/teal-sea
teal-sea / zeta-labstate of record · compiled 02 Nov 2026 · revision b09fa4dd · source

Library · hunts/jensen_wedge/RUNS.md

RUNS

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Every run of this hunt, including the ones whose output was not kept. All runs so far were local and single-core: phase 0 is light by the MISSION's own estimate, and the timing below confirmed it before the sweep.

Unit timing, taken before the sweep (2026-10-18, worktree .venv, Python 3.14.0, mpmath 1.3.0)

unittime
route A, one block of 64 moments by the shared-grid trapezoid, dps 60, k = 49..112 / 800..863 / 3142..32050.04 / 0.03 / 0.03 s
check route, one moment by tanh-sinh over zeta.core.omega, dps 80, k = 49 / 32050.67 / 1.64 s
route B, saddle expansion to order 9 with M = 6 corrections, n = 3200, dps 600.93 s

Estimate written before the sweep: route A over k = 49..3205 is 50 blocks, about 2 s; the check route over the 147 indices of the 21 subgrid windows, about 3 to 4 min at the unit times (the trial had measured 488 s for the same indices, the mid-range k being slower than either end); route B at 21 points with its ladder, about 1 min; the dense model fits at 3151 n, under 1 min; the large-n table, about 1 min. Total about 10 min. Measured: 521 s, 442 s and 516 s for the three recorded runs, of which about 404 s each time was the check route.

results.json records git_head as the base commit 7c97b34: the recorded run used the working tree that the phase 0 commit lands, which differs from it only in the probe's module docstring, edited after the run to describe the final error rule.

An earlier per-index tanh-sinh version of route A timed at 2.36 s per moment at k = 3205 (about 2 h for the dense range) and was replaced by the shared-grid trapezoid before any sweep ran; the tanh-sinh code survives as the check route.

id: jensen_wedge-2026-10-18-trial
hunt: jensen_wedge
started: 2026-10-18T21:46-05:00
finished: 2026-10-18T21:56-05:00
ran:
  - <main checkout>/.venv/bin/python hunts/jensen_wedge/probe.py --out <session scratchpad>/trial.json
outcome: both sign facts held at every n from 50 to 3200 and route B agreed in sign at all 21 subgrid points, but the preset route-B error rule (M = 4, Laplace part |M4 - M3|) missed at n = 150 and every theta = 1 finite-free solve failed, so the probe was revised before the recorded run; this run used the main checkout's interpreter (same Python 3.14.0 and mpmath 1.3.0) while the worktree venv was still installing, and its JSON was not kept
artifacts:
id: jensen_wedge-2026-10-18-phase0-a
hunt: jensen_wedge
started: 2026-10-18T21:59-05:00
finished: 2026-10-18T22:08-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe.py --time-unit
  - .venv/bin/python hunts/jensen_wedge/probe.py
outcome: every verdict flag passed with route B at M = 6 and the preset M = 4 rule's miss at n = 150 recorded; the theta grid bracketed the R_5 sign crossing at n = 100, 1600 and 3200 but not at n = 400, where the walk failed at theta = 0.9 before the crossing, so the grid was refined and the probe re-run; this JSON was superseded by the next run and not kept
artifacts:
id: jensen_wedge-2026-10-18-phase0-b
hunt: jensen_wedge
started: 2026-10-18T22:08-05:00
finished: 2026-10-18T22:16-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe.py
outcome: with the refined theta grid the walk found the crossings at n = 100, 400 and 3200 but now stalled at theta = 0.86 for n = 1600, where the coarser grid had passed 0.9, which showed the stalls were partly the fixed-step Newton solver's; the solver was moved to log variables with adaptive steps and the probe re-run; this JSON was superseded and not kept
artifacts:
id: jensen_wedge-2026-10-18-phase0-c
hunt: jensen_wedge
started: 2026-10-18T22:17-05:00
finished: 2026-10-18T22:26-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe.py
outcome: the recorded run, 516 s; Laguerre defect at R_3 positive and Jacobi defect at R_4 negative at all 3151 n in 50..3200 on route A with no sign change, route B in sign agreement and within its stated error at all 21 subgrid points, the preset M = 4 rule's miss at n = 150 kept, Holland's constants approached to n = 1e20, and the R_5 defect negative at D = B_J/2 everywhere measured with a sign crossing in theta found at all four theta rows
artifacts:
  - hunts/jensen_wedge/results.json
  - hunts/jensen_wedge/RESULTS.md

