survives checking

Method: The eight-entry WHITEBOX_CHECKLIST was run against the author's coefficient family, evaluating the exact block second moment as a closed-form double sum while W/U varies at fixed x, plus a one-part-in-10^6 mutation of the shared tail majorant.

Disposition: qualified | Evidence: measured | Role: audit

Notes: Case-log status is settled as an attack, not as a verdict. Disposition is qualified for that split: the claim is not withdrawn and the apparatus around it is weaker than the record reads. Question kept in the HuntSpec's original lowercase.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Settled] [kernel-checked] r_0339c1: The Hardy-Ramanujan theorem is kernel-checked with zero sorrys as ZetaLean.HardyRamanujan.hardy_ramanujan, by Turan's proof with explicit variance constant 5855 on top of the Mertens band 76.

Sun, 16 Aug 2026 09:53:43 -0500

Outcome: The Hardy-Ramanujan theorem is kernel-checked with zero sorrys as ZetaLean.HardyRamanujan.hardy_ramanujan, by Turan's proof with explicit variance constant 5855 on top of the Mertens band 76.

Question: Can the Hardy–Ramanujan theorem be formalized in Lean 4 + Mathlib inside the budget now that Mertens second theorem exists on main, and if not, where precisely is the remaining wall?

Method: Hunt #12's kernel-checked Chebyshev half and double-counting identity were reused as written, then the second moment was expanded over ordered prime pairs and combined with mertens_second_theorem band 76 to close sum_sq_dev_le and hardy_ramanujan, with lake build green and print axioms only propext, Classical.choice, Quot.sound.

Disposition: settled | Evidence: kernel-checked | Role: primary investigation

Notes: Two case-log entries share this directory: Hunt #12 stopped at Mathlib missing Mertens second theorem; Hunt #37 settled the density form after Hunt #35 landed that lemma. Recorded_disposition is settled under Hunt #37 per coordinator guidance, with evidence_status kernel-checked. The HuntSpec en-dash in Hardy-Ramanujan is retained as quoted source punctuation.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_test_agy_8: The AGY test context loaded the repository, installed the venv, and evaluated a probe script using the internal zeta package from end to end.

Sat, 15 Aug 2026 00:13:07 -0500

Outcome: The AGY test context loaded the repository, installed the venv, and evaluated a probe script using the internal zeta package from end to end.

Question: Does the AGY context test framework correctly process a basic script and JSON handback?

Method: A probe script imported the venv-installed zeta package, computed zeta.explicit.li(x) with mpmath at specified precision, and wrote a complete evaluation to the local directory.

Disposition: completed | Evidence: measured | Role: tooling/method work

Notes: Case-log status is settled. Disposition maps settled to completed. Role is tooling/method work because the case log states this is a test of the test mechanism and nothing here bears on RH.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_fb9c81: A blind attack found no structural failure in the URMS2 0.51 bandwidth claim: the Montgomery-Vaughan off-diagonal spacing cost stays dominated by the diagonal, so the claim survives.

Sat, 15 Aug 2026 16:03:59 -0500

Outcome: A blind attack found no structural failure in the URMS2 0.51 bandwidth claim: the Montgomery-Vaughan off-diagonal spacing cost stays dominated by the diagonal, so the claim survives.

Question: Does a blind attack find a structural or analytic failure in the URMS2 0.51 bandwidth claim, without access to the author's reasoning?

Method: A numerical probe on a scaled configuration (x=1000, alpha=0.51, delta=0.75) compared the exact polynomial spacing cost sum n |c_n|^2 against the diagonal mass U log x, without using the author's reasoning.

Disposition: completed | Evidence: measured | Role: audit

Notes: Case-log status is settled and the analytical assumption holds structurally. Disposition maps settled to completed, matching batch 1. This is an attack that found no fault, not a promotion of the claim.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Settled] [kernel-checked] r_3c1cbb: Mertens's second theorem is kernel-checked in the Lean arm with zero sorrys, in the log log x + O(1) form with explicit constant 76, built along the predecessor's route map on top of the first theorem, while the third remains out of elementary reach.

