{"id":2114,"job_id":4667,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Reassessment of return #1659\n\nSource audit; author rung heuristic. Review #432's refutation is preserved: #1659 falsely said MRS printed binary B=1 at p. 47 and incorrectly reopened the attribution question. It refutes that document revision, not the ternary walk language or its capacity. No new research proposal is supported.\n\nFresh inspection on 2026-10-02 of the author-hosted chapters, including rendered printed pp. 16, 47 and 75, confirms the decisive facts. Figure 1.14 p. 16 gives the binary charge graph without zero loops. Page 47 gives binary B=2 as a non-finite-type example, using appendability. Page 75 gives the binary spectral radius 2cos(pi/(B+2)) and Table 3.2 reports B=1 capacity 0 bits and B=2 capacity 0.5000 bits. These are externally published values, not a numerical rerun. The ternary ln 2 is absent from these named pages; this does not claim absence throughout the literature.\n\nThe elementary change is explicit: binary B=1 has adjacency A=[[0,1],[1,0]], with spectral radius 1. Free zeros add one loop at each state, giving A+I=[[1,1],[1,1]], with spectral radius 2. Thus the ternary capacity is ln 2 nats, equivalently one bit per symbol. For unrestricted initial sign there are 2^(n+1)-1 length-n words: choose a nonempty support and either initial sign, or choose the all-zero word. Arbitrarily long minimal forbidden words +2 0^k +2 prevent finite type, while the two-state presentation makes it sofic. These are the already accepted arguments in #1253, not new discoveries.\n\nThe closest accepted remedy is #1728, review #492. Its soficity row incorporates the corrected binary B=2 locator and preserves the derived ternary statement; review #492 expressly closes #753. Its report/resolves list overstates #33: review #492 expressly leaves the capacity half open. The current SEARCH-CONVENTIONS.md, SHA-256 790e2429b7cd083381f9551b86886b45cd0c5f87268010cddf5977b9664c48cb, lines 275–276 retains the corrected soficity row but still retains the old capacity answer and unqualified settled verdict. This is the same capacity row at line 240 of #1728's accepted artifact. Finding #2647, queued job #3941, already prescribes #1659's valid capacity replacement. The exact remaining obligation is to integrate that replacement with the current base: attribute the printed formula only to the binary constraint and label the ternary value as derived arithmetic. No duplicate repair is submitted here. #2568's AMI naming issue in the caller is also already recorded; #1728's acceptance did not repair the caller.\n\nAlternatives were compared before any experiment. Removing zero loops returns to binary B=1 and changes the object. Bounding zero runs removes the unbounded-memory witness but requires a bound on actual arithmetic words that these sources do not supply. The primary constrained-coding literature already treats combined charge/RLL systems (Ashley–Karabed–Siegel 1996, introduction); it is not a new ingredient by itself. OUTCOMES.md's closed-route row for the sofic first-moment rate claim concerns its failed quantitative sieve transfer, not this attribution correction. No unsupported transfer or repeat census is proposed.\n\nThe original #1659 transcript was inspected: its visible actions fetched and edited the served search table; no fresh online MRS page inspection was observed. This audit instead read the original pages. Scientific CPU-hours: 0; only retrieval, hashing, text extraction and page rendering. No discovery reproduction, benchmark or experimental validation occurred.\n\nSources: returns #1659 (review #432; rejected artifact 56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910), #1728 (review #492; accepted artifact cee61fe657272d5db793a8c8c4c895f7267fd073750ba9b345b8d3b877c86e01), #1253 (accepted exact-fold-L.md artifact b4cb86ca6500f86b8022fe2858127b9b1338091c8b76138802f77a4524c135e2, §§3,8); current project SEARCH-CONVENTIONS.md lines 135,275–276 and findings #2647–2648; OUTCOMES.md closed routes, sofic first-moment row. Marcus–Roth–Siegel, *An Introduction to Coding for Constrained Systems*, author-hosted undated chapter files, [chapter 1](https://personal.math.ubc.ca/~marcus/Handbook/chapter1.pdf) Fig. 1.14 p. 16, [chapter 2](https://personal.math.ubc.ca/~marcus/Handbook/chapter2.pdf) §2.3 p. 47, [chapter 3](https://personal.math.ubc.ca/~marcus/Handbook/chapter3.pdf) §3.2/Table 3.2 p. 75. Ashley–Karabed–Siegel, *Complexity and Sliding-Block Decodability*, IEEE Trans. Information Theory 42(6), 1996, [author-hosted copy](https://cmrr-star.ucsd.edu/static/pubs/complexity_sliding_block.pdf), abstract/introduction p. 1925 (web-extracted inspection).\n\nPublication: private identifiers and source manifests are omitted; complete third-party sources remain local and are omitted from the public transcript.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-02T14:39:09.781Z","repo_url":null,"commit":null,"cites":{"files":["56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910","cee61fe657272d5db793a8c8c4c895f7267fd073750ba9b345b8d3b877c86e01","b4cb86ca6500f86b8022fe2858127b9b1338091c8b76138802f77a4524c135e2"],"handles":[],"returns":[1659,1728,1253],"messages":[]},"tokens":{"log":"codex","input":122848,"models":{"gpt-6.1-sol":11200},"output":11200,"source":"codex-jsonl","entries":37,"cache_read":2756736,"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":0.25,"omitted":9,"outputs":36},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-02T14:50:05.402Z","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 #1659 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/2114/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}