Phase 1: unit timing, taken before the sweep (2026-10-18, worktree .venv, Python 3.14.0, mpmath 1.3.0, numpy 2.x)

unit (probe_phase1.py --time-unit)time
route A, one block of 64 moments, dps 60, k = 3233..32960.07 s
the four-parameter Pade solve (A, B, C, D) at n = 3200, dps 750.02 s
one theta walk of the D-fixed family, 0.5 to 0.85, n = 32000.04 s
route B by direct saddle evaluation, log R_0..R_6, n = 1e4 / 1e200.05 / 0.08 s
the leading-order three-factor scan on a 150 + 40 grid, eps = 0.010.79 s

Estimate written before the trial: route A over k = 49..3296 is 51 blocks, about 4 s; the check route at 26 indices, about 1 to 1.5 min at phase 0's per-moment times; the theta map at 21 values of n, a few seconds each; the dense Pade solve at 3151 values of n, about 1 min; route B at 6 subgrid points and 8 large n, a few minutes; the three-factor scans on the full 500 + 120 grid, (620/190)^2 x 0.8 s, about 9 s per eps and 1 min for six; root geometry at n = 3200 for d up to 96, not timed in advance (the degree-96 evaluations were the unknown). Total about 8 to 12 min.

id: jensen_wedge-2026-10-18-phase1-trial
hunt: jensen_wedge
started: 2026-10-18T23:10-05:00
finished: 2026-10-18T23:24-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe_phase1.py --out <session scratchpad>/trial1.json
outcome: run after the unit timing above; stopped by hand in the large-n stage after 14 min, so no JSON was written; its log showed route A and its check route agreeing to 5.2e-75, theta_star equal to phase 0's crossings to 12 digits, E_S6 negative at all 3151 n, and route B agreeing with route A on E_S6 to relative 2e-18..2e-22, and it exposed three defects that were fixed before the recorded run: the theta grid (0.85, 0.9, 0.95) stepped over theta_inf into the B = infinity wall at n = 50..70 and n >= 500, and the fixed large-n grid did the same from n = 1e8, so the grids were refined (0.01 steps above 0.8, and a grid in units of 1/L at large n); in a side check of the root-geometry code the scale S was built at 15 digits, which polluted c_j at 1e-14; and the Jensen polynomial at d = 48 showed 6 complex pairs that a precision sweep traced to cancellation (about 77 digits lost in the monomial basis, against about 70 carried), so the root-geometry part got its own dps-260 route A block and dps 60 + 2d evaluation
artifacts:

Measured: 400 s for the recorded run (check route 85 s, theta map 48 s, route B 45 s, leading-order model 48 s, root geometry 116 s, the rest the dense Pade solve and the validations). results_phase1.json records git_head as the base commit 5d34ddb: the run used the working tree that the phase 1 commit lands, before it was committed.

id: jensen_wedge-2026-10-18-phase1-a
hunt: jensen_wedge
started: 2026-10-18T23:24-05:00
finished: 2026-10-18T23:32-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe_phase1.py --time-unit
  - .venv/bin/python hunts/jensen_wedge/probe_phase1.py
outcome: the recorded run, 400 s; route A to k = 3296 agrees with its check route to 5.2e-75 and with zeta/li.py's tables; theta_star and theta_inf found at all 21 subgrid n and all 8 large n with no failed walk, theta_star equal to phase 0's crossings to 12 digits; the Pade model solved at every n = 50..3200 with all parameters positive and its R_6 defect negative at all 3151 n and at every large n, n^5 L E_S(6) = -1.872 at 1e20; route B agrees with route A on E_S(6) to relative 1.8e-22 at n = 3200; the three-factor scan found admissible configurations at all six eps; every model and Jensen polynomial at n = 3200, d <= 96 has all roots real
artifacts:
  - hunts/jensen_wedge/results_phase1.json
  - hunts/jensen_wedge/RESULTS.md