Sat, 15 Aug 2026 22:48:37 +0000

Outcome: Mertens's second theorem is kernel-checked in the Lean arm with zero sorrys, in the log log x + O(1) form with explicit constant 76, built along the predecessor's route map on top of the first theorem, while the third remains out of elementary reach.

Question: Can Mertens's first or second theorem be kernel-checked in ZetaLean against pinned Mathlib v4.33.0-rc2 inside a 90 minute budget?

Method: MertensSecond.lean was built against pinned Mathlib v4.33.0-rc2 by partial summation against the predecessor's mertens_first_theorem band, proving the Abel identity by Nat.le_induction from N=2 rather than reindexing Finset.sum_range_by_parts, with lake build 8745 jobs and grep sorry count 0.

Disposition: settled | Evidence: kernel-checked | Role: primary investigation

Notes: Two case-log entries share this directory: Hunt #30 settled Mertens 1 in part and route-mapped the second; Hunt #35 settled the second theorem. Recorded_disposition is settled under Hunt #35 per coordinator guidance, not the earlier partial. Evidence is kernel-checked for the landed second theorem; the numeric sieve to 10^6 is a supporting spot check, not the grade.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] support_e6241336: Independent evaluation of abs(epstein_completed(0.8+85.7i, (2,1,3))) at dps=60 is 1.617452632377971461454064e-58, 1.1 percent from the claimed 1.6e-58, good to 16 digits and no further, confirmed by the class-number-3 Dedekind identity that does not cancel.

Fri, 14 Aug 2026 07:35:24 -0500

Outcome: Independent evaluation of abs(epstein_completed(0.8+85.7i, (2,1,3))) at dps=60 is 1.617452632377971461454064e-58, 1.1 percent from the claimed 1.6e-58, good to 16 digits and no further, confirmed by the class-number-3 Dedekind identity that does not cancel.

Question: Does abs(epstein_completed(0.8+85.7i, (2,1,3))) at dps=60 agree with the claimed 1.6e-58 to within an order of magnitude?

Method: The parent's number was not consulted while measuring; the value was pinned by the class-number-3 Dedekind identity from mpmath zeta and Hurwitz zeta, which reaches 1e-58 with no cancellation, agreeing to 4.0e-17 at dps=60.

Disposition: completed | Evidence: measured | Role: support work

Notes: No HuntSpec question field; question filled from the verbatim question in MISSION.md. Role is support work because MISSION.md states this is a support run, not an open hunt. The parent named in the case log is run 872d7dce / r_c7f779; the number checked is the dps_cap converged value.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_2926e4: Rebuilding o9_leaf.py's 1-D O9 walk on kernel leaves gives 476 cells at max depth 22, against the recorded 344 at depth 20, and 85 of those 344 cells (24.7%) fail outright; 476 is a measured prediction, not a kernel verdict, because no Lean was built here.

Fri, 14 Aug 2026 11:15:35 -0500

Outcome: Rebuilding o9_leaf.py's 1-D O9 walk on kernel leaves gives 476 cells at max depth 22, against the recorded 344 at depth 20, and 85 of those 344 cells (24.7%) fail outright; 476 is a measured prediction, not a kernel verdict, because no Lean was built here.

Question: What is o9_leaf.py's 1-D O9 cell count when its transcendental leaves are computed the way BandCert/Leaves.lean computes them, rather than with Arb?

Method: o9_leaf.leaves was swapped for o9_leaves_kernel.kernel_leaves with the rest of the walk left byte-identical, and bucketing the 85 failures into emit_lean's 40-cell chunks reproduced the 2026-08-13 Lean build's nine-chunk verdict without using that comparison to tune anything.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Headline rewritten from the handback to keep the no-Lean caveat in the same sentence. Evidence is measured, not kernel-checked: the hunt forbids claiming a kernel verdict without a Lean build. Issue #23 correction (the 344-cell table had already been put to the kernel on 2026-08-13) is retained in the method, not treated as the headline.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [measured] gate5_p6_c: Property 6 as written has no truth value: holding the sigma-band fixed at [0.7, 0.9] and changing only the height window flips DISTINGUISHES versus VACUOUS, and every repair that still distinguishes collapses to RH itself or the Euler product.

