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Prove sharp P104 temporal rank bound and correction-budget obstruction - #2082
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Code-disjoint check of the finite premises behind #2082, #2090, #2113 and #2127 (and the budget line summarized in #2133), from the hash-pinned PR1972 witness only. Every checked premise reproduces exactly: - frozen chronology: max-flow = min vertex cut = 8, certified by weak duality (feasible flow plus separating cut); extremal min cuts are Q7..Q0 (cuts 1570-1597) and C#0..C#7 after their descents (2464-2524); the #2090 query cut and cones at cut 2429 reproduce; - union graph: the eight private descents separate; each reopens 52; - frame graph: 222/222 over 444 frames; - exact replay: rank 8, M^2 = 13M, (I-M)(I-M/12) = I, minor 1/256; - budget-line constants re-derived from the witness (328/9 slack). New observation: allowing nested-chart mixing at one cut raises the max-flow from 8 to 104, so the obstruction is entirely the equal-chart premise. No new kappa, supplier or selected-frontier change. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A2DF8QgsTwrE4t3793qQUx
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The native P104
G/2channel leavesI-G/2unimplemented. This contribution proves that no linear redesign using the frozen chronological common-frame access can complete identity transfer: a sharp eight-register cut limits source-to-target rank to8D, versus the required104D.The new package
research/p104-temporal-cut-obstruction/adds a written proof, exact source-bound certificate and independently implemented forward/reverse checkers. It saturates all common-frame communication at all 4,059 event boundaries, so the result covers arbitrary coefficients, extra same-frame gates and helper/target mixing, beyond the predecessor's particular scalar word. The originalG/2channel attains the bound.For corrections inserted between original events that restore every frame before the next original event, retain the original transports and add no storage lifetimes, the cut proves at least 96 additional positive-rank transports per call. Under the explicitly conditional fully hosted four-pair, nine-stage coverage contract, only
328/9rank units per call remain; the completed zero-saving moment is at least 7659/7592 > 1, independently of idle packing. As a concrete accounting illustration,208 added ranks/call imply a zero-saving moment of7785/7592 > 1under this contract; a fixed-coverage calculator cannot treat the added cost as free displacement of idle mass without a separate realization argument. Persistent changed-frame buffers, retiming, replacement/fusion of existing transports, new storage and changed global coverage are outside that corollary.This resolves a defined part of the revision-4
p104-side-correctionpriority and identifies the access/scheduling premise a successful completion must change. No new kappa, supplier admission, selected-frontier change or universal P104 barrier.Validation:
G²=26G,(I-G/2)⁻¹=I-G/24, and all 280 arbitrary-input columns including dirty restoration.Reproduce:
Started from canonical main
564148b82ae9df72163f22106f15e73efca8aff2. Exact source pins, overlap coverage, environment and open next questions are in the package. Native Clifford recompilation, chronological owner construction, all-size/precision/outer transfer and the selected full cold replay are not newly established or run; selected and frozen predecessor files are untouched.Credit: Rohan Arun / #1972 (scalar/frame channel), Chafik Boukhalfa / #1991 (native realization), Adam Gall / #1940 (schedule), with P104 geometry/decoder and coverage predecessors credited in the README. The concurrent final-query-cut correction claim is acknowledged; this is a complementary structural obstruction, not a duplicate construction or audit of unpublished work.
Prepared for David Arias with substantial OpenAI Codex assistance. Apache-2.0.