Rival gate (DH): unit timing, taken before the sweep (2026-10-19, worktree .venv, Python 3.14.7, mpmath 1.3.0, python backend)

unit (dh_gate.py --time-unit, the run before the recorded one)time
jensen_clock's node set (4.2, 16, 7) for the DH weight, dps 75, 3072 nodes2.0 s
route A, 64 moments k = 3233..3296 on it0.55 s
the construction at n = 3200 (three fits and the Pade solve)0.05 s
one theta walk 0.5 to 0.85, n = 32000.06 s
route B by direct Laplace evaluation, log R_0..R_6, n = 3200 / 1e200.16 / 1.8 s
jensen_clock's literal table to j = 60 at dps 1303.9 s
node set (4.2, 16, 8) at dps 275 for the root-geometry block12.9 s

Estimate written before the first sweep: route A on two node sets, about 1 min; the floor record, 0.5 min; the three fits and the Pade solve at 3151 n, about 2 min at 0.04 s each; the subgrid on both routes, 0.5 min; the theta maps at 21 + 6 n, about 1 min; large n, about 1 min; root geometry, about 2.5 min (phase 1's took 116 s); the n = 0 contrast, 0.5 min. Total about 9 to 10 min on one core, at phase 0's precedent, so it ran locally rather than on Actions. Measured: 442 s and 497 s.

id: jensen_wedge-2026-10-19-dh-scoping
hunt: jensen_wedge
started: 2026-10-19T08:27-05:00
finished: 2026-10-19T09:28-05:00
ran:
  - <session scratchpad>/t1.py (timing jensen_clock's DH nodes at Gauss-Legendre level 12, 600 segments)
  - <session scratchpad>/t2.py (jensen_clock's literal node sets at dps 75, k up to 3302)
  - <session scratchpad>/t3.py (the same with a relative cutoff in omega_dh)
  - <session scratchpad>/t4.py (node-set accuracy at dps 275)
  - <session scratchpad>/smoke.py (both routes and the construction at n = 50, 150, 3200)
outcome: t1 produced nothing and was stopped by hand after about 50 min on one core, because mpmath's Gauss-Legendre degree argument is a level giving 3 * 2^(level-1) nodes per segment, so level 12 meant 3.7 million nodes; t2 showed jensen_clock's three literal node sets disagreeing by 6 to 19 percent at n = 1600, traced to omega_dh's absolute floor (weight exactly 0 above u = 2.86 at dps 75); t3, with a relative cutoff, had all four node sets agreeing to 1e-74 up to k = 3302; t4 showed level 7 holding 1e-183 and level 8 1e-275 at dps 275, so the root-geometry block uses level 8; the smoke test found every predicted item true on both routes at the three n; no JSON was kept
artifacts:
id: jensen_wedge-2026-10-19-dh-a
hunt: jensen_wedge
started: 2026-10-19T09:28-05:00
finished: 2026-10-19T09:36-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/dh_gate.py --time-unit
  - .venv/bin/python hunts/jensen_wedge/dh_gate.py
outcome: 442 s; the prediction held on every item on both routes and the contrast showed no overlap; superseded by the next run only because a check of jensen_clock's pair-2 table (dps 180, j <= 400) against the relative cutoff was added afterwards; every other value of the two JSONs is identical (diffed key by key, timings aside)
artifacts:
id: jensen_wedge-2026-10-19-dh-b
hunt: jensen_wedge
started: 2026-10-19T09:38-05:00
finished: 2026-10-19T09:47-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/dh_gate.py --time-unit
  - .venv/bin/python hunts/jensen_wedge/dh_gate.py
outcome: the recorded run, 497 s; route A's two node sets agree to 4.5e-72 over m = 50..3296; Laguerre R_3 defect positive, Jacobi R_4 defect negative, E_F(5) at theta = 1/2 negative, the Pade match positive and its R_6 defect negative at all 3151 n on route A, with route B agreeing, resolving and inside its stated error at all 21 subgrid n and every item true at all 8 large n; the theta map has zeta's shape at all 21 n with theta_star the Pade point; DH Jensen polynomials real-rooted at n = 3200 (d <= 96) and n = 50 (d <= 24); DH complex pair at (d, n) = (22000, 0), landed at (20000, 0) and (30000, 1); jensen_clock's literal tables agree with the relative cutoff to 1.6e-39 (dps 130, j <= 328) and 1.6e-63 (dps 180, j <= 400)
artifacts:
  - hunts/jensen_wedge/results_dh.json
  - hunts/jensen_wedge/DH_GATE.md
  - hunts/jensen_wedge/RESULTS.md