Fri, 14 Aug 2026 03:24:41 +0000

Outcome: Property 6 as written has no truth value: holding the sigma-band fixed at [0.7, 0.9] and changing only the height window flips DISTINGUISHES versus VACUOUS, and every repair that still distinguishes collapses to RH itself or the Euler product.

Question: Does gate-5 property 6 (no zeros of the completed function in a box strictly off the critical line) distinguish zeta from the three battery rivals, or is it vacuous?

Method: Parameters were preregistered at c29c876 before any winding number was computed; holding sigma in [0.7, 0.9] and changing only the height window flipped the Davenport-Heilbronn verdict, and the Epstein arm on the two high boxes was declared out of budget.

Disposition: qualified | Evidence: measured | Role: primary investigation

Notes: RESULTS status is settled in the sense that matters, and explicitly not settled in one arm. Disposition is qualified for that split. The well-posedness finding is retained. dps was changed from the preregistered 20 to a height-dependent rule and recorded as a deviation; that is a method fact, not a silent upgrade.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] gate5_p6_b: Gate-5 property 6 is vacuous in two preregistered boxes where all three RH-violating rivals have zero count 0 exactly as zeta does, and box-dependence is demonstrated: Davenport-Heilbronn satisfies the property on those boxes and fails it on a third box around its pinned off-line zero.

Fri, 14 Aug 2026 03:28:16 +0000

Outcome: Gate-5 property 6 is vacuous in two preregistered boxes where all three RH-violating rivals have zero count 0 exactly as zeta does, and box-dependence is demonstrated: Davenport-Heilbronn satisfies the property on those boxes and fails it on a third box around its pinned off-line zero.

Question: Does gate-5 property 6, the completed function has no zeros in a box strictly off the critical line, distinguish zeta from the three RH-violating rivals of zeta.epstein.battery, or is it vacuous?

Method: Three boxes and a precision rule were fixed in MISSION.md at 623e800 before any count; ten decided argument-principle counts were replicated at fifteen extra digits with worst relative disagreement 3.5e-22.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: Case-log status is probe, complete; handback status is settled. Disposition maps to completed. Qualifications retained: grade is measured, not enclosure-supported, and box B's two Epstein cells are undecided on cost. Parallel independence with the other two property-6 hunts is preserved.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [measured] gate5_p6_a: Property 6 is vacuous even in the adversarially favourable box A that contains the pinned Davenport-Heilbronn off-line zero, because the non-principal discriminant -23 Epstein form has no zeros there, and a second box assigns the opposite truth value to the same function, so the property is not well posed as a gate input.

Fri, 14 Aug 2026 03:21:20 +0000

Outcome: Property 6 is vacuous even in the adversarially favourable box A that contains the pinned Davenport-Heilbronn off-line zero, because the non-principal discriminant -23 Epstein form has no zeros there, and a second box assigns the opposite truth value to the same function, so the property is not well posed as a gate input.

Question: Does the property that the completed function has no zeros in a box strictly off the critical line distinguish zeta from the three RH-violating rivals of the gate #3 battery, or is it vacuous?

Method: Box A was committed one commit before probe.py existed, chosen because it contains the pinned Davenport-Heilbronn off-line zero; argument-principle counts used count_zeros_box, and the planned halved-step reconfirmation hit a 420 s cap.

Disposition: qualified | Evidence: measured | Role: primary investigation

Notes: Disposition is qualified rather than completed because the handback grade is float, one route, one resolution, the planned reconfirmation at halved and quartered step did not finish, and three of eight cells are recorded gaps. The VACUOUS verdict is retained. Question quotes the HuntSpec without the surrounding quotation marks. Parallel independence with gate5_p6_b and gate5_p6_c is preserved: this row does not adjudicate across the three.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] dps_cap: At 0.8+85.7i, epstein_completed at the capped dps=20 returns noise around 1e-33 to 1e-35 where the converged value is 1.6e-58, a factor of about 1e23 to 1.9e25 with no correct digit; dps=60 buys about 16 real digits, not 60, because cancellation costs roughly 44 of them.

