Run 083 found that the lattice crosses before the graph of its 64 top-level blocks does in 85% of samples on T and X at L = 729, a block counting as open once it is crossed left to right on its own bonds; run 085 that the mean lead is 0.46 to 1.92 widths over the census. P-053 says the lead is a coupling with the square's shape: a block can be passed between any two of its sides, and the pairs of sides fall into classes (opposite, adjacent). The recorder perc_blocks.c keeps, per sample and per block, the bond count at which each pair of sides is first joined inside the block. If a block is passed between two sides once those two sides are joined inside it, does the block graph cross when the lattice does, sample by sample, and is it the adjacent pairs (the corners) that make it? And PN-006's House named a statistic of several blocks for T's fall in skewness between 729 and 6561, the laggard gap; this run records what scores it.

Sealed 2026-10-03, after runs 094, 095 and 092 were scored and before any twelve-event file at 729 or 6561 was read (codifier). Known at sealing, reproduced by the sighted pass from run 083's k and k_coarse columns: Λ_s = −0.594, −0.778, −0.811 on T and −0.525, −0.861, −1.019 on X at 81, 729, 6561; S_s = 0.661 (T) and 0.792 (X) at 729; the correlation of t with t_s 0.324 and 0.243; the share of blocks crossed when the lattice crosses 0.66, 0.60, 0.57 on both. Also known: run 085's census of the lag; the recorder's controls at 81 (16,000 samples on T2 and C2: shares against exact polynomials, symmetry within groups; exact_events.json); that the recorder's control files at 729 (1,000 samples each, seeds 8302, 8305) and its timing file at 6561 (20 samples) hold the twelve events and have been read for nothing but k, k_coarse and the open-block counts; the zero-compute readings of 2026-10-03 on run 083's samples (READING-PN006.md); PN-006's House final and its forecasts. Nothing under R_m, R_a or R_t has been computed at any size.

What this run is for. Run 094 closed "which rows": three contacts per side, however placed, reverse the carpet's order of T and X. What the ladder fixes and the carpet does not is how a block is entered and left. This run asks the cheapest version of that on the carpet itself: treat each side as one terminal and each block as a table of pair-joining times. If the table's rule tracks the lattice sample by sample (A) and the corners are what move it (B), the coupling has the square's shape and P-053's table is the object; if the rule over-passes, sides must be split and the object is the ladder's after all, with more than three terminals.

The codifier's lead, held with conviction. On like-for-like rules along and across alone do worse than run 083's site rule: Λ_a is about −0.9 on T and −1.0 on X (the middle thirds join later than the full sides). The corners move the crossing by C = 0.6 to 0.9 widths, more on T than on X, and Λ_t lands between −0.3 and 0 on both; S_t is near 0.4 and the correlation of t with t_t above 0.6. The corner events come earlier than along_mid by a third to a half of the block's own width in the median. At 6561 Λ_t is nearer zero on T than at 729 and further on X. On the laggard gap the codifier makes no clause: its lead is that G falls on both patterns between the sizes, T's by more, and that the median-G split moves g₁ by selection on both, as the K-split did (READING-PN006: +1.22 on T and +0.86 on X at 729).

Power. At 16,000 samples the jackknife error of a lag in widths is about 0.01, so A's band is 25 errors from its falsifiers and B's 0.30 is 20 errors from 0.10. S_t's error is of the same order.

Controls, all before any scored quantity is read. (i) The rule engine reproduces the recorder. t_s computed by table097.py from the along_full times equals the recorded k_coarse/M on every sample of all four files (the sighted pass argued the block graph gives perc_coarse.c's third union–find exactly: a source and a sink have no seam edge, no path runs on seams alone, and along_full is perc_coarse's opening). One mismatch withdraws the run. (ii) Exact inequalities, every block of every sample: along_mid ≥ along_full, across_mid ≥ across_full, each corner ≤ max(along_mid, across_mid) (two paths joining alternating boundary arcs of a planar block share a cell; the ring is kept at every level, holes inside do not matter); and t_t ≤ t_a per sample. Any violation withdraws the run. (iii) Reseed against the record. At 729: Λ_s and the share with t < t_s within 3 combined errors of run 085's values (lag085.json: T −0.7605 ± 0.0082 and 0.8509 ± 0.0028; X −0.8443 ± 0.0103 and 0.8518 ± 0.0028; a jackknife error against a bootstrap error, which agree on run 083's files). (iv) The opening order is uniform. The mean share of blocks open at k_coarse within 3 combined errors of the pattern's constant pooled over run 083's three sizes (T 0.7809 ± 0.0004, X 0.7406 ± 0.0004). (v) Symmetry. At 729, medians and 20–80 widths: along_full against across_full, along_mid against across_mid, the six pairs of corners, k against k_ns — 18 comparisons a graph, each difference jackknifed; the largest |z| over the 36 at most 3.8 (Bonferroni at p = 0.005). A failure of (iii)–(v) makes the run reported, not scored.