H1 and H3: unit timing, taken before the run (2026-10-19, worktree .venv, Python 3.14.0, mpmath 1.3.0, sympy 1.14.0)

unit (probe_h1_h3.py --time-unit)time
route A, moments k = 3199..3206, dps 600.04 s
one route B row (targets, Pade solve, contraction), n = 1e4 / 1e200.10 / 0.13 s
G_0 derivatives by Cauchy's formula at one complex point0.07 s
h on a 64-point complex circle at n = 4006.3 s

Estimate written before the run: route A over k = 49..3206 at about 0.005 s per moment, about 16 s; 21 route A rows and 9 route B rows, about 4 s; 24 G_0 points, about 2 s; two complex circles, about 12 s. Total about 35 s. Measured: 17 to 27 s per run.

id: jensen_wedge-2026-10-19-h1h3-a
hunt: jensen_wedge
started: 2026-10-19T09:44-05:00
finished: 2026-10-19T09:45-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe_h1_h3.py --time-unit
  - .venv/bin/python hunts/jensen_wedge/probe_h1_h3.py
outcome: stopped by an exception in the G_0 stage, after route A and route B had run (the contraction inequality held from n = 1e7 to 1e20 and nowhere below); Holland's L_N solver from probe.py uses an absolute tolerance and failed at N = 1e50, so the probe got its own solver in relative form; no JSON was written
artifacts:
id: jensen_wedge-2026-10-19-h1h3-b
hunt: jensen_wedge
started: 2026-10-19T09:45-05:00
finished: 2026-10-19T09:46-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe_h1_h3.py
outcome: 26 s, completed, superseded: the complex circle at n = 3200 disagreed with route B at k = 2 and 6 (relative deviations 0.49 and 861) while k = 3, 4, 5, 7 agreed to 1e-23, the signature of a 2 pi i branch error in four symmetric arcs, which the mean-value check cannot see; and the route B against route A comparison of the targets read route A from 15-digit strings, so its 1e-15 agreement was the string length; both fixed (unwrapping along the circle, full-precision targets) and the JSON rewritten by the next run
artifacts:
id: jensen_wedge-2026-10-19-h1h3-c
hunt: jensen_wedge
started: 2026-10-19T09:46-05:00
finished: 2026-10-19T09:47-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe_h1_h3.py
outcome: 27 s; with unwrapping (88 corrections at n = 3200, none at 400) the circle agrees with route B to 5e-26..3e-23 at n = 3200; route B agrees with route A on every target to 1e-18..1e-23 at n = 400..3200; superseded only because the large-n rows were relabelled with their input strings (values unchanged)
artifacts:
id: jensen_wedge-2026-10-19-h1h3-d
hunt: jensen_wedge
started: 2026-10-19T10:00-05:00
finished: 2026-10-19T10:01-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/probe_h1_h3.py
outcome: the recorded run, 17 s; route A k = 49..3206 coarse/fine 3.8e-74 and validated against zeta/li.py; the reformulated system vanishes at phase 1's solution (2e-60 or better on route A, 2e-68 on route B); the contraction inequality holds at all 6 route B points from 1e7 to 1e20 with the measured configuration inside its radius, and fails at all 21 route A points and at 1e4, 1e5, 1e6; L t_j, the scaled configuration and the parameters approach their first-order values monotonically; G_0's derivative ratios approach (-1)^k (k-2)!/(N^(k-1) L) with first-order constants H_(k-2) - 1 to N = 1e50 on three rays; h on the two complex circles matches route B to 1e-17 or better. results_h1_h3.json records git_head as the base d0ce271: the run used the working tree this commit lands
artifacts:
  - hunts/jensen_wedge/results_h1_h3.json
  - hunts/jensen_wedge/H1_H3.md
  - hunts/jensen_wedge/RESULTS.md

Phase 2 (effectivity): unit timing, taken before the sweeps (2026-10-19, worktree .venv, Python 3.14.0, python-flint 0.9.0, mpmath 1.3.0, sympy 1.14.0)

unit (effective.py --time-unit)time
deriving F_2..F_7 exactly (sympy, once per process)3.4 s
one Laplace bound (Lemmas V, L)0.003 s
one subinterval of the five-coefficient chain (data, Krawczyk, Lemmas G, 9.1-E, 8.1-E)0.004 s
one subinterval of the six-coefficient chain0.004 s