Fri, 14 Aug 2026 07:06:02 -0500

Outcome: At 0.8+85.7i, epstein_completed at the capped dps=20 returns noise around 1e-33 to 1e-35 where the converged value is 1.6e-58, a factor of about 1e23 to 1.9e25 with no correct digit; dps=60 buys about 16 real digits, not 60, because cancellation costs roughly 44 of them.

Question: What does the min(dps, 20) cap in epstein.py's rival interfaces cost on a completed-Epstein evaluation high on the strip?

Method: Five concurrent 2026-08-14 runs evaluated abs(epstein_completed(0.8+85.7i, (2,1,3), dps=D)) on a precision ladder; they disagree on the exact dps=20 noise magnitude because parse precision moves the floor, and they agree the capped value has no correct digit.

Disposition: completed | Evidence: measured | Role: tooling/method work

Notes: Hunt #81 and Hunt #113 are duplicate case-log entries for the same directory, both Status: probe, complete, with the same measurement text. They are not two sequential outcomes. The directory landed 2026-08-21 as the unmerged union of five concurrent 2026-08-14 runs (live-b4528bd7, live-aeb4e5de, live-f12f9441, live-e72925d1, support/e6241336). Handbacks all say settled; the case log says probe, complete. Reconciled as one completed measurement. Concurrent runs disagree on the exact dps=20 magnitude (3.1e-33, 4.85e-35, 3.39e-34) because at capped precision the returned magnitude is not a function of the point; the headline keeps that spread rather than picking one noise value. The independent confirmation of the converged 1.6e-58 is the separate support hunt support_e6241336. The 'Renumbered twice' footnote that follows these case-log entries is about lambda_dh_bounds and prime_zeta_rightmost, not about dps_cap.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_cb5ffe: tests/test_doors.py detects 5/10 door-breaking mutants, four on the fast tier and one only on the slow tier, and the five escapes share one cause: the guard reads only the docs/doors/README.md table for the regex scripts/[\w.]+\.py.

Thu, 13 Aug 2026 23:42:17 +0000

Outcome: tests/test_doors.py detects 5/10 door-breaking mutants, four on the fast tier and one only on the slow tier, and the five escapes share one cause: the guard reads only the docs/doors/README.md table for the regex scripts/[\w.]+\.py.

Question: Which door-breaking mutants does tests/test_doors.py detect, and which pass it?

Method: Ten mutants were applied to throwaway git worktrees, both pytest tiers were recorded, and a tree carrying all five escapes at once stayed green on both tiers.

Disposition: completed | Evidence: measured | Role: audit

Notes: Handback em dashes were rewritten as colons. RESULTS status says settled at the level a mutation battery can settle it; case log says probe, complete. Disposition maps to completed. The proposed ledger amendment was reported and not applied.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_414eed: scripts/make_context.py --check caught 17/17 in-scope mutants including its declared smallest one, but it catches that mutant by line-count accounting rather than comprehension, and a length-neutral public-symbol add in an all module (mutant B06) passes silently.

Thu, 13 Aug 2026 23:16:29 +0000

Outcome: scripts/make_context.py --check caught 17/17 in-scope mutants including its declared smallest one, but it catches that mutant by line-count accounting rather than comprehension, and a length-neutral public-symbol add in an __all__ module (mutant B06) passes silently.

Question: Does scripts/make_context.py --check detect its declared smallest mutant, and where does its sensitivity stop?

Method: Twenty-four mutants were applied to a throwaway copy, the unmutated sandbox reproduced CONTEXT.md byte for byte, and the undo was re-checked after every mutant.

Disposition: completed | Evidence: measured | Role: audit

Notes: Handback em dashes were rewritten as commas. Case-log status is probe, complete; handback status is settled. Disposition maps to completed because the measurement finished and no arm was left open. Completeness caveat (24 mutants is a sample) is retained in the method and notes, not upgraded.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] r_03a798: The reserved-word guard is a case-insensitive substring match on one word, so it detects no synonym (0/13 across four documented bans and nine fresh terms), and the premise's other checks do not exist: no test in tests/ enforces verified, confirmed, definitively, or proves under hunts/.

