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Normalize the zero-retention QQ16 decoder with paid rank-one children - #2707
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…t (answers #1166 c18956869) In the PR1664 scalar common-frame transport model, holding an array at a fixed frame is free (Lemma 2). The moment charges frame catch-up, exactly min over meeting levels of rho_r|L-h_r| + rho_p|L-h_p| + rho_o|L-h_c| (Proposition 3, both directions, consumer explicit). The pinned #1094 template advances every pair through nine 8-coordinate levels (own call or idle sweep), so a record consumed at its family's current frame pays 8 x levels advanced per independent row (Corollary 4). - Law vs conventions: equals (C)'s mass when the family advances one level per lifetime call; 0 for pair-3 Y streams across six calls (S 6, C 48); 48 vs C 24 for a deferred pair-0 record; (S) under-prices PR2540 16 vs 128. - INIT64 + d_A (P_final, P_rank, P4): 3648 units/replica >= 896 no-saving threshold, rejected under either convention; d_A alone 960; cheapest 62 stated captures 1952. Published (C) 3712 = law + d_A,0 lifetime off-by-one. - Gap-1 centre sharing (f0->f2): prior information obstructions (PR2199, #2391/#2461) plus catch-up >= 64 per set; rejected. - QQ16 retained caller: retention row = its 16 H8 (128), proved under rho = 16 and attained; dominated in the moment by pending #2707. - Pricing reproduces the #1166 break-evens 573 (S) / 71 (C) with pinned ceiling.py and independently with Decimal; frame model checks 10,748 + 4,044 instances by BFS and 2,432 by echelon Dijkstra; 12 + 2 controls. No new kappa, no supplier, selected frontier unchanged. Physical storage remains UNKNOWN. Prepared by thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Relabel as a research note (scoped lemma + conditional negative result) and state the stakes, base commit and premises up front. - Route (a): make the observation contract explicit (P_obs) and restate P_rank modulo everything the contract lets the consumer combine. Price the published all-initial variant (#2074 c18950926): 3456 end / 1152 earliest decoder, cheapest-62 1824 / 608 (kappa cap 0.0015234 < selected). Cite the price-gate capture times and check that local calls/bridges force them. Write the per-cut Theorem B argument with its premises. - Route (b): no predecessor information obstruction exists for f0->f2 (PR2199 OQ2 open; #2391/#2461 cover f0->b1 only); the no-gain verdict now rests on catch-up alone, under stated premises. - Route (c): reduced to the one-charge clarification; the #2707 comparison is credited to #2707/PR2681 and the maintainers' review (incorporated on main). - Withdraw the "48 vs (C) 24" lagging-pair example: X_(0,U) is last written at event 6, so the record duplicates an observed row (rho_r = 0). Checked, with a control. - Corollary 4 stated in coordinates with rho_r modulo available rows; hosting checked at all 17 route instants (2,300 distinct slots), and independently by a per-family hosted height replay under both tie conventions. - Frame model: GF(2)^3 now complete (34,454 instances). Independent controls rejected for their stated reasons, count enforced. PRICE-GATE.json storage ceiling reproduced exactly. Credit PR2511, PR2681; full fork SHAs recorded. Prepared by thakrarsagar with substantial AI assistance from Claude (Anthropic, Claude Opus 5.5); reviewed only by AI passes in the same automated loop. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Change and mathematical scope
PR2681's zero-retention QQ16 decoder uses 112 rank-one and 448 rank-eight children. This implements the same complete logical decoder with 336 positive rank-one children and no rank-eight children. At each actual stage-2 port, a source-derived affine map takes F17 to
F16 C_q; paid signed line normalizations enter the common F16 query frame and restore F17 afterward. The new 3,823-event word returns all 224 original arrays in F17, leaves all 224 current borrowed fields untouched, uses 224 owned output banks and at most sixteen owned scratch arrays, and retains no early values across B1.The exact local invoice is 336 H1 children, 672 monomial wrappers, 464 full-cover maps and 25,840 real scalar primitives. Against PR2540's retained-record decoder, the child-moment numerator is
112 - 16*8^(1-a), strictly negative for0 <= a <= 1/16, proved using8^15 > 7^16. This changes the predecessor's child-cost comparison. The extra 192 wrappers, 256 maps and 8,368 scalar allowance remain liabilities: physical hosting, movement, rounded precision and the output consumer are unresolved. This is a finite local construction with an exact phase proof, not a full supplier, optimum or new kappa.Task and overlap
The fixed
portable-replaypicker was preserved; TASK records a changed scope after bounded engineering screens found adjacent acceptance audits covered. The concrete new result is the physical frame lowering of PR2681 atea96706295631be10d92ae149b63c3e24acaeabc; its logical inverse, scalar word and source reconstruction are credited and retained. The advance claim records the bounded question and stopping condition.Construction base: canonical main
1884c509efc004524786e9b7cfcc4aca572316d5, priority revision 5. Precommit canonical main refreshed tob5ea56e0a5ac4552166253b1fa4be0753bb38c30; all five scientific inputs, three provenance inputs, guidance and runner/baseline scripts remain byte-identical. The frozen scientific base and pins are intentionally retained. Overlap combines the dated complete 817-PR/1,279-Discussion snapshot with the newest 100 open PRs and exact source head/comments; it is bounded coverage, not a universal novelty claim.PR2651 coalesces banks while retaining sixteen early values. PR2678 separately prices adapters from the F17 endpoint. PR2692 and PR2628 address errors in the different PR2540 word; their bounds are not transferred here.
Validation
Native Windows CPython 3.12.7 registered replay passes the full primary and four export/integrity groups. Evidence covers both 224-array inverse orders, the intermediate B1 boundary, arbitrary owned dirt, every physical frame/ownership event, 1,210,496 literal character identities, all 114,688 signed native basis columns and all 336 child occurrences. Eleven semantic controls reject missing/wrong normalization, phase shifts, restoration, borrowed writes, dirt, scratch leaks and native wrapper defects. Source bytes are authenticated before execution; Git-free read-only export, complete pin inventory, typed-receipt rejection and exclusive regeneration pass.
A separate OpenAI Codex agent imported no candidate executable: it independently derived all 224 affine shifts from the selected archive/registry, walked all 3,823 physical events, compared the complete logical-event projection with the retained source, and checked the signed kernels and invoice. Its native CPython 3.14.5 optimized primary also passes. The written character proof explicitly extends through every owner coordinate and every payload tensor factor. No hosted CI, selected cold replay, formal-kernel or independent human review is claimed.
Credit
Credit Arham Tahir's PR2681 for the complete logical decoder and retained checker; ywz65's PR2540; Ali Romman and the QQ16 contributors; starship-s, thakrarsagar, Ross Richardson and the retained source/native lineage. Exact predecessor bytes, attribution and notices are retained. New work by ywz65 with substantial OpenAI Codex assistance in derivation, implementation, writing and separate-agent review. Apache-2.0.
Open next questions
The package README records two concrete next obligations: identify a caller with a favorable complete map/wrapper/hosting invoice, and bind precision to this actual changed word. Neither is supplied by the child-moment improvement. Stop at this local module until those contracts are pinned.