Reported, not scored. Λ, S and the correlation of t with t_x under each of the four rules, at all four graphs; C at both sizes; the shares with t before, at and after each rule's crossing; the medians of the twelve events in widths from the lattice's median, and the six second-order numbers of P-053's table (variance of the symmetric and non-symmetric combinations and the cross term) at both sizes; the same-side events' medians. For PN-006: G on T and X at 729 and 6561 with errors and the g₁ of the halves above and below the median G (House F1 and its null); the share with t > t_s at 729 (F4); the open-block-count split of g₁ within the part t ≥ t_s at both sizes (Ledger); the SD of along_full times among the blocks open at the lattice's crossing within that part, raw and in widths, at both sizes (Lateral); g₁ of the parts t < t_s, t = t_s, t > t_s at both sizes (the codifier's CASE-28 lead, to be pooled with run 083's). The crossing link's block and the two cluster sizes it joined: their distributions, unread here. Wall time and peak memory per graph.

The reductio this seal passed first. By construction: t_t ≤ t_a, so C ≥ 0 and B asks how far above. R_m, R_a and R_t all use the middle thirds, so B compares like with like; R_s uses the full sides and is kept only as run 083's reference and control (i). Seam edges are free: where the lattice needs a seam bond between two clusters at matching cells, the rule assumes it; that is the over-passing A's upper falsifier reads, and S_t is what stops a cancellation of that against the thirds' lateness from passing A. Negation: the coupling is not in pairs of sides — then Λ_t stays strongly negative and A falsifies below, or S_t stays at S_s; or sides are not terminals — A falsifies above. Limits: a pattern that is one straight corridor has R_a = R_t; T and X have 12 and 4 corner-only cells among their 32 two-neighbour cells, so the corner entry has work to do on both. Cost: 729 in minutes; 6561 at 6.9 thread-seconds a sample (the recorder's timing, 20 samples at 2 threads under load) is 15 thread-hours a graph: two to eight hours each on the free M5, a night for both.

Reviewed before commit by a sighted pass and second reading (a Code chat, 2026-10-03), whose edits are folded in: clause B restated on like-for-like rules as the corner's shift C (the first draft compared R_a with the full-side rule and could hardly fail); a per-sample condition S_t added to A against a pass by cancellation; B's thresholds given as numbers and the reading for a positive Λ_a written; θ₂'s chain allowed to miss b*; control (iv) on a pooled constant with combined errors; control (v) as a Bonferroni bound on jackknifed differences; the 6561 cost corrected from 4.8 to 6.9 thread-seconds a sample; the recorder's md5, field order and C4.blk2 named.

Scored 2026-10-04 — falsified

Scored on 2026-10-04. A scoring reader, given the results file, the sealed clauses and this note without the lead, checked every number these files carry and each outcome; its edits are folded in.

From: the owner's proposal of a dial for every block (P-053, 2026-10-03; PG-01's line L15), sealed after run 094 closed "which rows"; and, for PN-006's House, the laggard gap. What the run did to it: a block passed between two sides once those sides are joined inside it, with the opposite pairs read on middle thirds, does not cross when the lattice does. The corner's shift is large, 0.70 and 0.77 widths, and the table still trails the lattice by 0.62 widths on T and 1.68 on X.

Controls. All five pass. (i) t_s from the along_full times equals the recorded coarse crossing on every sample of all four files. (ii) No violation of any exact inequality in 3,072,000 block-samples, and t_t ≤ t_a on every sample. (iii) Against run 085 at 729: z = −0.27, −0.27, −1.75, +0.44; the −1.75 is X's Λ_s, the quantity X's bars were set from. (iv) z = +1.19, +0.73, −1.21, +0.47. (v) Largest |z| of 36 is 2.40 (bound 3.8).

