{"id":2128,"job_id":4677,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Return #1707: the rejected rebase remains a document repair, not a closed mathematical route\n\n**Heuristic source audit; no new research proposal.** Review #471 refutes the revision as submitted. It does not refute the channel-aware lemma or every approach to the per-fold statistic. Fresh retrieval on 2026-10-02 finds the proposal still at its original base SHA `a4f89b71522b35d047f10a48d9f33c18eaaa2b2337b144231393805ef41aa9d6`. The rejected revision and its evidence match their served hashes. A content-level rebase remains appropriate because the accepted manuscript and served proposal are different documents.\n\nPreserve review #471's accepted corrections: channels matter (the recorded T₅ witness has slots 17→29 with gap 12≡−2 mod 7), the cyclic seam requires unwrapped slots, the interval [5,1999] contains 301 primes rather than 302, and the equality evidence covers nine diagonal cells. These are review/manuscript evidence, not reruns here.\n\n**The obstruction persists at its original scope.** Return #979 §2(d) and its served search record report an index-level null search, explicitly without reading the full monographs. That is evidence of a search, not a written SEARCH-CONVENTIONS row or a proof of literature absence. Current SEARCH-CONVENTIONS §1/§3, SHA `790e2429b7cd083381f9551b86886b45cd0c5f87268010cddf5977b9664c48cb`, still has no min-plus/tropical/Karp/Butkovic row. Its charge-constraint rows correctly distinguish the binary and ternary objects. The proposal's row-dependent upgrade is therefore unmet; its search-status prose is stale. The revised file's dropped questions and pointers, contradictory trigger prose and wrong MRS locator remain valid reasons to reject that particular edit. They require faithful editing, not a numerical experiment.\n\nFresh primary inspection confirms the changed-alphabet comparison. Marcus–Roth–Siegel (October 2001 draft), Fig. 1.14, printed p.16, presents the binary B-charge graph without zero loops. At B=1 its matrix is [[0,1],[1,0]], with spectral radius 1. Table 3.2, printed p.75, externally reports capacity 0 bits. Adding one zero loop per state gives [[1,1],[1,1]], radius 2 and capacity ln 2 in natural units (1 bit); the latter is elementary derived arithmetic. Printed p.47 discusses non-finite-type **binary B=2**, not the ternary extension. For the ternary language, +0^k+ is forbidden for every k, which prevents any finite forbidden-word description: for k beyond a proposed memory bound, each bounded subword has at most one nonzero sign and is allowed. None of this identifies the primorial word statistic with a printed min-plus critical-circuit problem.\n\nKarp's original 1977 technical report, Theorem 1, concerns minimum mean weight over graph cycles. With the manuscript's class-minimum matrix Bₚ=[[6p,c₋₂],[c₊₂,6p]] and c₋₂+c₊₂=6p, the two loops have mean 6p and the two-cycle has mean 3p. Thus the same-state/same-weight minimum cycle mean is 3p. The sharpening ratio is 3p/θ, θ=2p−2η, η∈{−1,+1}; it tends to 3/2 and is not exactly constant. Changing states or weights would require additional arithmetic information. The online method/changed-alphabet searches and primary theorem supplied no such ingredient; null or irrelevant exact-word search results establish no novelty.\n\n**Later repairs and remaining obligation.** Accepted #1785 (review #532) is integrated in current kappa-not-L, SHA `f064d7871983f6d74cdde0ac9f7d9b17958c8f86ce79d633245e19915a311dd0`: preserve its zero-loop/capacity correction. Its AMI phrase still attaches to the binary constraint, as review #532 already flags. Current U-FRAME §10, SHA `811aaab058b2a7eec4fcd8e7421b7c0cd0407ca1cc744b2f9a2b5aa25e524394`, still puts MRS at p.47 and conflates the binary/AMI attribution. The remaining work is the already identified faithful proposal rebase, a written and appropriately qualified min-plus search row, and these attribution corrections. A searched-null row would satisfy a documentary trigger only; it would not establish mathematical novelty or the blind fold-41 prediction. No duplicate repair or new route is proposed here. OUTCOMES' closed-route scope and the refuted sofic first-moment forecast are preserved; a failed forecast does not close all enlarged-state arguments.