The falsification harness: how five claims died in one day

A methods retrospective. Everything in docs/00–16 is about the mathematics; this document is about the refereeing. It exists because 2026-08-05 produced an unusually clean natural experiment: five independent claims of Riemann-zero structure arrived in a single day from exploratory "rogue lab" sessions, and the repository's existing controls refuted all five — four rejected, one confirmed-negative by its own pre-registered prediction — without any of the verdicts depending on taste.

The problem this solves is asymmetry. A plausible spectral "explanation" of RH now costs minutes to generate — a discretized operator, a fitted spectrum, an evocative physical story — while a referee's rebuttal traditionally costs days. The instruments below make the rebuttal cost minutes too. None of them require knowing whether the claim is true; they only require that the claimant's evidence survive contact with controls. Per the honest-scope rule (docs/08), nothing here is evidence for or against RH itself. The harness adjudicates a weaker and more decidable question: is the demonstration about ζ at all?

1. The instruments

Four standing pieces, all in-tree before the claims arrived:

1. The counterexample battery (zeta.epstein.battery, docs/09 gate #3). The Davenport–Heilbronn function satisfies a Riemann-type functional equation, has real Dirichlet coefficients and a real Hardy-style Z — and violates RH. Any claimed structure that "explains" why zeros stay on the line must fail for DH, or it explains nothing. Crucially, the battery also catches tests of the battery: case 2 below flunked it by testing the wrong function.
2. The counting gates (zeta/spectral_gate.py). A claimed zero-counting model must (a) grow logarithmically with the cutoff in the 1:2 ratio the explicit formula forces, (b) predict a held-out cutoff, (c) move by ≥ 10% when the primes are swapped for decoys, and (d) be invariant under permuting the primes. Thresholds are pinned constants, declared before any model runs.
3. Pre-registration in the plan document. A review of a sprint plan records its predicted outcome in the repository, before the first run (docs/16 carries a complete worked example: prediction, outcome entry, closure). The corollary that had to be enforced this week: the review section belongs to the reviewer, and a pre-registered prediction may never be edited away by the party it constrains.
4. Reserved language. "Certified" belongs to zeta/rigor.py alone; everything else is at best accurate. A verdict sentence must say which it is.

2. One transferable checklist

Every rejection this week reduced to one of five checks, each cheap enough to run before reading a claim's prose:

• Count the free parameters against the data. An affine fit (2 parameters) of seven increasing eigenvalues onto seven targets dominated by a smooth trend produces small relative errors for any input. If a claim's headline is a calibration, refit the same spectrum to made-up targets first.
• Ablate the claimed mechanism, both directions. Replace the special structure (primes, polygon areas, coefficients) with noise; if the result survives, the structure was not load-bearing. Then run the battery: hand the same construction a known impostor and require a fail.
• Distrust thresholded quantities. A floating-point rank is a function of its SVD tolerance; a "detected peak" is a function of its scan window. Demand the sensitivity table, or sweep it yourself (blind, full-range).
• Check the trivial explanation for any inequality. "All eigenvalues ≥ 1/4" is implied by a positive potential of mean ≈ 39; it needed no arithmetic input at all.
• Ask what the identity already implies. A construction whose input is the primes and whose output is peaks at the zeros has rediscovered the explicit formula (docs/04, zeta/weil.py), not new physics.

3. The case log (2026-08-05)

Structural claims below are pinned at reduced size by tests/test_rogue_lab_controls.py; the quoted percentages are session measurements at the original sizes, reproducible from the committed scripts.

Case 1 — the geometric dust torus (ontology/10_geometric_dust_torus.py). Claim: a torus Laplacian plus a potential built from polygon area remainders calibrates to the zeros with sub-1% error, with min eigenvalue ≥ 1/4. Controls: the affine fit gives ~20% mean error against the real zeros, ~19% when the potential is replaced by noise, ~23% against invented targets; the eigenvalue bound follows from positivity of the potential. Verdict: two-parameter curve fitting; rejected.

Case 2 — the Dirichlet xp "imposter gauntlet" (ontology/13_dirichlet_polya_hilbert.py). Claim: weighting a divisor-graph xp operator by Dirichlet coefficients keeps ζ's spectrum on the line while throwing Davenport–Heilbronn off it. Controls: the "DH coefficients" used were the raw character mod 5 — i.e. L(s,χ), whose zeros are on the line — while the true DH coefficients are real (1, κ, −κ, −1, 0; zeta.epstein.dh_coefficient), so the genuine counterexample yields a real antisymmetric matrix and passes, as does random real noise. The gauntlet is a realness detector, misclassifying in both directions. Verdict: rejected; the battery exists precisely to catch this.

