Forty-nine numbered documents. The first five are a single argument and are meant to be read in order; everything after 14 is a record of a particular piece of work and can be read on its own.
docs/doors/ is a different thing: one short page per audience (learn, refute, certify, discover, contribute, adopt) plus one per department. Start there if you want a task rather than a subject.
A bare docs/NN reference anywhere in this tree always means the document with that number, and tests/test_docs_numbering.py fails if two documents claim one number, if a heading disagrees with its own filename, or if a citation points at a document that does not exist.
The course
00 → 01 → 02 → 03 → 04 is one argument: theta is the heat kernel, Poisson summation gives its modular identity, the Mellin transform turns that into the functional equation whose mirror axis is Re(s) = 1/2, and the explicit formula rebuilds the primes from the zeros.
| Doc | One line |
|---|---|
| 00 | The statement, the stakes, the status, and the honest scope of this whole repo. |
| 01 | Euler–Maclaurin continues ζ by hand; how ζ(−1) = −1/12 is forced, not chosen. |
| 02 | Theta as the heat kernel; Poisson summation; θ(1/x) = √x·θ(x) in one line. |
| 03 | The Mellin bridge: modularity in, ξ(s) = ξ(1−s) out, derived line by line. |
| 04 | Zeros ↔ primes as an identity: ψ(x) as a sum of waves, one per zero. |
| 05 | Heat flow on Ξ; zero collisions; Λ ∈ [0, 0.2] and RH ⟺ Λ = 0. |
| 06 | The spectral dream and the Montgomery–Odlyzko law, measured on your laptop. |
| 07 | A catalogue of statements exactly equivalent to RH, and why equivalence is not progress. |
| 08 | The failure catalogue: what each known technique provably cannot do. |
| 09 | What "RH needs new mathematics" actually means, with the Weil precedent. |
| 10 | The Weil explicit formula as a trace formula; Selberg's working analogue; Connes' program. |
| 11 | The field with one element, Deninger's dynamics, and the hunt for geometry under ℤ. |
| 12 | Eight problems that fell, the mechanism that killed each, and an honest scoring of RH against the board. |
| 13 | External zero/value tables, finite-moment estimation, error separation, and the theorem-gated scorecard. |
| 14 | Eleven recurring ways new mathematics has appeared, scored against the missing Frobenius over ℤ. |
The record
What was built, what was measured, and what did not survive.
| Doc | One line |
|---|---|
| 15 | The F1 discovery engine: prime orbits, a cohomology scaffold, and what it could not reach. |
| 16 | Poisson-summation cokernel: the implementation blueprint. |
| 17 | The falsification harness: how five claims died in one day. |
| 18 | Five longshots, each run to the wall that stopped it. |
| 19 | Research dossiers: an experiment in AI-native mathematical state. |
| 20 | Verification integrity: the referee, refereed. |
| 21 | Forward-deployed verification: can a report refuse a crossing? |
| 22 | Detection strength of RH equivalences, stress-tested against the Davenport-Heilbronn imposter. |
| 23 | Rival distance and detector independence: closing two declared blind spots. |
| 24 | The local positivity attempt, run to its wall. |
| 25 | The director run: the laboratory pointed at itself, and six of its own claims died. |
| 26 | The adopted builds: the decision of 2026-08-11, made runnable. |
| 27 | State of the transplant: what is kernel-checked, what is refuted, what is open. |
| 28 | E0: the independent checker reproduced the audit's blind spots exactly. Read its correction notice. |
| 29 | The de Bruijn-Newman constant of the Davenport-Heilbronn function. |
| 30 | The rightmost zeros of the prime zeta function. |
| 31 | Erratum to Bian, Lemma 12: C_{kappa,2} is -4 kappa, not -4. |
| 32 | The Palomar arm: what an outside mechanical check adds, and what it does not. |
| 33 | Pitch classes against the colour wheel. |
| 34 | The Riemann zeros in tuning units. |
| 35 | The unspent fact: what out-of-band positivity is worth, and why nobody can claim it. Superseded 2026-09-06: hunt #118 closed it as a ceiling, the worth is zero to any unconditional certificate, and the page carries the correction inline. |
| 36 | Thirteen worked demonstrations, the figure gallery, the repository map, and the standing limitations. |
| 37 | The methods index: every reusable identity, lemma, control and technique the hunts produced, with grade and provenance. |
| 38 | The quasi-Riemann claim: OpenAI's 7/8 zero-free half-plane of 2026-10-06, read against this tree, rebuilt here and accepted by two kernels. |
