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Connect current CRT numerical offsets to the physical Beneš row query - #5496
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…ared ROM-bank storage (no new κ) Independently audits the multi-target loop of PR #5496's current-row CRT join. Its published complete joined fixtures have one active target. Conditional on the inherited numerical Entry (PR #5353, #5219, #5053) and ROM producer (PR #5092) theorems, which are hypotheses here, the loop is proved to compose across several right targets: idle records are still consumed, each active target gets its own current offset, padded coordinates are queried, one physical ROM bank is reused at growing and shrinking widths, and all owned work retires. No defect was found. A new exact count of the producer's 52-role bank for a nonempty active set, with guide width P and largest active width H, is B(P,H) = 5P*2^H*(H^2+3H+1) + 2^H*(4H-1) + 48P + 2H + 104 cells; each role is nondecreasing in width at fixed P. At P=11 the h=3 -> h=2 fixture retains 9,086 cells, while billing only the last width counts 3,084 and omits 6,002. Nine caller cases with 13 complete producer calls and twelve control groups pass against an independent CRT/Beneš oracle. Upstream input production, the paid next-row source update, three-epoch key transport and all-size acceptance stay open; no program, invoice, selected record or κ changes. Adds research/crt-multitarget-row-audit/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Jur4aiU6BBSmBiaRjkbECf
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The current CRT RowEntry produced numerical offsets but its caller comparison still used a host logical row query. This package connects that actual offset stream to the unchanged encoded Beneš ROM producer, queries its original physical ROM backing at the current padded coordinate, and returns the micro-row coordinate stream. It disposes of the selected ROM, unused all-layer output, headers and numerical context with explicit local time and retained-backing bounds.
The source-relative proof covers the admitted mixed-width domain, W=P compatibility, successive-right-modulus offsets, current-coordinate countdown, and full successful ownership restoration. Peer review repaired a linear topology-membership scan and a fixed interpreter watchdog. The complete small h=2 pipeline passes normal/optimized and Git-free replay, including the padded-coordinate case, two idle rows, invalid-left identity and four semantic/cleanup fault controls. Exact source and typed-receipt corruption controls reject; committed bytes, source ancestry and36-file export integrity pass.
The separately budgeted four-axis h=4 whole-ROM attempt timed out at180seconds without a completed receipt; ATTEMPT.json records its exact attempted source hashes. No completed h=4 result is claimed. Separate small row invocations use harness input serialization. Full three-epoch key transport, uninterrupted physical whole-level execution, binary numerical lowering and outer multiplication remain open. No selected-frontier or kappa change.
JoyboyBrian, with substantial OpenAI Codex assistance. Retains Ali Romman's RowEntry and all pinned CRT/Beneš/arena predecessor attribution. Claim: #4709 (comment)