Clause A — falsified on both patterns: by Λ_t on both, by S_t on X. Λ_t = −0.6190 ± 0.0074 on T and −1.6822 ± 0.0157 on X; the band was ±0.30 and the falsifier −0.55 (9 and 72 errors past it). S_t = 0.8467 ± 0.0081 on X against a falsifier of 0.79 (7 errors). On T, S_t = 0.6683 ± 0.0064 sits at its bar of 0.66 (1.3 errors over); that bar was run 083's S_s, and this run's own S_s on T is 0.6528 ± 0.0056, 1.3 errors under it; at 6561 T's S_t is 0.6548 ± 0.0108. With T's S_t set aside, A and the run are unchanged. The seal's fixed readings that apply, as sealed: pairs of sides do not carry the coupling, and it sits in where on a side a route enters or in several blocks at once; and the rule does no better than the site rule sample by sample. The rule tested put the opposite pairs on middle thirds (see "What it means" below).

Clause B — confirmed. C = +0.7035 ± 0.0081 on T and +0.7710 ± 0.0075 on X; the bar was 0.30. That is the corner's shift against the along-and-across rule on the same thirds, whose adjacent pairs open at the later of the two.

The run — falsified, by the seal's rule (falsified if either clause is). Fixed readings that do not apply: "A falsified above with B confirmed" (A fell below); Λ_a ≥ 0 (it is −1.32 and −2.45); the cancellation half of the S_t reading (the mean is not inside the band).

What the lab reported beside the clauses. - The four rules at 729, lag in widths. Full sides, all six pairs (R_s): −0.764 on T, −0.871 on X. Middle thirds, all six (R_m): −1.229, −2.339. Along and across on the thirds (R_a): −1.323, −2.453. The table (R_t): −0.619, −1.682. In steps: moving all six pairs to the thirds costs 0.47 and 1.47 widths; splitting along from across costs a further 0.09 and 0.11; the corners give back 0.70 and 0.77. Against run 083's rule the table gains 0.14 on T and loses 0.81 on X. - Sample by sample. By correlation and by spread no rule beats R_s, at either size (the seal's S_t reading): the correlation of t with the rule's time is 0.327 and 0.254 under R_s and 0.274 and 0.171 under R_t at 729 (0.314, 0.233 and 0.264, 0.139 at 6561); the spread is 0.653 and 0.788 under R_s, 0.668 and 0.847 under R_t. By mean lag the table is closer than R_s on T, by 0.14. Across the four rules the lag moves by 0.70 (T) and 1.58 (X) while the spread stays in 0.65 to 0.70 and 0.79 to 0.92. - Shares. Under the table the rule crosses before the lattice in 13.1% of samples on T and 1.3% on X, and with it in 4.9% and 0.7%; under R_s, before in 4.0% and 9.4%. - When the events happen, in widths from the lattice's median, at 729. On T the corners come with the full sides (−0.352 against −0.355, means over the four and the two) and 0.42 before the middle thirds (+0.068). On X the corners come at +0.467, 0.37 before the middle thirds (+0.832) and 0.93 after the full sides (−0.467). The middle thirds are 0.42 (T) and 1.30 (X) later than the full sides in median. Same-side events are later than the corners on both: +0.50 on T, +0.75 on X. - At 6561. Λ_t = −0.651 ± 0.015 and −1.820 ± 0.030; S_t = 0.655 ± 0.011 and 0.853 ± 0.012; C = 0.686 ± 0.014 and 0.750 ± 0.013; Λ_a = −1.337 and −2.570. From 729: C falls by 1.1 and 1.4 errors; Λ_t moves by −0.032 ± 0.017 on T (1.9 errors) and −0.137 ± 0.034 on X (4.1). Every event's median moves later in widths by 0.05 to 0.23 between the sizes, each by 3 errors or more. - The lattice itself. g₁ of t: T +0.341 ± 0.028 at 729 and +0.273 ± 0.029 at 6561; X +0.308 ± 0.036 and +0.340 ± 0.038. - Blocks open (crossed west to east on their own bonds) at the crossing. 38.6 and 38.0 at the lattice's crossing against 50.0 and 47.4 at R_s's, at 729; 36.5 and 36.3 against 49.9 and 47.4 at 6561. Consistent with run 083's shares. - Decided by the lab, not in the seal, and changing no outcome: S and SD(t) with ddof 1 (moves S_t by 0.00002); w recomputed inside each jackknife replicate (sets every error, and so the "1.3"); control (iv) checked on each of the four files. - Not read: the six second-order numbers of P-053's table (recorded at both sizes); the crossing link's fields; the same-side events beyond their medians. - Cost. T4 5,870 s and C4 5,208 s at 8 threads on the M5 (5.9 and 5.2 thread-seconds a sample; the seal sized 6.9), peak 3.5 GB.