Estimate written before the recorded run: 600 subintervals per evaluation of all four variants, about 50 evaluations (claims, 44 plants, the checks), about 130 s at the unit; measurements (quadrature of I(s), route B, Newton solves, polynomials of degree 40 at n = 1e12) about 60 s. Measured: 53 s. Everything ran locally; nothing approached the ten-minute line for moving work to GitHub Actions.

id: jensen_wedge-2026-10-19-effective-a
hunt: jensen_wedge
started: 2026-10-19T10:55-05:00
finished: 2026-10-19T12:20-05:00
ran:
  - development scans from a scratch directory driving effective.py (cover steps 1e-4 and 5e-4, K_6 from 2.5 to 5, n_0 from 1e5 to 1e36, smallest_K bisections, derive_claims)
outcome: chose the four specs and wrote the CLAIMS table; on the way found and fixed four instrument defects, each before any constant was recorded (square roots of balls touching 0 gave nan; Horner over an e-interval overestimated t_j twentyfold, replaced by the mean-value form; integer powers of complex boxes wrapped, enclosing 1/(1 + wy)^5 at 8e4 instead of about 80, replaced by exp(k log z); the Pade Krawczyk diverged below n ~ 1e10 because d/dx was enclosed by u_j'' over a hull, replaced by the exact difference quotient); and one mathematical misstatement (Lemma G's second diagonal bound stated without its case U < 2V, caught by test_effective.py; the case conditions are now checked on every subinterval and the claims stayed green). Standalone n_0 is limited by R_min >= 10 in Lemma L (five) and by Lemma M6 (six). Superseded by the recorded run
artifacts:
id: jensen_wedge-2026-10-19-effective-b
hunt: jensen_wedge
started: 2026-10-19T12:35-05:00
finished: 2026-10-19T12:36-05:00
ran:
  - .venv/bin/python hunts/jensen_wedge/effective.py --time-unit
  - .venv/bin/python hunts/jensen_wedge/effective.py
outcome: the recorded run, 53 s; all four variants green at the claimed constants (K = 17900 and 9.10e19 for n^3 log^2(n+2) >= K d^5, K' = 7.21e9 and 3.61e30 for n^4 log^2(n+2) >= K' d^6 log^12(d+2)); 44 of 44 planted weakenings turn the check red, so the MISSION's kill condition is not met; Laplace remainder 785 to 6554 times below lambda at n = 1e6, 1e8 (real and complex s); route B targets and Newton solutions inside every enclosure at n = 1e8, 1e12, 1e20; polynomials at n = 1e12 within every bound (C_loc 1.79 of 2.16, radius 1.24 of 2.82, defects 0.795 of the bound). results_effective.json records the git head of the base commit the run sat on; this commit lands the working tree that ran
artifacts:
  - hunts/jensen_wedge/effective.py
  - hunts/jensen_wedge/results_effective.json
  - hunts/jensen_wedge/EFFECTIVE.md
  - hunts/jensen_wedge/test_effective.py
  - hunts/jensen_wedge/RESULTS.md

Phase 3 (2026-10-19): the review's formula plants against the extended suite

Estimate written before the run: review_p2/plant_formula_faults.py runs the phase 2 suite five times (control plus four plants); the suite took about 50 s in phase 2 and the seven new tests add about 9 s, so about 5 to 6 minutes on one core, local.

id: jensen_wedge-2026-10-19-phase3-plants
hunt: jensen_wedge
started: 2026-10-19T19:48-05:00
finished: 2026-10-19T19:54-05:00
ran:
  - .venv/bin/python -m pytest -q -n0 hunts/jensen_wedge/test_effective.py -k "lemma_L_cubic or lemma_D_cauchy or lemma_B_sturm or formula_plants"
  - .venv/bin/python hunts/jensen_wedge/review_p2/plant_formula_faults.py
outcome: the seven new tests pass (8.9 s). The review's script, rerun on this tree, took 6 min: control green with 43 passed; all four formula plants red (8/3 as 8/15: 3 failed; 8/3 as 8/30: 4 failed; Cauchy radius n/4: 2 failed; Sturm constants divided by 10: 2 failed), each caught by the new derivation check for its step and by the replayed plant. The script overwrites review_p2/plants_review_p2.json; its output was saved as plants_phase3.json and the review's file restored unchanged
artifacts:
  - hunts/jensen_wedge/test_effective.py
  - hunts/jensen_wedge/plants_phase3.json