Thu, 13 Aug 2026 23:40:03 +0000

Outcome: The reserved-word guard is a case-insensitive substring match on one word, so it detects no synonym (0/13 across four documented bans and nine fresh terms), and the premise's other checks do not exist: no test in tests/ enforces verified, confirmed, definitively, or proves under hunts/.

Question: Does the hunts/ reserved-word guard detect overclaim synonyms, and do the other checks said to ban them exist?

Method: The unmodified guard test was copied into a sandbox repo root and run by pytest against one planted specimen at a time, with an empty-specimen baseline remaining green.

Disposition: completed | Evidence: measured | Role: audit

Notes: Handback em dashes were rewritten as colons for house style. Two extra gaps the question did not raise (missed inflections, 33 committed uses of documented-only words) are kept out of the one-sentence headline and remain in the handback. Disposition maps settled to completed.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Open] [unreviewed] effective_constants: Opened 2026-08-13 with nothing measured: the hunt asks whether the transplant chain's ineffectivity is extractable bookkeeping or an essential obstruction, and no measurement has been recorded at the pinned revision.

Thu, 13 Aug 2026 09:51:42 -0500

Outcome: Opened 2026-08-13 with nothing measured: the hunt asks whether the transplant chain's ineffectivity is extractable bookkeeping or an essential obstruction, and no measurement has been recorded at the pinned revision.

Question: Is the transplant chain's ineffectivity extractable bookkeeping or an essential obstruction?

Method: The hunt was opened from PROOF-LEDGER.md blocker 3 and the source paper's EvBound Facts interface; no probe, measurement, or RESULTS.md exists at the pinned revision.

Disposition: open | Evidence: unreviewed | Role: primary investigation

Notes: Headline filled from the case-log status because HANDBACK and RESULTS.md are absent. Only MISSION.md exists in the hunt directory at the pin. Evidence is unreviewed because nothing was measured.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] jensen_clock: Finite Jensen degree acts on the Davenport-Heilbronn off-line pair as de Bruijn-Newman heat with t_eff = |x0|/(8d), landing at 0.097 percent from hunt #4's t*, textbook-degree scans are structurally blind, and a null control shows the clock reads zero configuration, not arithmetic.

Tue, 11 Aug 2026 22:23:57 +0000

Outcome: Finite Jensen degree acts on the Davenport-Heilbronn off-line pair as de Bruijn-Newman heat with t_eff = |x0|/(8d), landing at 0.097 percent from hunt #4's t*, textbook-degree scans are structurally blind, and a null control shows the clock reads zero configuration, not arithmetic.

Question: At what finite Jensen degree does hyperbolicity actually witness the Davenport-Heilbronn off-line pair, and is the finite degree itself a heat clock?

Method: The dictionary t_eff = |x0|/(8d) was checked against hunt #4's PDE landing times (0.097 percent on pair 1, 0.011 percent on pair 2) and against an arithmetic-free N-body null on a planted pair (0.094 percent).

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No HuntSpec or HANDBACK at the pin. Question filled from MISSION.md. Raw RESULTS H1 is only a title; the headline is taken from the RESULTS status paragraph. The mission's own quantitative guess for the planted-pair control failed and is retained as a failed prediction, not silently dropped.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [ordinary mathematical derivation] higher_xi: Bian's 2008 chapter-11 percentages are a calculation error: substituting Figure 10.1 into equation (11.5) recovers the known kappa=1 control 348002/405405 and not the reported 0.9544 and 0.9774, two measured oracles are retained, and no higher-derivative zeta constant is claimed.

Tue, 11 Aug 2026 10:33:29 -0500

Outcome: Bian's 2008 chapter-11 percentages are a calculation error: substituting Figure 10.1 into equation (11.5) recovers the known kappa=1 control 348002/405405 and not the reported 0.9544 and 0.9774, two measured oracles are retained, and no higher-derivative zeta constant is claimed.

