Is the hyperbolic angle η between the quasi-stationary mode r of the block operator T and its time-reverse r_rev = Z l, measured in the split-signature form G = Z⁻¹, zero to the float floor on blocks whose mask is invariant under the left–right reflection σ_v, positive on every block whose mask is not, and increasing with the size of the mirror break b = max|T − T_rev|?

Statement

Codifier, at sealing (2026-10-26, 12:40): the draft's clause R1 (η = 0 on census hosts) is control (ix), not a clause, because a mirror-invariant mask forces T = T_rev and so η = 0; where the text below says R1 it means control (ix). The scored clauses are R2 and R3. The run number is 139; the anchor premise's files keep their name anchor139_, and the anchor run takes the next number when it is sealed.*

A block of the carpet can be crossed left to right or right to left. The two crossings give two operators on the 512 wet-sets of a side, T and T_rev, and the premise found they are the same matrix seen through a mirror: T_rev is T's adjoint in a form Z⁻¹ that has 256 plus signs and 256 minus signs. That form is not a Euclidean metric but a Minkowski-like one, so "angles" in it can be hyperbolic. The quasi-stationary mode is the shape the wet frontier settles into before it dies out. Its time-reverse is the same shape read from the other side. On a block whose mask is its own mirror image the two coincide. On F14, whose mask is not, the derivation found them separated by a hyperbolic angle of 0.106, a rapidity, while the ordinary cosine between them hid the difference at 0.9995. This run asks whether that angle is the mirror break's fingerprint across blocks it has not seen: zero where the mask is mirror-symmetric, positive where it is not, and larger where the break is larger. Every census block is mirror-symmetric by construction (P1), so the seven of run 135's list stand for all 63: a symmetric mask gives T = T_rev to rounding, and seven builds are the budgeted way to measure the floor that fact leaves on the run's own machine.

Resolution

What float64 resolves for η, as measured (P5) and as derived.

1. The eigenvectors. λ_q is simple with gap g = |λ_q| − |λ_3| of 0.81 (F14) and 0.60 (g57). Rounding in r and l is of order ε ‖T‖₂ / g ≈ 3e−15 per unit norm.
2. The forms. a = rᵀGr cancels: |a| ≈ 2.0e−3 per unit norm while ‖G‖₂ = φ⁹ = 76.01. The worst-case bound on δa is near 1e−11, but P5 measured c − 1 = 1.1e−15 on g57, where c = 1 exactly, so the realised error on c is at the 1e−15 level: the cancellation is benign because G's entries are in {−1, 0, 1} and the sums are short.
3. c and η. arccosh has infinite slope at 1: η ≈ √(2 (c − 1)) near zero. A floor of 1e−15 on c is a floor of √(2 · 1.1e−15) = 4.7e−8 on η at η = 0; that is exactly g57's unperturbed value, and perturbing T by up to 100 ulp does not move the maximum, because the floor is the rounding of c − 1 and not a response to T. At η = 0.106 the floor is δc / sinh η ≈ 1e−14 (measured 8.0e−14 at 100 ulp). The lines follow: R1's 1e−6 is twenty times the floor at zero (c − 1 ≤ 5e−13); R2's 1e−3 (c − 1 ≥ 5e−7) is a thousand times R1's line; control (ii)'s 1e−9 on F14 is 10⁴ times the floor there.
4. Per-host floor. The lab prints f_host = √(2 · 10 ε ‖G‖₂ / |a|) as the a-priori floor at zero (4.7e−8 at |a| = 2e−3 if δc ≈ 10 ε ‖G‖₂ / |a|; P5's measurement is the check) and the measured η_noise. Multiprecision is needed when η_noise > 1e−7: when |a| per unit norm falls below about 1e−6 (a nearly null quasi-stationary vector; then c − 1 loses the digits the floor relies on), when the gap g falls below about 1e−3, or when η must be resolved below 1e−6, as it would be to test η ∝ b at small b or to score the band 1e−6 to 1e−3 that this seal leaves unanticipated. The 512 × 512 stage is not the limit; the digits are lost in the frontier pass's weights, and a multiprecision run would need mask_states in mpmath or exact rationals, the tool question the d4 premise flagged for I5.
5. What η cannot see. η is a function of the plane span(r, r_rev) only, invariant under scaling and sign of r and l and under T ↔ T_rev. It is blind to the elliptic (rotation-like) part of A unless that part turns the plane definite, which is why the elliptic branch is reported and not scored.

Power

Without data (ESTIMATE throughout).

