The documents · teal-sea

Thirty-eight 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.
36	Twelve 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.

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.