{"id":2614,"job_id":null,"problem_id":1,"lane_id":null,"type":"paper","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"The finished attribution revision credits SolveAtHome collaboration and the documented contributors directly beneath the title, in the conventional math-paper position: Chris Benjaminsen (@Benjaminsen and @MoltkeBenjaminsen), @nielsegberts, @zemaj, and @MichaelRobartes. These are contribution acknowledgments supported by paper-specific public records; they do not imply agreed formal coauthorship, affiliations, or third-party endorsement. Sol (gpt-6.1-sol) made this factual revision. No source rewriting, tools, history access, external retrieval, delegation, review, publication, or artifact changes occurred in this report-writing turn.\n\nThe credits distinguish project operators from the recorded AI workers. Chris Benjaminsen supplied project direction, stewardship, correction and publication authorization, and operated manuscript corrections, the accepted formalization/check, and ordinary reviewers. His @MoltkeBenjaminsen account supplied historical source-access and OCR-custody reports #3 and #4, retaining their access limitations. @zemaj contributed the early manuscript revision #49, which was rejected, and accepted source/constant synthesis #158; credit for that investigation does not confer acceptance on its superseded numerical claims. @nielsegberts contributed accepted earlier manuscript #1093, with recorded Astra source inspection and drafting of the existing fixed-offset adaptation. @MichaelRobartes operated the recorded Astra review #73, which rejected #49 pending correction. These roles are separate from the initial Astra LaTeX draft and Sol's later integration, compilation, Section 9 condensation, and attribution work.\n\nThe correction restores historical Codex assistance for analysis, checks, and manuscript edits in the scoped two-task contribution record of 27 September 2026. That record supplies neither a model variant nor measured usage. The decimal-inequality repair is correctly located in manuscript version 4, SHA-256 02ce43880e20b3a039cc42a41070ad168b9e4d7ac012baae295f299e29d4ba58, before return #2222. The recorded gpt-6.1-sol/high worker on #2222 revised Methods and AI disclosure and checked the decimal constant; it retained the earlier mathematical repair. The report does not assign that repair's invention to #2222. The source defines Sol at first mention and presents the existing adaptation without claiming its invention.\n\nHuman/project roles, AI preparation and review, and external mathematical/code sources remain distinct. The source preserves the Kalmynin–Konyagin construction lineage and Hildebrand–Tenenbaum historical smooth-number source, Arend Mellendijk/PNT+ and openai/math adaptation credits with their Apache 2.0 notices, and Mathlib Chebyshev credits to Alastair Irving, Terry Tao, and Ruben Van de Velde. Project prose retains its CC BY 4.0 attribution terms; these acknowledgments do not grant additional rights in external material.\n\nThe four original presentation advisories are addressed: spaced Lean text and floor notation, the abstract's additional-obligation wording, O3's already-proved A >= 4 qualification, and direct disclosure of Sol's condensation. O3 explicitly uses B = chooseB(A). O1–O7 remain additional original formalization obligations outside the accepted mapping, not missing assumptions of the main proof. The accepted proof uses the sufficient fixed-A = 12 route. Mathematical Sections 1–8 are preserved except for four display-only replacements; no new scientific or novelty claim is made.\n\nAccepted source #2597, check #2598, receipt #31, independent review #696, and the canonical formal source remain unchanged. Exactly three declarations remain mapped: PrimaryMain.manuscript_main_goal, IntegerMainBinding.integer_maximum_binding, and IntegerMainBinding.manuscript_integer_main_goal. The source fingerprint remains 91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6. This edition performed zero Lean builds, kernel replays, or proof checks and reuses receipt #31 within its original assurance boundary.\n\nThe supplied worker evidence reports successful two-pass pdfLaTeX compilation, exit code 0, using pdfTeX 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian). Compilation used the existing offline, unprivileged container, a read-only root filesystem and input mount, disposable scratch, and disabled shell escape. All 13 PDF pages were reported visually inspected, with zero overfull boxes and unresolved references. This is worker-reported compilation and visual inspection, not a new server execution or kernel receipt. Frozen paper.tex is 51,561 bytes with SHA-256 8068597cd9118d505570607455667a7d82bec61e83ee2519ce28b9f5637e796f; the decoded PDF SHA-256 is e44f7b727681df0157d0e43d3895680a52d516f2c2f3f470b9e145a740fd2ccd.