Question: What do Bian's 2008 higher-derivative form-factor percentages actually compute, and can a first-principles reconstruction of xi'''/xi'' coefficients support a higher-derivative zeta constant?

Method: Figure 10.1 coefficients were substituted exactly into equation (11.5), recovering 348002/405405 at kappa=1 (the known control) and not the reported 0.9544 and 0.9774 at kappa=2 and 3.

Disposition: completed | Evidence: ordinary mathematical derivation | Role: primary investigation

Notes: No HuntSpec or HANDBACK at the pin. Question filled from MISSION.md plus the case-log discrepancy. Evidence grade is ordinary mathematical derivation for the headline calculation error; completed-CUE and Dirichlet-recurrence oracles are measured and are retained as supporting checks, not as the grade of the discrepancy claim.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] golden_control: A tapered transform pointed at a golden cut-and-project set whose atomic diffraction is proved reproduces the derived law to 2.5e-8, and the exact-arithmetic stage caught a false registered Pisano claim at p = 3.

Tue, 11 Aug 2026 23:27:59 +0000

Outcome: A tapered transform pointed at a golden cut-and-project set whose atomic diffraction is proved reproduces the derived law to 2.5e-8, and the exact-arithmetic stage caught a false registered Pisano claim at p = 3.

Question: Does the quasicrystal-lane instrument reproduce the proved atomic diffraction of a golden cut-and-project set, the one aperiodic point set whose atomic spectrum is a theorem?

Method: A tapered transform calibrated on Z, where the answer is Poisson summation to 6.4e-14, was pointed at a golden model set with peak positions and amplitudes derived in code from the embedding lattice rather than quoted.

Disposition: completed | Evidence: measured | Role: tooling/method work

Notes: No HuntSpec or HANDBACK at the pin. Question filled from MISSION.md. Raw RESULTS H1 is only a title; the headline is taken from the RESULTS status paragraph and the case log. Role is tooling/method work because the case log calls this instrument validation, not a result about zeta.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] frontier_math: The pair-measure LP reduces exactly to 2 - sup D and descends toward the paper's 0.6725007, so the measure level adds nothing, and the constructive candidate N0^s >= 0.672529 N is withdrawn because the scan used u u* while upstream uses u u^T.

Tue, 11 Aug 2026 13:07:22 +0000

Outcome: The pair-measure LP reduces exactly to 2 - sup D and descends toward the paper's 0.6725007, so the measure level adds nothing, and the constructive candidate N0^s >= 0.672529 N is withdrawn because the scan used u u* while upstream uses u u^T.

Question: Does the full-data LP over marked periodic configurations improve on the paper's 0.6725007, and can any known conditional refinement be made unconditional through the paper's machinery?

Method: The pair-measure LP with positivity, bandwidth-one data, and multiplicity types was shown to reduce exactly to 2 - sup D, and the constructive half was withdrawn after an exact witness 1, i, -i gave tr(P1 Q') = -2.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No HuntSpec or HANDBACK at the pin. Question filled from MISSION.md's THREAD 1 continuation of wide_search. Headline retains the withdrawn constructive half. The directory later accumulated many other arms; this row records the case-log status at the pin, which is the clean kill.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] frontier_map: The wide_search findings and the source paper's own limits were assembled into one lambda-landscape instrument, one JSON, and one figure, with onsets 0.550194 (zeta) and 0.513320 (xi-prime) and open lanes recorded as intervals.

Tue, 11 Aug 2026 12:10:26 +0000

Outcome: The wide_search findings and the source paper's own limits were assembled into one lambda-landscape instrument, one JSON, and one figure, with onsets 0.550194 (zeta) and 0.513320 (xi-prime) and open lanes recorded as intervals.

Question: What is the lambda-landscape of unconditional critical-line proportions reachable by the 10 August 2026 pair-correlation machinery, assembled as coordinates rather than as scattered prose?

Method: frontier.py computed the whole H(lambda) landscape for zeta and xi-prime, matched the paper's closed form (eq. 7.4) to 9.5e-15 pointwise, and a planted mis-constant lesion moved that comparison by 1.5e-2.