• R1 cannot surprise. All 63 census masks are σ_v-invariant (P1), so T_rev is the operator of the same mask and T = T_rev to rounding (g57: 3.6e−14), r_rev = r is forced, and η sits at the floor. R1's failure modes are the code and the build. Its value is the floor on the run's own builds (OPS) and the anchor for control (vi). Seven hosts, not 63, because the seven are run 135's budgeted list and each further census build costs 1,000 to 5,000 s for the same forced answer; generator 7 is the one cheap spot check outside the list, conditional on its stored wall time.
• R2. On F14, η = 0.106 at b = 0.221, a hundred times R2's line in a square-root quantity: a block with a break in c − 1 ten thousand times smaller than F14's would still clear 1e−3. A fresh block fails R2 only if r_rev ∝ r despite T ≠ T_rev, which requires A r to lie in the span of r (A's hyperbolic pair G-orthogonal to the mode), a measure-zero event unless a symmetry forces it; P2's exclusions remove the one symmetry that does. The mask-level breaks are 12 to 24 cells against F14's (not recorded here; F14's entrywise b is 0.221). Expected: 16 of 16 confirm, η in 0.02 to 0.4.
• R3. To first order, r_rev − r is A's action on r divided by the gaps to the other modes, so η scales like ‖A‖/g, not like b alone; b is a max-entry norm of A and g varies between hosts (0.60 and 0.81 on the two seen). The b-only Spearman is attenuated. If the true ρ is 0.7, power at n = 16 and the 0.4265 line is about 0.9; if 0.5, about 0.6; if the gap's spread across the fresh masks is as wide as between F14 and g57, ρ could sit near 0.4 and power near 0.4. At n = 16 R3 is marginal and is kept; it is unscored below 14 by the codifier's ruling. Reported beside so a failure can be read: the partial rank correlation of η against b given g, and the Spearman of η against ‖A‖_F/‖T‖_F and against the mask-level break (12 to 24 cells).

Combining rule

Run 138's strict rule. Withdrawn if any control fails or the run's noise premise exceeds the ceiling 1e−7 on any host. Otherwise falsified if any falsifier fires, on any host. Otherwise confirmed if R1, R2 and R3 all hold as written. Otherwise unanticipated, with the clause that fell between the lines named (R3 unscored counts as between the lines).

Reported beside

Per host: c − 1 (the linear quantity behind η); the next two non-trivial modes' η and η_ell (F14's were 0.27086 and 0.45277, spent); the sign of a (the quasi-stationary mode was of negative type on both hosts seen; a candidate clause for a later run, not scored here); S = (T + T_rev)/2's reliable eigenvalues above the d4 premise's floor and its complex pairs with their ⟨x,x⟩_G (neutral is forced); A = (T − T_rev)/2's leading ± pair, real (a boost) or imaginary (a rotation), with its eigenvectors' ⟨x,x⟩_G; ‖A‖_F/‖T‖_F; the number of one-way pairs of Q against the json's predicted_oneway_pairs (run 131's rule, not scored); the structural one-way count between T and T_rev (T ≠ 0, T_rev = 0) and its product shape. F15 at its p* with all of the above (not scored). Across fresh hosts: η against ‖A‖_F/‖T‖_F, against the mask-level break, and the partial given g; η against the gap alone. The per-host floor f_host and the measured η_noise. Build wall time and peak RSS against P7's estimates.

Sealed 2026-10-26

As written. The lab chat reads this file above "Not part of the seal" only, plus rapidity_premise.py (eta), rapidity_fresh_masks.json, rapidity_premise.log (controls (ii), (iii), (viii)), ops.py, transfer_op.py (mask_states, generator), transfer_op.json (p* at star; index 7's wall_s) and k5.log (controls (i), (iv), (v)). It does not read any REPORT.md, the programme file, or any lead. Memory off.

The codifier’s lead is kept for the private site.

Scored 2026-10-26 — unanticipated

A blind scorer read the seal above the line and RESULTS139.md (636bfd5) and nothing else (R28_reading/139/scorer139.md). Scores are as written.

Controls. All nine pass. The largest η_noise is 5.96e−8 (g58), under the 1e−7 ceiling; control (ix) holds on the eight census hosts built (g57–g63 and g7). Not withdrawn.

R2, between the lines. All 16 fresh hosts are scorable. Eleven are on the hyperbolic branch with η from 0.030 (R05) to 0.141 (R03). Five (R06, R10, R12, R14, R15) are on the elliptic branch: c < 1, so η = 0, with η_ell from 0.013 to 0.306. No host has both η and η_ell below 1e−6, so the falsifier did not fire. On five of sixteen broken blocks the quasi-stationary mode and its time-reverse span a definite plane at an ordinary angle, not an indefinite one at a rapidity.

R3, between the lines. ρ(η, b) = −0.0328 at n = 16 (the five zeros tied at average rank), between −0.426471 and +0.426471. The scorer's two other readings (rank by c − 1: −0.0588; hyperbolic hosts only: n = 11, unscored) are also between the lines.

Combining rule. No control failed, no falsifier fired, R2 and R3 did not hold: unanticipated, with R2 (the elliptic branch) and R3 named.

Beside, not scored. Spearman of η against the gap 0.636, against ‖A‖_F/‖T‖_F 0.072, against the mask-level break 0.082; partial of η against b given the gap −0.089. a is negative on every host. F15 at its p*: η = 0.2505.