Within a group of patterns that share one core, how much does a pendant part lower the lattice threshold at L = 729? The sign is fixed by containment; the size is not. Is the size a property of the part and of the cell it hangs on, about the same on three different cores, and does it carry over to the cut-2 groups?

Sealed 2026-10-03, late, before any of the nineteen lattices is drawn (codifier). Known at sealing, and cited as the pre-seal glimpse: every number in CASE-29's tables; READING-TWINS.md (each group shares one core; the pendant counts below); the sighted pass of the first draft, which reproduced the ten stored values from their files, found the seeds, the costs and the md5, and found that the first draft's sign clauses could not fail. Nothing has been sampled for the ten unmeasured members.

What this run is for. READING-TWINS.md found that the members of a group differ by islands, by pendant parts, and in group B by the position of four cells. The sighted pass added the relation that decides signs: when one member's ring-connected cells contain another's, its lattice contains the other's at every level, so it crosses at least as early at every setting. Within the groups: #22 ⊂ #24 ⊂ #23; #38 ⊂ #42 ⊂ #43; #46 ⊂ #47; #49 ⊂ #50; #57 ⊂ #59 ⊂ #58 and #57 ⊂ #60; #61 = #62 ⊂ #63; #53 = #54 = #55. So the sign of nearly every difference is a theorem and was dropped from the clauses. What the record does not hold is the size. Two sizes are on record: four one-cell parts on H's core lower the threshold by 0.0024 (#62 against #63), and going from four two-cell parts to eight one-cell parts on G's core by 0.0028 (#58 against #60).

The codifier's lead, held with conviction. The size belongs to the part and the cell it hangs on. Four one-cell parts on the (1,4)-type cells cost about 0.0024 on any of the three cut-4 cores; a second cell on a part adds a few ten-thousandths at most (#24 against #23 is 0.0003 ± 0.0002 on record); and the cut-2 groups have the same scale per part. Where it breaks: if #22 sits within 0.0008 of #24, the 0.0024 on H was a property of H's core; if #49 sits within 0.0012 of #50, pendant parts matter only where the crossing is wide.

Objects. Nineteen lattices at L = 729, in this order, with perc seed 9871 + j and bootstrap seed 298001 + j for j = 0 to 18: cut 4, 8,000 samples each — #22, #24, #57, #58, #59, #60, #61, #62, #63; cut 2, 72,000 samples each — #38, #42, #43, #46, #47, #49, #50, #53, #54, #55. Ten are new (#22, #42, #43, #46, #49, #54, #55, #57, #59, #61); nine are redraws of stored members, so that every difference is taken on one machine with one recipe. Seeds 9871 to 9890 and 298001 to 298010 were checked unused by the sighted pass; the lab checks 298011 to 298019 before any draw and stops if one is taken.

Pendant parts (READING-TWINS.md): #22 none, #24 four, #23 four of two cells; #57 none, #59 four, #58 four of two cells, #60 eight; #61 none, #62 none, #63 four; #38 none, #42 four, #43 four of five cells; #49 none, #50 eight; #46 twelve, #47 four and four three-cell loops; #53, #54, #55 none.

Controls, all before any scored quantity is read. (i) The sampler reproduces a stored file: 1,000 samples of cen60_3 on perc seed 7123 equal the first 1,000 lines of samples071/cen60_3.txt. (ii) Each graph's bond count equals the census's, and its md5 is recorded before sampling. (iii) Each redraw agrees with its stored value: none of the nine differs by more than 3.5 combined errors, with the stored errors as filed (census068.json, bands071.json, twins086.json; #60 against both its stored draws). (iv) Islands only: #54 − #53, #55 − #53 and #61 − #62 are each within 3 combined errors. (v) Containment: none of #22 − #24, #57 − #59, #59 − #58, #57 − #60, #61 − #63, #62 − #63, #38 − #42, #42 − #43, #46 − #47, #49 − #50 is negative by more than 3 combined errors. (vi) The known splits reproduce: #58 − #60 and #62 − #63 are each positive by at least 5 combined errors. A failed control means the instrument or the reading is wrong. No clause is scored until it is explained, and the run is withdrawn if it cannot be.

Reported, not scored. Every difference above with its error. (#57 − #60) beside twice (#57 − #59): whether eight parts on the (1,3)-type cells cost what twice four parts on the (1,4)-type cells do. #38 − #43 beside #38 − #42: depth on cut 2. #46 − #47: its size. w and g₁ of each lattice, and the differences in w within groups. The House's and the seats' forecasts for PN-007 (panels/SEAT-RECORD.md), scored on the same-run differences with the bars they named (0.0004 on cut 4, 0.0013 on cut 2).

Why each clause can fail. (1) Neither #22 nor #57 nor #59 has been drawn; containment bounds D_A and D_G below by zero and nothing bounds them above. (2) #59 has not been drawn; containment gives only that the difference is not negative. (3) No cut-2 pair has been compared at all. The comparisons the record or the containment already decides are controls (iv) to (vi), not clauses.