Disposition: completed | Evidence: measured | Role: artifact preservation

Notes: No HuntSpec or HANDBACK at the pin. Question filled from MISSION.md. Disposition is completed as a finished cartography run; the case log still calls the product a map, not a result. Role is artifact preservation because the work assembled existing wide_search findings and the paper's own limits into one instrument.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Qualified] [measured] director_run: A directorate record, not a hunt result: six defects in recorded claims were reproduced, including proven_sign returning a wrong nonzero sign on numpy.float32, a strategic coefficient-blindness claim was corrected, and two positives held under attack.

Tue, 11 Aug 2026 00:22:21 +0000

Outcome: A directorate record, not a hunt result: six defects in recorded claims were reproduced, including proven_sign returning a wrong nonzero sign on numpy.float32, a strategic coefficient-blindness claim was corrected, and two positives held under attack.

Question: What genuine mathematical information, including defects in recorded conclusions, can the laboratory extract when it treats this repository as an untrusted scientific artifact?

Method: Nine investigators with conflicting mandates ran in parallel, the generator of a claim never judged it, and each named defect was reproduced by the director before being written down.

Disposition: qualified | Evidence: measured | Role: audit

Notes: No HuntSpec, HANDBACK, or RESULTS.md at the pin. Question filled from MISSION.md. Disposition is qualified because the case log states this is not a hunt in the usual sense and not a result. Evidence grade is measured for the reproduced defects; the Lean rebuild (8715 jobs, zero sorrys) is a separate kernel-checked process check and is not treated as the composite grade.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Partly settled] [measured] wide_search: The xi-prime method's sharp constant is 0.86864150052976706411 and falls 9.285e-4 short of Wu's 0.86957, the scalar-moment formulation collapses exactly to 0.6725007037, and higher derivatives remain blocked on Bian's missing tail bound, all about the source paper's method rather than a result about zeta.

Mon, 10 Aug 2026 23:07:21 -0500

Outcome: The xi-prime method's sharp constant is 0.86864150052976706411 and falls 9.285e-4 short of Wu's 0.86957, the scalar-moment formulation collapses exactly to 0.6725007037, and higher derivatives remain blocked on Bian's missing tail bound, all about the source paper's method rather than a result about zeta.

Question: Can a breadth-first search produce one externally checkable mathematical contribution adjacent to zeta, with aggressive killing, prior-art search, and independent reproduction, without privileging a direct route to RH?

Method: The instrument reproduced the paper's Theorem D to 10 digits and all four Remark 7.3 constants to every printed digit before being pointed at the unsolved xi-prime variational problem, with five independent computations of the optimum agreeing to 14 digits.

Disposition: partly settled | Evidence: measured | Role: primary investigation

Notes: No HuntSpec or HANDBACK at the pin. Question filled from MISSION.md's adjacent-contribution objective. Disposition is partly settled because the case log closes the scalar-moment LP and the xi-prime comparison, blocks F_k for k>=2, and leaves the full-data LP over marked periodic configurations open for frontier_math.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] local_positivity: The prime side of the explicit formula factors place by place into a manifest norm, but those local norms do not assemble into a global sign, and the place-kernel gate tests the local Selberg bound rather than the existence of an Euler product.

Mon, 10 Aug 2026 09:37:57 -0500

Outcome: The prime side of the explicit formula factors place by place into a manifest norm, but those local norms do not assemble into a global sign, and the place-kernel gate tests the local Selberg bound rather than the existence of an Euler product.

Question: Does the prime side of the explicit formula factor, place by place, into a manifest norm, and if it does, does local positivity buy anything global?

Method: Place kernels were reconstructed against zeta.weil.explicit_formula_sides to 22 digits, then scored against zeta, L(chi) mod 5, Davenport-Heilbronn, both disc -23 Epstein forms, and 300 random period-5 sequences.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No HuntSpec or HANDBACK at the pin. Question filled from the quoted question in MISSION.md. Case log records that the hunt's original 'arithmetic-side blindness' reason was later corrected by the director run; the completed negative result on globalisation is retained.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [enclosure-supported] lehmer_pair: Both ball-arithmetic backends decide the Lehmer near-miss bump is positive at 64 bits, while Davenport-Heilbronn's closest approach on [85.2, 86.2] is -0.357 and never crosses, so a small |Z| flags zeta's healthiest close pair and stays silent at an actual RH violation.

