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This closes Nick Petalas6696 Open next question1: the fixed
(38,2,2)tariff for a covering nine-query path-lowered even-subset word is 486.The increment is a modest source-composition/pricing corollary. apoursh6059 Lemma2, following Arham Tahir1340's table, already bounds any nine-point support in F2^5 by28 nonzero pair differences. Hence R>=68 is a prior geometric consequence. Only that unrestricted point-set lemma is used; the partitioned-walk price frontier is not transferred.
At Q9, closure/nonzero increments give X>=2 and X=2mod4. The credited X2 minimumR70 costs342+140+4=486, attained by the existing source path. Every other layer hasX>=6, so the credited R68 bound gives price>=342+136+12=490. Thus the proposed X6 sweep is unnecessary for this fixed tariff. Geometry, X2floor/labeledcount and attaining path remain predecessor credit; no new2600-support census, floor law, witness or all-price frontier is claimed.
Independent source-premise/ABI verification uses the complete X2 forest quotient:3,780 graphs/120coordinate labelings/453,600 labeled walks. Primary center/matching/subset enumeration and oracle376,992-edge-combination scan/parity BFS agree on every actual record, including all117,180 minimum entries and repeated prefixes. Both strict normal/optimized oracle commands read the submitted FLOOR and witness word as data, verify exact path-local lowering, free noncommuting dirty endpoint, literal inverse and full invoice. The credited81-instruction word hasQ9/R70/X2;322map leaves,81echo nodes,2source XORs,81dispatches and4borrowed dirty rows total486. This is the inherited abstract complete-call tariff, not a new physical implementation.
Both blind-first codes, four source objects, cases/schema and original receipts/artifact remain unchanged. Ten primary and16 oracle internal controls plus23 reviewed external actualCLI rejections pass. All four registered commands, committed byte/declared-source-history/mode checks, final official export/declaredFLOOR input check and four read-only Git-free empty-PATH cold commands pass. Final tested tree6c91ce47b2a174b755258fb52c5764bb2dfb2c0c. Only validation prose/run records changed after the science freeze. Hosted CI SUCCESS on original run41752666667:711 helper tests/24 skipped; all four registered commands, both actual3,780record/117,180minimum-entry and dirty-word checks, and both staged/unstaged drift gates. Synthetic test commit d0fe440 has the exact tested tree and expected main/PR parents; no actual merge. Source-history/mode/export/cold checks above are local. No rerun or dummy commit. The only prose refinement clarifies that the remaining non-path question concerns the486tariff/X2source-cost classification; genericR68 projection/geometry remains prior coverage.
Current main7c49fe32c55de02c2c873655c804b16e4c3fef0a, eight guidance bindings and selected6030 refreshed unchanged. Fresh complete open traversal observes656bodies through6705 (unrelated rational-rank engineering); exact source heads/feedback, targeted all-state sets, helper and liveHub checked. No matching fixed486 closure identified within the stated non-atomic/lexical/sparse coverage. Changed independent-moment scope is this fixed-price corollary; full supplier acceptance remains separate.
Credit apoursh6059; Arham Tahir1340/1898; Nick Petalas6696/6695/5935; Wentao Li2677/2686/2643; ywz65/2455; Ross Richardson943/1370 and retained source/normalizer/compiler lineage; classical parity, incidence forests, BFS and bookkeeping. Exact notices/source pins retained. Prepared for ToikY with substantial OpenAI Codex and separate AI primary/oracle/static review, Apache-2.0; no human/formal-kernel acceptance.
Arbitrary non-path restored programs, all positive prices, changed primitives, native delivery/routing/restoration, stock, precision/compiler, supplier/recursive/outer bills remain outside this result. No newκ/frontier or merge requested; maintainer edits and auto-merge disabled.
Publication-boundary update: newly posted6706 was read in full and concerns unrelated complex block4 time-unrolled cuts. Canonical main and all eight guidance/selected bindings were fetched and compared again unchanged; all ten B10 PRs read back open/unmerged with maintainer edits/auto-merge disabled.