| 39 | Start here for the current results. Five results built on the 7/8 half-plane: a prime between consecutive seventh powers (with an explicit density estimate; audited by a separate agent, reviewed by no person), a prime between consecutive ninth powers from the half-plane alone, class numbers up to 1500, small witnesses with constant 1, Linnik's exponent 7/3. |
| 40 | One form per discriminant: a composite-defect table whose hypothesis a(1) = 1 fails on 27 of its 41 rows, the check that would have caught it, and the eleven overclaims an adversarial audit found in the write-up of that finding (hunt #127; the repair to doc 34 landed in #296). |
| 41 | The module that missed the guard: the Epstein evaluator's failure surface in height and precision before #291, a loss derived rather than fitted, and a guard an adversary walked straight through because every rung of its fault ladder varied the wrong thing (hunt #129; the precision lift that fixed the routine landed in #291). |
| 42 | A law read off a diagonal: an elementary certificate barrier measured on a grid instead of a diagonal, a headline withdrawn when an adversary noticed the model comparison was not like for like, and the zero-weight cells that turn out to be what holds the excess up (hunt #130). |
| 43 | What happens to a claim after it is recorded: a measurement of this laboratory rather than of zeta, how much of the record has a guard behind it, how rarely a correction installs one, and a correction rate withdrawn when a blind audit scored the classifier near chance and re-earned on a disjoint sample (hunt #131). |
| 44 | The constant in the wedge: explicit constants for Holland's Jensen hyperbolicity wedge (K = 17 900 with GORTTW's corollary, 9.10e19 without) and c = 1 in GORTTW's theorem, the earlier deposits that claimed the 2/3 wedge first, the Davenport-Heilbronn rival the construction cannot tell from zeta, and a test suite that claimed more than it checked (hunt #135). Nothing in it bears on RH. |
| 45 | RH to height 100, kernel-checked by Lean and independently accepted by con-ron --verified on the exported whole closure: every zero of Mathlib's riemannZeta in the open strip with 0 < Im rho <= 100 is on the critical line and simple, exactly 29 distinct zeros (hunt #137). Nothing above 100 or about RH itself. Earlier height-50 and docs/39 results retained. |
| 46 | Same-verifier Arb replay of Berzai's Davenport-Heilbronn v6 census (Zenodo 10.5281/zenodo.23585903): 400/400 windows and 1,268/1,268 listed zeros recomputed with an Arb outward majorant replacing the one binary64 bound, zero failures, 27,614 zeros below height 20,000 reproduced. Not an independent implementation; limits and a receipt audit with planted lesions included. |
| 47 | The Davenport-Heilbronn zero, kernel-checked: davenport_heilbronn_strip proves in one statement that some entire function with the Davenport-Heilbronn Dirichlet series and functional equation has a zero s with 0 < Re s < 1 and Re s ≠ 1/2 (the witness is DH); it bundles dh_analytic_half (DH is entire, with zeta's kind of series and functional equation) and dh_zero_located (a zero of DH in the closed square of half-width 3/64 about 0.808517 + 85.699348 i), and dh_separation_hundred adds that below height 100 Mathlib's riemannZeta has no such zero; zero sorry and only the three standard axioms over 215 generated ball-arithmetic sites (hunt #145). The assembly's davenport_heilbronn : davenport_heilbronn_statement is weaker: the statement, as defined, is also met by the trivial zero s = -1 (lean/ZetaLean/DHTrivialZero.lean), so it carries none of this. A fresh replay of the whole closure by Lean's own kernel accepted it (leanchecker --fresh, 2026-10-27), and the independent con-ron --verified accepted the dependency closure of the 18 final declarations split site by site (216 shards, same day). Pending external verification: no outside review yet. Nothing about RH. |
| 48 | The Weil functional's degeneracy: three measurements (hunts #155, #156, #157) of how W sits against its norm, the constraint they put on a proof, and a prior-art scan with three PARTIAL verdicts. Nothing in it is evidence for RH. |
Adding one
Take the next free number from scripts/science_preflight.py rather than guessing it: two documents once shared number 21 because a session working from a snapshot could not see the tree it was writing into. Give the file an H1 of the form # NN. Title matching its own filename, and add a row here.