A reductio pass over the whole record outside the carpet thread — stale back-links, controls that do not control, agreements built in by construction, two-level laws, and misquoted theorems

What this is. On 2026-09-29 the owner asked for OPS.md's reductio pass (six pushes: limits, invariance, twins, neighbours, joint consistency, transforms of the statement) to be run back over everything outside the carpet runs 049–063. Six read-only agents each took a slice — cases 01–13, cases 14–24, runs 017–037, runs 038–048, open probes, notes — with the carpet thread's lessons (N-037, P-048) as the back-propagation list. This note keeps what they found. Standing of each item: verified means the codifier re-checked it; two readers means two agents reached it independently from different slices; everything else is one agent's reading and must be checked before any record is changed on its strength. Nothing here is a result.

Five patterns across the record

1. Stale back-links. Later runs answered earlier questions and the earlier records never learned of it. P-025's "one remaining question" and N-026's open ≈39,000-vs-≈100,000 question were answered by run 031 (b₅ = 90,112); P-045 is still open after runs 044–047 answered it; N-035's register reading was falsified clause by clause by run 048 (and 050) and its body never changed; N-028 reports run 039's construction as having "survived" while 039's sealed outcome is falsified; P-009's premise was withdrawn inside P-008; harvested.md says a file does not exist that does. Fix is mechanical: when a run is scored, every record in its builds_on, settles or related gets a dated pointer to the verdict. That is a health check a Code chat can add.

2. Controls that do not control. The single largest failure class outside the carpets. - Run 033: the sealed band [0.45, 0.85] contains both controls (Ã₃ at 0.47, the non-amenable H at 0.77), so the pass cannot separate the classes; the real content, an ordering, was unsealed. - Run 024: the "reversible" baseline, an open Jackson tandem, is itself non-reversible (Kolmogorov fails) and keeps product form by quasi-reversibility; and at buffer K = 30 blocking fires only on negligible states, so "blocking does not kill product form" was never exercised. Two readers. - Run 022: the cat-map control is labelled "a real resonance"; a linear cat map has trivial Ruelle spectrum, so it is an artifact control and the label is inverted. Two readers. - Run 043 and P-045: the only control is a random graph, so the instruments separate "symmetric Cayley graph vs random" and are read as growth-class signatures. The exact twin that would expose it: the hypercube Q₁₀ (abelian) has return floor 180/N against the coset graph's 76/N. Rule proposed: every control is itself pushed with the twins question — does it differ from the object only in the variable under test? An abelian twin (torus or hypercube) beside every random control on the host thread.

3. Agreements that could not have failed. The carpet lesson "a pass without the mechanism" in its purest form. - Run 028: the eight "term for term" values are exactly (N − 1 + log₃2)/(N + 1). Verified — every one of 0.315 … 0.848 matches to three places. Both sequences read degree and precision off the defining series, so agreement is arithmetic. And its blocker is mis-posed: where Krasner applies, the minimal degree is squeezed between the bound and deg(x_N) itself, so it is a property of the element; "sequence dependence" can only live between those precisions. Two readers. CASE-07's "ℂ_p is rigid by completion" is also false (Ax–Sen–Tate: continuous automorphisms abound). - Run 037: multiplication mod 113 in discrete-log labels is addition mod 112; the unsealed character regularities may be facts about ℤ/112. Twin test: train addition mod 112. - Run 039: the two-band rounding is fed χ, whose weight is 86% in that span, and its own table gives balance 322 at the π/10 row — not a bisection. Two readers (runs 038–048; notes on N-028).

4. Two-level laws. The instruction "an exact identity at one level of a self-similar host is a prediction for the next level" has been broken outside the carpets too: 11/16 (levels 4, 5 — and level 3 is 16/16, so the sequence is 1, 11/16, 11/16); N-026's systole 2ⁿ (levels 3, 4); N-034's edge-disjoint squares with cycle length 2ⁿ⁻¹ (levels 3, 4), on which run 041 withdrew a clause. Cross-thread prediction from P-048: Grigorchuk coset graphs are finitely ramified, so exact spectral decimation should recur at every level while optimised quantities (minimum cuts) need not — spectra recurse, cuts don't — which run 038's failed ¾ − 1/16 already fits. Exact test: every level-3 band lands on a level-4 band.