Cost. About 30 s per cut-4 lattice and four to nine minutes per cut-2 lattice at 72,000 samples on four cloud threads (run 086's times); under two hours in all. The M5 is drawing run 097 and is not used.

New statistic names go into lab/db/statistics.json in the run's own commit, never into a rows list.

Scored 2026-10-03 — confirmed

Scored on 2026-10-03, Phoenix time; the draws ran 05:34 to 06:19 UTC on 2026-10-04. A scoring reader, given the results file, the sealed clauses and this note without the lead, checked every number and outcome; its edits are folded in.

From: the eigenbasis chase's third branch (is there a second thing the lattice reads beside the formula), through CASE-29 and the returns inkling (N-040). What the run did to it: a pendant part costs the same order on three different cores, a second cell on a part adds nothing measurable on G, and on group C the cost is ten to fourteen times larger.

Controls. All six pass. (i) 0 of 1,000 lines differ. (ii) All nineteen graphs; the census stores no bond count at this size, so the lab checked the one-block bond count against the census and the full graph's against an independent count. (iii) Largest +2.27 combined errors (#60 against run 071; +0.59 against run 087); #63 is −1.99 against run 071 and −1.30 against run 087, so run 071's two values are the outliers, in opposite directions. (iv) −0.84, −0.88, −0.20. (v) Most negative −0.24. (vi) +12.23 and +16.69.

Clause 1 — confirmed. D_A = +0.00193 ± 0.00020 and D_G = +0.00260 ± 0.00020, both inside +0.0015 to +0.0035; D_A is 2.1 errors above the band's lower edge. H in the same run: #61 − #63 = +0.00263 ± 0.00019 and #62 − #63 = +0.00267 ± 0.00016. A reading beside the clause: G and H agree; A is lower than G by 0.00067 ± 0.00028 (2.4 errors) and lower than H pooled by 0.00072 ± 0.00025 (2.9 errors). The size is of one order on the three cores and is probably not equal.

Clause 2 — confirmed. #59 − #58 = −0.00004 ± 0.00018: on G a second cell on a part adds at most about 0.0003.

Clause 3 — confirmed as written. #49 − #50 = +0.00288 ± 0.00016, above +0.0024 by three errors. #38 − #42 = +0.02654 ± 0.00018, above +0.0012. The clause was one-sided, so the outcome word is confirmed. Its prose, "the same scale per part", fails on C: #38 − #42 is twenty-two times its bar and ten to fourteen times every four-part difference outside C (#38 − #43 is +0.02692 ± 0.00017). Per part: 0.0066 on C, against 0.0005 to 0.0007 on A, G and H and 0.00036 on E. A reading, not scored and not separated by this run: in C the four parts hang on the middle cells of the ring's sides, where the ring is one cell wide with the three cells inside it removed, which is the two-cell bottleneck itself. C differs from the other groups in core and in where the parts hang together, so this run cannot say which of the two carries the factor. The skewness moves with it: g₁ is +0.046 on #38 against +0.212 on #42 and +0.230 on #43.

What the lab reported beside the clauses. - Whether parts add. #57 − #60 = +0.00480 ± 0.00020 against twice (#57 − #59) = +0.00520 ± 0.00039. The difference is −0.00040 ± 0.00033 from the three files' errors (1.2 errors): consistent with adding, not shown. - The return that closes on a different side. #46 − #47 = +0.00005 ± 0.00019: twelve one-cell parts against four one-cell parts and four three-cell loops. A reading: the four loops together cost what eight dead ends on the same cells do, to about 0.0004. The run has no member of D without parts, so the bound cannot be set against what a part costs on D. - Depth on cut 2. #42 − #43 = +0.00038 ± 0.00017 (2.25 errors), five-cell parts against one-cell. A reading at that level, and it points the other way from clause 2's null on G. - Width. Parts narrow the pile at this size on G, H and E (#57 − #60: +0.00180, 6.3 errors; #61 − #63: +0.00148, 5.9; #49 − #50: +0.00124, 5.7), not on A (−0.00027 ± 0.00027), and widen it on C (#38 − #42: −0.00103, −4.2). D shows none. One size, so this says nothing about the rate. - #60. The known split #58 − #60 is +0.00225 ± 0.00018 in this run. On record it is 0.0028 against run 071's #60 and 0.0025 against run 087's.

PN-007's forecasts are scored from these differences in panels/SEAT-RECORD.md, each new member against the measured member the case named for its group (#24, #38, #47, #50, #53, #60, #63). On that reading seven of the ten differ beyond the bars the panel named (#22, #42, #43, #49, #57, #59, #61).

What this does to the lines. L9: inside a polynomial group the threshold moves with the pendant parts; islands change nothing to within about 0.0005 (control iv). L15 and N-040: the cost of four one-cell parts is of one order on three cut-4 cores, which is what the returns inkling needed in order not to break at clause 1 (codifier's reading). On C the cost is an order larger, and this run does not separate the part's place from the core. The loop of #47 shows no extra cost at this precision.

On the seal. Clause 3 was one-sided and could not register a surprise on the high side. A size clause carries two bounds from now on. One new statistic name, p_med_diff, was added by the lab to lab/db/statistics.json in the run's commit.