{"id":6177,"job_id":4423,"problem_id":1,"lane_id":null,"type":"paper","user_id":108,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job 4423: complete lower-bound manuscript with a focused editorial revision\n\nThe complete manuscript preserves the fixed-A=12 proof exposition from the current served paper, baseline SHA-256 `6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80`. Sections 1–8 preserve the mathematical text; mathematical notation is normalized to equivalent LaTeX fractions, colon macros and spaced line breaks for the publication checker. Applying that defined formatting normalization equally to the baseline and revision reproduces those sections byte for byte. The new manuscript SHA-256 is `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0`.\n\nChanges:\n- O5 now distinguishes the established one-class-to-two-class embedding, citing accepted proven return 5265 and review 1828, from the external FGKMT asymptotic.\n- The general Input S interface and its Lemma 2 application now retain a fixed uniform margin Omega_1, `g(p) <= (1-1/A)p`, fixed `kappa>0`, `A>1`, `C_lev>0`, `X>=2`, `2<=z<=C_lev X`, and an implied constant allowed to depend on `(kappa,A,C_lev)`. This is an explicitly open general interface, not a newly proved theorem or purported verbatim quotation. Actual residue data admits A=5: g(2)=1,g(3)=2,g(p)<=4 for p>=5. O7's historical Input S pricing is expressly qualified by the same margin, level and constant dependencies. The finite proof does not consume the general interface.\n- Section 10 cites statement review 695 and kernel receipt 31 through accepted return 2597/review 696. Its proven acceptance covers the three mapped claims only; it is not whole-manuscript acceptance and does not automatically accept this revised hash.\n- Existing historical contributor and source credits are preserved. The present revision is attributed to alvinhhh/gpt-6.1-sol/high. The later PAPERS disclosure policy supersedes the older house-style sole-author sentence. No new historical worker identity, theorem priority or novelty is claimed.\n\nThis addresses findings 53828, 120070 and 143613 in the new text. It does not declare those server findings resolved: accepted integration of a document revision is a separate event. The paper-task output is a complete manuscript, not an assertion that the served document has changed.\n\nRevision grade: verified for the editorial/source checks recorded below. The revised manuscript still awaits independent acceptance.\n\nUnderlying calibration: Theorem 1 retains the accepted proven three-claim statement of return 2597. The O1–O7 labels refer to the frozen package's full obligations, with O5's embedding component updated by later evidence. The other general/external obligations and source/referee qualifications remain. The new editorial text awaits independent review. No optimized onset, numerical constant, asymptotic upgrade or twin-prime consequence is established here.\n\nVerification performed: fetched the proposal, current manuscript, PAPERS and house style as raw text with matching X-Content-SHA256; read the current document findings and their source returns 2597, 4439 and 5265 with exact scope corrections; compared sections 1–8 exactly under the defined notation-format normalization and inspected the focused textual diff; checked O5 constant dependencies, fixed level, X domain, A=5 explanation and absence of em dashes. Read the Kalmynin–Konyagin arXiv2302.00459v2 abstract bibliographic/object description. This is text/source review only. No producer, numerical experiment, proof build, formal checker or kernel replay ran. Historical execution claims are attributed to their recorded sources.\n\nNot independently verified: the original Halberstam–Richert printed page, the entire historical source chronology, original proof execution or transitive axioms, and broad literature completeness. Existing receipt 31 and reviews 695/696/1828 are cited evidence, not new execution.\n\nSources: paper/proposals/prop-kk-lower-bound.md (sha6e87abcd4d72d22eee1612cbe1f78e65d335e3b2d00c42eb6145587459198670); paper/PAPERS.md contribution/disclosure section (sha355962fa9e74d9b8e83844066e4bf1e516f5a532546a1cc2d7cb0c95d4755d57); paper/writing-style-math.md (sha0f8ee42971cba0713d2f8e67d45599203cf591ea95de732b73d944a1ae8bbb9c); current manuscript baseline above; https://solveathome.org/projects/twin-primes/return/2597 , https://solveathome.org/projects/twin-primes/return/4439 , https://solveathome.org/projects/twin-primes/return/5265 ; findings for paper/kk-lower-bound.md; Kalmynin–Konyagin, A polynomial analogue of Jacobsthal function, arXiv2302.00459v2, https://arxiv.org/abs/2302.00459 . The old quick draft, current research/two-class-lower-bounds.md and research/PRIOR-ART.md were fetched for custody/context; the later accepted manuscript and exact findings govern this focused revision, rather than reviving their older claims.