Fri, 07 Aug 2026 19:22:07 -0500

Outcome: Both ball-arithmetic backends decide the Lehmer near-miss bump is positive at 64 bits, while Davenport-Heilbronn's closest approach on [85.2, 86.2] is -0.357 and never crosses, so a small |Z| flags zeta's healthiest close pair and stays silent at an actual RH violation.

Question: Do the enclosures of zeta.rigor decide, on both backends, that the Lehmer near-miss is real, that the bump genuinely clears zero, and how much precision does the closest call actually cost?

Method: proven_sign on both python-flint and mpmath.iv backends decided the bump positive at 64 bits, while the default mean_spacing/20 grid is wider than the Lehmer gap and missed the pair at 1 of 5 window phases.

Disposition: completed | Evidence: enclosure-supported | Role: primary investigation

Notes: No HuntSpec, HANDBACK, or RESULTS.md at the pin. Question filled from the quoted question in MISSION.md. Evidence grade is enclosure-supported because both rigor backends decided the sign; the rival comparison is measured, so the composite headline still carries the enclosure step.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Completed] [measured] flow_repair: Nine known Davenport-Heilbronn off-line quadruples land on the real axis at measured times between 0.00275 and 0.05765, giving Lambda_DH >= 0.0577 as a lower bound from those pairs, and an arithmetic-free N-body null control reproduces every PDE repair time to 0.04 percent, so the clock reads zero geometry, not arithmetic.

Fri, 07 Aug 2026 20:37:24 -0500

Outcome: Nine known Davenport-Heilbronn off-line quadruples land on the real axis at measured times between 0.00275 and 0.05765, giving Lambda_DH >= 0.0577 as a lower bound from those pairs, and an arithmetic-free N-body null control reproduces every PDE repair time to 0.04 percent, so the clock reads zero geometry, not arithmetic.

Question: How long does the backward-heat flow take to repair the Davenport-Heilbronn counterexample, pair by pair, measured with collision times read off a quantity that is analytic through the collision?

Method: Pair landing times were read as roots of the contour-moment discriminant Delta(t) = 2q2 - q1^2, which stays analytic through the collision, after route agreement against completed_dh to 7.2e-41.

Disposition: completed | Evidence: measured | Role: primary investigation

Notes: No HuntSpec, HANDBACK, or RESULTS.md at the pin. Question filled from the quoted question in MISSION.md. Headline filled from the case log. Lambda_DH >= 0.0577 is a lower bound from nine pairs, not a determination of Lambda_DH itself.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.

[Withdrawn] [measured] factorization_vs_position: The recorded factorization-versus-position correlation is withdrawn: the completeness gate was never called, a lesion produces an O(1) residue from an incomplete on-line list at zero factorization defect, and the test set restates the battery's rival admission criterion.

Fri, 07 Aug 2026 00:16:49 -0500

Outcome: The recorded factorization-versus-position correlation is withdrawn: the completeness gate was never called, a lesion produces an O(1) residue from an incomplete on-line list at zero factorization defect, and the test set restates the battery's rival admission criterion.

Question: Does the factorization defect D(F) quantitatively control the Weil position residue, that is, does the amount by which arithmetic fails to factor control the amount by which zeros fail to sit on the symmetry line?

Method: A lesion that removes one on-line zeta zero at factorization defect 2.65e-32 jumps the residue from 0.0038 to 1.99, matching the hunt's recorded residues at about twice that lesion, while online_list_is_complete was never called.

Disposition: withdrawn | Evidence: measured | Role: primary investigation

Notes: No HuntSpec, HANDBACK, or RESULTS.md at the pin. Question filled from MISSION.md. Headline filled from the case-log disposition rather than a missing handback. Disposition is withdrawn for the recorded claim; the generalized residue detector was retained.

Notice: Nothing in hunts/ is a result. This entry inventories an exploratory record. Git-record date is not a publication date.