Zeta Lab · the record

The documents

37 numbered documents, a course and a working record, with the entry guides and the demonstrations you can run from a clone.

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The course

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

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.

Ways in

Guide	For you if you want to	First command
learn	see the classical machinery run at arbitrary precision	`.venv/bin/python scripts/06_tour.py`
refute	test a claim about the zeros against the control battery	`.venv/bin/python scripts/23_gate_3_battery.py`
certify	work in a regime where nothing is measured, Lean proofs and interval enclosures	`cd lean && PATH="$HOME/.elan/bin:$PATH" lake build`
discover	run the conjecture funnel and see its measured hit rate	`.venv/bin/python scripts/13_discovery_run.py --dry-run`
evaluate	run an LLM against a proof-backed grader rather than an LLM judge	`uv run --directory environments/bloch_certificate bloch-smoke`
contribute	return an agent-assisted finding as a checkable research pull request	`.venv/bin/python scripts/71_contribution_check.py hunts/<short-name>`
adopt	(demoted) the validation framework, and why it was frozen	`.venv/bin/python -m pytest -q -o addopts='' tests/test_harness_protocol.py tests/test_department_conformance.py`

12 demonstrations you can run

What it shows	Command
Rebuild the primes from the zeros	`python scripts/03_primes_from_zeros.py`
Find every zero below height 100 and verify RH there	`python scripts/02_find_zeros.py --T 100`
Derive the functional equation from heat flow	`python scripts/01_verify_functional_equation.py`
Test the zeros against random-matrix theory	`python scripts/04_gue_statistics.py`
Run the heat flow and watch zeros collide	`python scripts/05_heat_flow.py`
Balance the Riemann–Weil explicit formula, then probe Weil positivity	`python scripts/07_weil_positivity.py`
Watch a zeta-shaped function fail RH	`python scripts/08_wrong_shape_zeta.py`
Prove it instead of measuring it	`python scripts/09_certified_verification.py`
Watch RH as positivity and as real-rootedness	`python scripts/10_li_and_jensen.py`
See the one RH that is a theorem	`python scripts/11_finite_field_rh.py`
Run four exact equivalences at once	`python scripts/12_equivalence_faces.py`
Run the conjecture factory, and measure its own hit rate	`python scripts/13_discovery_run.py --dry-run # a full pass, nothing written`