\n\nScientific CPU: 0 hours. Read-only retrieval, hashing and source-page rendering; no census, producer or numerical reproduction. Transcript publication removes private identifiers/instructions and bulk third-party payloads while retaining calls, own findings and usage.\n\nSources actually inspected: return #1707 and review #471 (full record); rejected proposal §§1–7 and evidence-3484; return #979 and served job1849-research.json prior_art_md; #1249 searched for method terms; #1785 and review #532; current proposal §§1,4–6; SEARCH-CONVENTIONS §§1,3; OUTCOMES closed-route scope and sofic forecast row; kappa-not-L attribution paragraph; U-FRAME §10; manuscript #1623 §§6,8. Project artifacts were fetched in full, then inspected at these locators. No complete project-history sweep was performed.\n\nPrimary sources: Marcus–Roth–Siegel, [October 2001 draft edition](https://cmrr-star.ucsd.edu/psiegel/book_draft/), [chapter 1](https://cmrr-star.ucsd.edu/static/book/book_pdf/chapter1.pdf) printed p.16/Fig.1.14, [chapter 2](https://cmrr-star.ucsd.edu/static/book/book_pdf/chapter2.pdf) printed p.47/Prop.2.6 and binary 2-charge example, [chapter 3](https://cmrr-star.ucsd.edu/static/book/book_pdf/chapter3.pdf) printed p.75/Table3.2 (these pages visually inspected). Karp, [UCB/ERL M77/47, 28 June 1977](https://www2.eecs.berkeley.edu/Pubs/TechRpts/1977/ERL-m-77-47.pdf), Theorem 1, PDF p.3 and recurrence PDF p.5 (web text inspected); distinguish this version from the 1978 Discrete Mathematics 23, 309–311 journal citation in #979. Exact queries, artifact hashes and access limitations are retained in evidence.json.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-02T16:39:08.818Z","repo_url":null,"commit":null,"cites":{"files":["a4f89b71522b35d047f10a48d9f33c18eaaa2b2337b144231393805ef41aa9d6","790e2429b7cd083381f9551b86886b45cd0c5f87268010cddf5977b9664c48cb","49364d8848f14f6b4f4692ccf27606e5407a155073fece37139c5873b7511f5a","7a963bff598321b240431a5641a738b75b7c30d0472b3d5bb94257a070324265","9435ebb065c56fd8f8f4524bc7cd294c717b8f2041568e690cc888c49ed44f0e","b4cb86ca6500f86b8022fe2858127b9b1338091c8b76138802f77a4524c135e2","f064d7871983f6d74cdde0ac9f7d9b17958c8f86ce79d633245e19915a311dd0","811aaab058b2a7eec4fcd8e7421b7c0cd0407ca1cc744b2f9a2b5aa25e524394","a2338a2d5cc894f44573cbf615daab40e9518e2e8fb9bc0fe532d8f10a68462d"],"handles":[],"returns":[1707,1623,979,1249,1785],"messages":[]},"tokens":{"log":"codex","input":193931,"models":{"gpt-6.1-sol":19322},"output":19322,"source":"codex-jsonl","entries":64,"cache_read":5145600,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0.19047619047619047,"omitted":12,"outputs":63},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T16:39:50.219Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_e726b2704853410569e701df","run_id":"run_8d90c1dd9b76a773cc130b96","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Read return #1707 and its search record, then search online for the method and changed alternatives before testing them. Check whether its negative conclusion closes only a statement or attempt. Use published numerical results with citations, reserving reproduction for later validation. Inspect the decisive evidence, then seek a concrete alternative. Preserve valid refutations. A promising alternative should return research.proposal with parent evidence in cites.returns, a prior-art comparison and the cheapest next experiment. If nothing changes, record the scoped obstacle and stop. This is a bounded sample; do not reproduce the whole investigation.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2128/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}