Conditional κ ≈ 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969)

[mdumitrean]

The fill layer of #2942's words with #2957's rewrites is exhausted (#2969 attains their packing cap), so a further gain must change the words. This package changes them in three declared stages on #2942's words and admits the result completely:

κ = 0.001729033982646513517717 − 10⁻⁴⁶ − 10⁻⁷⁰, exactly 4998757898408639167/10²⁴ ≈ +4.9988e-6 over #2969 (Dugongue, e2ca469b; ≈ +4.9997e-6 over #2966, +5.3166e-6 over #2957, +6.2177e-6 over #2942).

What changes

1. Joint rank-7 end frames (frame-only). 22 restored helpers end one dimension lower, at five shared rank-7 subspaces (V45 = E_7 ∩ E_42 ∩ E_45 for Conditional κ ≈ 0.0017228163198632: four paired extractions at normal 45 on #2917's words (+3.16e-7 over #2930) #2942's pivots 249/251/265/267; groups A–D with Conditional κ ≈ 0.001721588647: nine additional paired helper extractions #2917's 331/299 and sixteen entering helpers). 22 end frames and 139 gate frames change, each to a hyperplane of the old one; no gate, scalar, entrance or cleanup changes. Every single lowering loses (−14,905 … −58,943 units against break-even); jointly the shared restore partners drop into W once: +22,972 / +42,541 / +42,541 / +17,170 / +17,170.
2. Five more paired extractions. The lowered partners make normals 42 (226, 228, 230) and 7 (363, 395) profitable (+66,903); Conditional κ ≈ 0.001720398337: two-sided helper extraction and charged T74 packing #2908/Conditional κ ≈ 0.001721588647: nine additional paired helper extractions #2917's construction, one declared frame change, 91 private buffers.
3. Jeremy Kothe's fourteen Conditional κ = 0.001723717415070738: fourteen declared gate rewrites (five classes) on #2917's words with #2930's cap-attaining fill #2957 rewrites, composed exactly. All apply with exact preimages after re-addressing (A +261 vs Conditional κ ≈ 0.001721588647: nine additional paired helper extractions #2917); Conditional κ = 0.001723717415070738: fourteen declared gate rewrites (five classes) on #2917's words with #2930's cap-attaining fill #2957's applier is vendored byte-identical; the delta is the same −52,350, additive.

	local profile per call	width inventory	buffers	κ (− 10⁻⁴⁶ − 10⁻⁷⁰)
#2942	{1:2434, 2:632, 3:286, 4:104, 5:26, 8:8}	{7:62, 8:100, 9:218}	86	0.001722816319863214327996
#2966 / #2969	{1:2430, 2:628, 3:282, 4:110, 5:26, 8:8}	same	86	0.001724034272523452177412 / 0.00172403522474810487855
this PR	{1:2445, 2:706, 3:232, 4:108, 5:18, 8:8}	{6:16, 7:52, 8:99, 9:213}	91	0.001729033982646513517717

Fresh 9 → 7 extractions are an exact negative over all 43,435 rank-7 subspaces (a 7-dim subspace lies in exactly three hyperplanes, which must all pair), consistent with @RossRichardson's #2918.

Validation

• Registered (run_registered.py, stdlib, ~1 min): pins; producer reconstruction of every stage word; stage-1 subspace/fit checks; Conditional κ ≈ 0.001720398337: two-sided helper extraction and charged T74 packing #2908's unchanged two-sided certificate at every extraction step; Conditional κ = 0.001718657437166855: dirt-entry rewrite of helpers 530 and 542 on #2802's construction #2833's auditor forward and dual on every stage word (91 restored endpoints at the end); frame accounting; 86 semantic rejection controls across the three stages; owner engine with five controls (six width classes, physical 66,813); the moment auditor re-pinned to Compose normal-45 extraction and fourteen gate rewrites: candidate κ ≈ 0.0017240352247481 #2969 (strict gain); Fractions-only cap certificates of the parent and every stage, the recorded 1.782e-9 literal gap, exact gains over Compose normal-45 extraction and fourteen gate rewrites: candidate κ ≈ 0.0017240352247481 #2969/Conditional κ = 0.001724034272523452: fourteen declared gate rewrites (five classes) on #2942's words and literal allocation #2966/Conditional κ = 0.001723717415070738: fourteen declared gate rewrites (five classes) on #2917's words with #2930's cap-attaining fill #2957/Conditional κ ≈ 0.0017228163198632: four paired extractions at normal 45 on #2917's words (+3.16e-7 over #2930) #2942; stored receipt binding.
• Complete replay (reproduce.py): exact Git exports of Conditional κ ≈ 0.001720398337: two-sided helper extraction and charged T74 packing #2908/Conditional κ ≈ 0.001721588647: nine additional paired helper extractions #2917/Conditional κ ≈ 0.0017228163198632: four paired extractions at normal 45 on #2917's words (+3.16e-7 over #2930) #2942/Conditional κ = 0.001723717415070738: fourteen declared gate rewrites (five classes) on #2917's words with #2930's cap-attaining fill #2957/Conditional κ = 0.001724034272523452: fourteen declared gate rewrites (five classes) on #2942's words and literal allocation #2966/Compose normal-45 extraction and fourteen gate rewrites: candidate κ ≈ 0.0017240352247481 #2969, fresh retained bootstrap, Conditional κ ≈ 0.001721588647: nine additional paired helper extractions #2917's derived source, the new overlay stage rank7-joint-endframes (its rebuild block accepts inherited endpoints lowered to a subspace and warps whose B positions move), 91-buffer adapters whose admission control count is derived from the six width classes (139), fresh native chains for both providers, complete admission against Compose normal-45 extraction and fourteen gate rewrites: candidate κ ≈ 0.0017240352247481 #2969: PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE, PASS_RELEASE.

Scope and next

Conditional finite supplier/outer certificate with all inherited hypotheses; no selected-frontier change, no unconditional theorem, no independent human review. Checked after packaging (README, Open next questions): the lowering/extraction iteration is at a fixed point on this word (only 586/588 keep slack, −3,345 units each; normals 7/42/45/52 have pairing rank 0; the best other rank-8 block is −29,645), other stage-2 orders tie at best (+66,903), and hidden quartets, entering-helper directions, output-carrier renaming and #2957's rewrite classes (5,893 candidates per provider) give no improvement. Open: re-pairing the B phase around the normal-7 pivots, input changes placed later in A, and integral packing at the cap (the remaining 1.8e-9).

Credit: @jeremykothe2 (#2957/#2948/#2966) for the fourteen rewrites of stage 3 and their applier, composed here exactly, as #2966 did with our #2942 words; @Dugongue (#2969) for the comparator composition; Jeremy Diviney (#2908); Mason Hale (#2917); RossRichardson (#2918); Yiyang Lu (#2857/#2848); Tekalign; icekylinx; themilkman216. Marius-Paul Dumitrean, prepared with substantial AI assistance (Claude Code). Apache-2.0.