Status: probe, complete. The quasicrystal lane now has its ground-truth universe: the tapered-transform instrument, pointed at a golden cut-and- project set whose atomic diffraction is proved, reproduces the derived law to 2.5e-8 — and the exact-arithmetic stage caught the author mis-remembering a classical theorem, which is the house rule doing its job.
Everything is the accurate regime (numpy float64; exact integers for the Pisano stage). Raw numbers in results.json; predictions pre-registered in MISSION.md. Nothing here is about ζ's zeros and nothing is evidence about RH; this is instrument validation against a proved answer, in the same spirit as zeta/finitefield.py for the RH lane.
What was measured
- P1 (calibration on ℤ): holds, at machine precision. The tapered transform of the integer lattice matches Poisson summation at 2π, 4π, 6π to 6.4e-14, off-peak response 4e-16 of scale. The one constant of the instrument (taper mass T√(2π)) is thereby fixed by an elementary identity and transfers unchanged.
- P2 (the theorem reproduced): holds, far past the registered bar. The golden model set (window [0,1), density measured 0.44722 vs derived 1/√5 = 0.44721, defect 9.5e-6): the twelve strongest predicted peaks sit within 8.7e-9 of the numerically derived dual-module positions (registered: 1e-3) and the measured amplitudes match the window-transform law |W|/covol·|sinc(k\*|W|/2)| within 2.5e-8 relative (registered: a few percent). The Fourier module and the intensity law were derived in code from the embedding lattice, not quoted.
- P3 (silence off the module): holds, 300× past the bar. 200 random frequencies away from every visible module point: median response 1.0e-5 of scale, versus the weakest tested peak at 9.7e-2 — a 9717× separation (registered: ≥ 30×; ζ's prime-power gate measured 26.8× with 1000 zeros, so the theorem-universe instrument has headroom of two orders over the arithmetic one, as it should: nothing here is truncated by a finite zero list).
- P4 (lesions): hold. Gaussian jitter suppresses each peak by the Debye–Waller factor: fitted log-slope vs −σ²/2 within 1.0% (σ = 0.05) and 0.8% (σ = 0.10). A Poisson set of matched density and extent shows max response 7.1e-3 at the peak set — 14× below the weakest true peak.
- P5 (the golden thread): one exact identity holds, one registered claim was wrong and the computation caught it. χ_DH² = χ₅ pointwise mod 5 — the rival's quartic character squares to the ℚ(√5) character, exactly. But the registered Pisano statement π(p) | p − χ₅(p) is false, first counterexample p = 3 (π = 8 ∤ 4): the author remembered the split case and half of the inert case. The statement that holds, checked for every prime p < 500, p ≠ 5: π(p) | p − 1 when χ₅(p) = 1 and π(p) | 2(p + 1) when χ₅(p) = −1. The miss stays on the books — it is precisely the failure mode the derive-never-remember rule exists for, and the exact stage caught it on first contact.
- P6 (precision response): holds, monotone. Doubling extent and taper twice: max amplitude defect 8.6e-9 → 1.8e-9 → 1.0e-10.
What this buys the tree
The quasicrystal gate's headline on ζ (atoms at log prime powers, 26.8× separation) was measured with an instrument that had never been run against an aperiodic set with a proved atomic spectrum. Now it has been: the same transform architecture reproduces a theorem to eight digits, its silence is real silence, its lesion response is quantitative, and its one constant is pinned by Poisson summation. A future session pointing this machinery at a zero measure inherits a control that cannot be argued with.
Disposition
Instrument kept; no claim promoted; no ledger entry. The conductor-5 observation (the rival's character squares to the golden field's) is pinned arithmetic, not a lead. One registered prediction failed and is recorded above with its counterexample.