5. Misquoted theorems in cases and probes. One agent each; to be checked against the literature before any case is edited. CASE-06 "chirality iff indicator 0" (10d Majorana–Weyl and 6d quaternionic Weyl spinors are chiral); CASE-09 branch 1 (quadratic Dirichlet characters are real but their family is symplectic; elliptic curves carry an alternating pairing but their family is orthogonal — a consistent reversal, which is itself the case's best new hypothesis: family type comes from the pairing on the family's cohomology); CASE-11 (Chowla–Selberg is proved through the Kronecker limit formula, which is lattice Poisson summation — so its "likely resolution" contradicts the proof); CASE-23 (a nontrivial eigenvalue of modulus 1 means no total-variation mixing; "⟺ real spectrum" is a false converse); CASE-16 (area in dimension 2 is topological by Gauss–Bonnet with a 6g−6 deformation space — rigidity does not license the volume); P-024 (Mermin's rule is π_{c−1}(M), not π_{c−1}(S^{c−1})); P-012 (COW and atom-recoil interferometry deliver absolute scales); P-025's "intermediate × manifold is structurally empty" (whether a finitely presented group of intermediate growth exists is open). And N-020: verified — float and true π expansions first differ at term 13 while q₁₃ = 52,746,197 < 2²⁶; the first q ≥ 2²⁶ is q₁₄. The note's bound is wrong; roughly q_n·q_{n+1} ≲ 2⁵¹ is the working criterion.

New hypotheses the transforms produced (not implied; each is its own lead)

• Family type is the opposite of the sampled type (CASE-09, from Katz–Sarnak's two standard families).
• Spectra recurse, cuts don't, on finitely ramified hosts (from P-048 back-propagated).
• Zero unique-neighbour expansion, generally: if H ⊇ ⟨s²⟩ for every generator s, each vertex outside H has two neighbours inside, so U(H) = ∅; for involution-generated groups the criterion is that every generator outside H has a partner t with st ∈ H — exact test on IMG's quotient.
• CASE-22's null case: at q = 9, a = ±6 a supersingular curve exists, the lattice degenerates, and the complement's top eigenvalue should be exactly 0 — which only the positivity reading predicts.
• P-030: a learned binary sieve should order its steps by ord_p(2), not by p (31 before 11 and 13).
• CASE-02: the "3" of triality is the largest branching valence of a finite-type Dynkin diagram (the 3-armed star has Cartan determinant 4; the 4-armed star is affine D̃₄, determinant 0).

Cheap exact tests, in order of value

1. Run 024 rerun with a small intermediate buffer (2, 3, 5) and the service rule stated; Kolmogorov on the K = 30 generator. Seconds.
2. Grigorchuk level-3 bands against level-4 bands (spectra recurse?), and N-034's cycle length at level 5 on the graph already on disk (predicted 16). Seconds to minutes.
3. Run 033 resealed on the ordering or the β fit; Basilica cogrowth predicted at the free rate. Cheap DP.
4. CASE-22 at q = 9 (exact determinant). Minutes.
5. Abelian twin (Q₁₀, torus) beside every random-graph control in runs 043–047. Seconds.
6. Run 028's minimal degree at intermediate precisions for one element. Minutes.
7. Run 037's twin: addition mod 112. One training run.
8. CASE-01: inverse participation ratios of the 8 Chern-band states at 64 and 512 sites. Exact, cheap.

What is not claimed

The agents read excerpts and quote theorems from memory; every literature item above is unchecked. The two verified items and the three two-reader items are the firm ones. The cases were written as open questions, and a case that misquotes a theorem is still a question worth having — the fix is a dated correction under the case, not a rewrite.

Back-links (2026-09-29)

Dated pointers added by the codifier from lab/backlinks.py; nothing above this heading was changed.

• Run 024 — falsified. lab/runs/024-product-form-reversibility.md: HALF WRONG - state-dependent service kills it, blocking does not
• Run 033 — confirmed (2026-09-27, measured). lab/runs/033-host-primes-cogrowth.md: CONFIRMED — κ = 0.665.
• Run 043 — falsified (2026-09-28, measured). lab/runs/043-growth-axis-on-one-tree.md: FALSIFIED — the relator clause's falsifier fires: Basilica's unique-neighbour minimum at N/8 is 1 of its control's 101 at best-of-20 and 0 of 94 at best-of-40, u/u_random ≤ 0.10, so the square obstruction of N-034 is not specific to the Klein-four contraction;