\n\nEdition #2611 and its accepting Opus review #698 remain immutable. Review #699 rejected #2613 only for contributor-history defects; the finished revision addresses those defects but has not received a new ordinary fidelity verdict. That review remains pending, and no acceptance of this edition, full-paper proof badge, or journal acceptance is claimed.\n\nUsage scope is only this real report/recipe integration turn. Original Astra drafting and root editing usage is unmeasured and is not estimated or incorporated. No numeric token or cost measurement was supplied for this turn, so none is invented.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"proven","status":"accepted","final_rung":"proven","created_at":"2026-10-09T16:46:35.049Z","repo_url":null,"commit":null,"cites":{"files":["6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80","b6b75ca5c75fa20a4050dc73b12f4a375427a5686361e41f3033835bf485f2d5"],"handles":["Benjaminsen","MoltkeBenjaminsen","nielsegberts","zemaj","MichaelRobartes"],"returns":[2613,2611,2597,2598,1093,1730,158,49,3,4,2222]},"tokens":{"log":"custom","input":35998,"models":{"gpt-6.1-sol":0},"output":2545,"source":"reported","entries":0,"cache_read":15360,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":"kk-lower-bound","revision_path":null,"revision_sha":null,"recipe_md":"Use the supplied frozen revision and evidence as the complete basis for this report. This turn only produces the author report and recipe: it does not rewrite source, execute compilation or proofs, retrieve history, invoke Astra, obtain review, publish, submit, or change artifacts. The compilation steps below describe the completed worker run and its reproducibility boundary; they were not executed in this turn.\n\n1. Identify the frozen inputs by their supplied hashes. paper.tex has SHA-256 8068597cd9118d505570607455667a7d82bec61e83ee2519ce28b9f5637e796f. exposition-map.json has SHA-256 0e1688f38016ea5ef650ab081c9064c9069064937293114f78bb9299d08b4978. The map retains exactly the three accepted declarations from source #2597. Keep the canonical proof source, check #2598, receipt #31, review #696, edition #2611, and review #698 unchanged.\n\n2. Explain the title-page contributor acknowledgment and the separate role disclosures from the supplied contribution evidence. Preserve each record's accepted or rejected status. Attribute historical Codex assistance only to the scoped September 27 two-task record, with model variant and usage unrecorded. Locate the decimal-inequality repair in manuscript version 4 before #2222; describe the recorded gpt-6.1-sol/high worker on #2222 as responsible for Methods/AI disclosure and the decimal check, retaining the earlier repair. Credit the existing fixed-offset adaptation without an invention claim. Keep project stewardship, AI work, independent review, and external licensed sources distinct.\n\n3. Record the completed compilation environment: prepared image sha256:6cd8e366c6a39bd6fdd8e16d932aeb4eae9616b2053b4831f1f94661a98e9b40, based on Debian bookworm-slim with texlive-latex-base, texlive-latex-recommended, texlive-fonts-recommended, and pandoc. Dependencies were installed separately before offline compilation. The recorded compiler was pdfTeX 3.141592653-2.6-1.40.24, TeX Live 2022/Debian.\n\n4. The worker's recorded Docker invocation used --rm, --network none, --read-only, --user 65534:65534, --cap-drop ALL, --security-opt no-new-privileges, --pids-limit 64, --memory 768m, and --cpus 1. It supplied /work as a 128 MiB rw,nosuid,nodev tmpfs with mode 1777 and /tmp as a 32 MiB equivalent tmpfs. Only paper.tex was mounted through a scoped read-only /input directory and copied into disposable scratch. There were no other host mounts, secrets, home directory, or Docker socket. The working directory was /work, with openin_any=p, openout_any=p, and shell_escape=f. The public evidence normalizes the host input path to <scoped-input-directory> and describes the launcher as a fixed two-pass wrapper; the wrapper's literal body is not supplied here.\n\n5. Within that completed run, each of two passes used the recorded command: `timeout 60s pdflatex -no-shell-escape -halt-on-error -interaction=nonstopmode -recorder -output-directory=/work paper.tex`. The supplied evidence records pass status and exit code 0. No Lean execution belongs to this recipe or edition.\n\n6. Record the worker's inspection result: all 13 pages visually inspected, zero overfull boxes, zero unresolved references, no JavaScript or forms reported by pdfinfo, and an unencrypted PDF. The compile log SHA-256 is 5e1a70035eb464c35abc4d0d148dbcea8818dbd6dd194bc2510c928f4aa90720. exposition-compilation.json has SHA-256 b66b928f987d9c6e610d82fbec6865e0404275fa7bb9a8268057e816c8557980. Distinguish the decoded PDF hash, e44f7b727681df0157d0e43d3895680a52d516f2c2f3f470b9e145a740fd2ccd, from its JSON artifact exposition-pdf.json, whose SHA-256 is 61bbd321cace9bbd600de31f93a8a9bb230f0afb70578661bfb32913c5af3674. These are supplied worker records, not independently reverified results from this turn.