For PN-006 (scored in panels/SEAT-RECORD.md against the forecasts recorded there). - The laggard gap. G is 0.705 ± 0.006 (T) and 0.872 ± 0.009 (X) at 729; 0.646 ± 0.009 and 0.881 ± 0.014 at 6561. G(T) − G(X) is −0.167 ± 0.011 at 729 and −0.235 ± 0.017 at 6561: negative at both, more so at 6561 (by 0.068 ± 0.020). T's G falls by 0.060 ± 0.011 (5.7 errors); X's moves by +0.009 ± 0.017. - The split at the median gap (halves cut at the median of t_s − θ₂). g₁ of the half with the larger gap minus the other: +0.236 ± 0.043 on T at 729 (5.5 errors) and +0.017 ± 0.049 on X; at 6561, +0.213 ± 0.039 and +0.168 ± 0.075. On T the gap falls by 5.7 errors while this split does not move (−0.023 ± 0.059); on X the split goes from 0.3 errors to 2.2. - The share with t > t_s. 0.0401 ± 0.0016 on T at 729 and 0.0230 ± 0.0018 at 6561; on X 0.0935 and 0.0658. - Ledger's split within t ≥ t_s (ties to the high half; X's median count changes from 46 to 45 between sizes). +0.970 ± 0.098 (T) and +0.812 ± 0.179 (X) at 729; the change to 6561 is −0.14 ± 0.16 on T (−0.9 errors) and −0.21 ± 0.20 on X (−1.0). - Lateral's spread, ratio 6561 / 729. In widths: 0.886 ± 0.015 on T and 0.930 ± 0.015 on X per sample (0.887 and 0.933 pooled); T − X is −0.045 ± 0.021 (2.1 errors). Raw: 0.404 and 0.278, where X shrinks more. - Where T's fall sits (CASE-28). On these two files T's g₁ changes by −0.068 ± 0.040 in all, by −0.061 ± 0.035 in the part t < t_s, −0.029 ± 0.081 in t = t_s, −0.047 ± 0.285 in t > t_s and −0.009 ± 0.082 in t ≥ t_s. Run 083's estimates were −0.036 ± 0.038 (t < t_s) and −0.168 ± 0.100 (t ≥ t_s) in RESULTS083, and −0.036 ± 0.047 and −0.168 ± 0.090 in READING-PN006. Pooled, as the seal provided: −0.050 ± 0.026 and −0.072 ± 0.063 (with the reading's errors, −0.052 ± 0.028 and −0.080 ± 0.060); the tie part pools to −0.083 ± 0.063 with READING-PN006's −0.164 ± 0.099. Neither part's fall is resolved, nor their difference, and the share of the part t < t_s changes from 0.850 to 0.873 (5.5 errors), so the fall can sit in the mixing. g₁ of a mixture is not the sum of its parts'.

What it means for the programme (the codifier's readings). L15's table as sealed, one terminal per side with the opposite pairs on middle thirds, is not the boundary state. With rung 3 on two sets of rows (084, 094) that is three finite objects scored against the carpet and none for it. What is and is not shown about other one-terminal tables: - The rule with full sides for the opposite pairs and the recorded corner events for the adjacent ones was not sealed and is computable from the four binaries. Its six times are each no later than the table's, so its lag is at least −0.62 on T and −1.68 on X, and it over-passes in at least 13.1% and 1.3% of samples. The results give no bound on it from the other side. - On T the table misses −0.55 by 0.07 widths with its opposite pairs 0.42 late, so the thirds may be why the lower falsifier fires there. On X the full-side rule with every pair open is already at −0.87 and the corners come 0.93 later than the full sides; clearing −0.55 there is unlikely. - A also needs a spread of 0.50 or less. Across four rules the spread never leaves 0.65 to 0.92 and the correlation never exceeds 0.33. Nothing here suggests a one-terminal rule reaches 0.50. - In 85% of samples the lattice crosses before R_s does, so its route passes at least one block not yet crossed west to east on its own bonds. The recorder's same-side events and the crossing link's fields are on disk and unread; the seal's fixed reading points there. Any further rule needs its own seal before it is computed.

How the tools did. The sighted pass rewrote clause B on like-for-like rules and added S_t against a pass by cancellation. B then measured something. The S_t guard was never exercised, since the mean was not in the band. The bars sat 7 to 72 errors from the values, except T's S_t (1.3): that bar was set at a reseeded estimate with no margin. Under-specified: the seal's reductio named the thirds' lateness only as one half of a possible cancellation, not as a way for A to fail by itself, and no joint reading was fixed for A falsified below with B confirmed, which is what happened. The scoring reader changed the note in forty places; the largest were the claim about what the unsealed rule could do, which the draft left unbounded on one side and unsupported on the other, and a reading of the open-block counts that the counts do not support.