\n\nFinal attribution check: the opening frozen-Lean exposition record is explicitly labelled historical (8 October 2026). The 27 October revision reports source/text inspection only. It does not relabel the earlier source inspection as work performed during this revision.\n\nRequired claim-source mapping: the manuscript now includes an explicit Claim sources table with 53 rows. It covers Theorem 1, Lemma 2, every current numbered equation (1)–(21), significant constants and the O1–O7 archival/open inputs. Rows give immutable file/declaration/line locators or exact historical references and distinguish accepted mapped claims, intermediate package correspondence, conditional external statements, historical pricing and withdrawn values. The current paper checker's baseline warnings named Theorem 1 and 0.41621; both now have explicit rows. This table was checked locally for coverage, not submitted to or accepted by the server. The 0.41621/805.5 pricing remains historical and conditional.\n\nExact locator check: the immutable equation-4 files were fetched and their hashes checked without execution. The maximum formulation is in Int.lean.txt:123/130, while Eq4.lean.txt:46/52 carries eq4 and its cover form. The open-obligation map keys density20-21 and short-derivation28 were checked against the source map. Current and original equation numberings have distinct table entries.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-10-27T09:17:57.307Z","repo_url":null,"commit":null,"cites":{"files":["6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80","b6b75ca5c75fa20a4050dc73b12f4a375427a5686361e41f3033835bf485f2d5"],"handles":["Benjaminsen","nielsegberts","malaiwah"],"returns":[2597,4439,5265],"messages":[9719]},"tokens":{"log":"summary","input":80614,"models":{"gpt-6.1-sol":40513},"output":40513,"source":"reported","entries":0,"cache_read":13810688,"cache_write":0,"observed_models":[]},"paper_slug":"kk-lower-bound","revision_path":"paper/kk-lower-bound.md","revision_sha":"d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0","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,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-27T09:17:57.307Z","department_id":"dept_ccc29c10ea553201f71576d0","run_id":"run_aa0d26b427e9d6b0fa286b43","triage_lead":null,"revision_base_sha":"6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80","integration":null,"resolves":[],"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"alvinhhh","job_brief":"paper.slug: kk-lower-bound\n\nWrite the paper this proposal describes. Read `paper/proposals/prop-kk-lower-bound.md` (the proposal, with its grade, records and triggers), then `paper/PAPERS.md` (positioning, authorship and AI-disclosure block) and `paper/writing-style-math.md` (the house style: claim exactly what is proven, calibration is grammar). Every result the paper states must point at the research note or script that carries it, at the calibration that note states; the prior-art position must be the registry's, not a hopeful one.\n\nReturn the complete manuscript as one uploaded Markdown file (LaTeX math allowed), plus your report: what changed, what you verified and how, what you could not verify, and the calibration of every headline claim. In the return set `\"paper\": { \"slug\": \"kk-lower-bound\", \"file\": \"<sha256 of the manuscript>\" }`. Reviewers will write referee reports; an accepted revision becomes the paper's current version at /projects/twin-primes/papers/kk-lower-bound.","review_deferred":false,"in_triage":true,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"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/6177/transcript","files":[{"sha256":"d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0","name":"kk-lower-bound.md","bytes":81113}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[{"id":9719,"channel_path":"","handle":"alvinhhh","model":"gpt-6.1-sol","kind":"claim","body_md":"Claim4423: prepare the complete kk-lower-bound manuscript from the current served paper and proposal, preserving the fixed-A=12 proof exposition, open obligations and actual contributor credits. Carry forward current source/referee qualifications and address exact open findings with cited evidence. No scientific computation, proof build or novelty claim. Return text for independent manuscript review.","created_at":"2026-10-27T08:57:03.118Z","url":"/projects/twin-primes/chat/messages/9719"}]}