Case 3 — the Sierra–Townsend density fix (ontology/15_fixing_the_density.py). Claim: discretizing H = x(p + 1/p) forces the Riemann–von Mangoldt E log E level density. Measurement: the spectrum is an equally spaced ladder (gap CV ≈ 2.5%, linear density) whose scale tracks the arbitrary momentum box; by mode 100 it counts 100 levels where the zero-counting law says 20.5. Verdict: rejected.

Case 4 — the acoustic absorber (ontology/16_adelic_acoustic_absorber.py). Claim: a "prime crystal" chokes transmission exactly at the zeros. A blind full-range scan confirms peaks near 14.13, 21.02, 24.97, … — the one claim that reproduces. But the reflection amplitude is the Fourier transform of the weighted prime staircase minus its main term: the explicit formula, already in zeta/weil.py and zeta.explicit.prime_spectrum, with primes as input. Verdict: true, known, and not an operator; filed as a rediscovery.

Case 5 — the Poisson cokernel sprint (docs/16, scripts/32_poisson_cokernel_matrix.py). The system working end to end: the plan was reviewed with three blockers and a pre-registered prediction (ablation ≈ 0%, gate rejects); the prediction was restored after being edited away; the build confirmed it (ablation 0.0%, growth ratio 8.9); a follow-up showed the entire singular-value spectrum indistinguishable under prime ablation at every tolerance from 1e−2 to 1e−12; the p-adic tensor factors were then implemented as demanded and the gate still failed (4.8%). Verdict: matrix route closed by experiment — a negative result with a chain of custody, which is the only kind that stays closed.

4. What the week actually demonstrated

The interesting output is not that four claims were wrong; generating wrong claims is now free, so that was guaranteed. It is that verdict cost collapsed to claim cost once the controls were standing infrastructure: each rejection above was one short script reusing in-tree instruments, and each verdict survives independent rerun because the evidence is committed next to the claim. The one confirmed claim was identified as a rediscovery in the same pass, by the same instruments.

The discipline that cannot be automated remains the social one: reviews are appended, never rewritten; predictions are filed before runs; the reviewer owns the review. The one attempted violation this week (the self-approval edit, reverted in 6c70907) was caught by git history, not by any gate — version control is the fifth instrument.

5. Postscript: the instruments became a protocol (2026-08-06)

The four instruments of §1 were, at the time this document was written, four unrelated pieces of zeta/ that a referee had to know about and invoke by hand. They are now roles in harness/protocol.py, with the subject factored out:

A Battery bundles the four; a Department is a battery plus a door plus reference claims whose verdicts are known. The rule that follows is the one this document argued for implicitly and now states as code: no department without a battery — work whose claims nothing in the tree can falsify is a probe, not a department.

Two things this changes, and one it does not.

It changes who has to remember. §2's checklist was addressed to a person. tests/test_department_conformance.py is parametrized over the registered departments, so the checklist now runs itself, and a subject added without a referee fails the suite rather than merely disappointing a reviewer.

It changes what "the harness" is portable to. protocol.py names no quantity any laboratory computes and imports nothing from zeta — enforced by an AST scan, a sys.modules check and a lexical scan, the same three the funnel's seam already had. Whether the four roles carve a second subject well is untested: there is one department, so the generalisation currently has one instance behind it (ROADMAP.md, known gap 2).

It does not change §4's conclusion. Verdict cost collapsed to claim cost because the controls were standing infrastructure; making them a protocol lowers the cost of standing up the next set, and automates none of the social discipline — reviews appended not rewritten, predictions filed before runs, the reviewer owning the review. Version control is still the fifth instrument.

One immediate dividend, recorded because it is the failure mode the protocol exists to prevent. zeta.factorization.factorization_defect (Gate 4 as a decision statistic: D = 0 exactly when f has an Euler product) looked like an ideal distinguishing claim. Run through the battery it is not, because the Epstein form (2,1,3) does not represent 1, so that series has a₁ = 0 and the statistic raises rather than returning a number. run_battery records the exception and leaves distinguishes False: a rival that did not answer has not been excluded. A verdict that had counted the crash as a refutation would have promoted D from "works on three of four subjects" to "the decision procedure for Gate 4" — and it would have been a flattering bug of exactly the kind §3's case log is a catalogue of.