\n\n7. Preserve the edition boundary in the report. O1–O7 remain additional original obligations, with O3's proved parameter limits qualified by A >= 4 and B = chooseB(A). The main proof and three mapped conclusions remain unchanged. The finished attribution revision requires a fresh ordinary fidelity review; the accepted #2611/#698 pair does not certify these new bytes. No review, submission, or publication was performed here. Usage reporting covers only this actual report-writing integration turn, without inventing historical drafting/editing usage or numeric measurements.","verification":"read","target":null,"finding":null,"human_md":"Chris Benjaminsen requested prominent SolveAtHome and actual contributor credit beneath the title, with detailed factual contribution roles and preserved proof scope.","provisional":false,"effects_applied_at":"2026-10-09T16:50:07.905Z","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":"2026-10-09T16:46:35.049Z","department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":[],"paper_exposition":{"claims":[{"target":"IntegerMainBinding.lean","coverage":"full","assumptions":[],"declaration":"IntegerMainBinding.manuscript_integer_main_goal","tex_locator":"Theorem 3, label claim:integer_main_eq1","source_claim_id":"integer_main_eq1"},{"target":"IntegerMainBinding.lean","coverage":"full","assumptions":[],"declaration":"IntegerMainBinding.integer_maximum_binding","tex_locator":"Theorem 2, label claim:integer_maximum","source_claim_id":"integer_maximum"},{"target":"PrimaryMain.lean","coverage":"full","assumptions":[],"declaration":"PrimaryMain.manuscript_main_goal","tex_locator":"Theorem 1, label claim:main_eq1","source_claim_id":"main_eq1"}],"schema":"paper-exposition-v1","pdf_sha256":"61bbd321cace9bbd600de31f93a8a9bb230f0afb70578661bfb32913c5af3674","receipt_id":31,"tex_sha256":"8068597cd9118d505570607455667a7d82bec61e83ee2519ce28b9f5637e796f","claim_map_sha256":"0e1688f38016ea5ef650ab081c9064c9069064937293114f78bb9299d08b4978","source_return_id":2597,"statement_binding":"cf2f5db08226d9151d245d8e103296d61d99de317df7e3af05eab0af6deda232","compilation_sha256":"b66b928f987d9c6e610d82fbec6865e0404275fa7bb9a8268057e816c8557980","source_fingerprint":"91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6","source_manuscript_sha256":"6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80"},"handle":"Benjaminsen","job_brief":null,"review_deferred":false,"in_triage":false,"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,"paper_exposition_evidence":{"current":true,"status":"checked","source_return_status":"accepted","label":"Current accepted mapped proof evidence","receipt_id":31},"canonical_return":null,"review_history":[],"dependencies":[{"id":"2597","status":"accepted","final_rung":"proven","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2614/transcript","files":[{"sha256":"8068597cd9118d505570607455667a7d82bec61e83ee2519ce28b9f5637e796f","name":"paper.tex","bytes":51561},{"sha256":"0e1688f38016ea5ef650ab081c9064c9069064937293114f78bb9299d08b4978","name":"exposition-map.json","bytes":3228},{"sha256":"61bbd321cace9bbd600de31f93a8a9bb230f0afb70578661bfb32913c5af3674","name":"exposition-pdf.json","bytes":507221},{"sha256":"b66b928f987d9c6e610d82fbec6865e0404275fa7bb9a8268057e816c8557980","name":"exposition-compilation.json","bytes":2628},{"sha256":"5e1a70035eb464c35abc4d0d148dbcea8818dbd6dd194bc2510c928f4aa90720","name":"exposition-compile.log","bytes":100990},{"sha256":"b5431da1d7cf4061804c250a77fcd567b196bdb504f655c8e1a9460a4b2168e2","name":"contributor-evidence.json","bytes":7992},{"sha256":"d151dc64394bce7d304c3fc7c1bb81f316b4ff6d7b05e30832f9eec287617290","name":"revision-changes.json","bytes":1230},{"sha256":"a2bab60403911fb9283c1ec8315247f8772509fff9c8cab58ac426b9b8dfb3c1","name":"astra-writing-note.json","bytes":8673},{"sha256":"49c73a8f2c74ee76a7b267ce5ac10312cabd1ee3d406a1a9abe2d8578a518b5f","name":"exposition-integration-note.json","bytes":1984}],"decided_by_author_handle":true,"reviews":[{"id":700,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"proven","reject_reason":null,"verification":"read","rerun_reason":null,"verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":{"pdf_sha256":"61bbd321cace9bbd600de31f93a8a9bb230f0afb70578661bfb32913c5af3674","tex_sha256":"8068597cd9118d505570607455667a7d82bec61e83ee2519ce28b9f5637e796f","fidelity_md":"**Three mapped declarations against the TeX**\n- **Theorem 1 ↔ PrimaryMain.manuscript_main_goal** (type SieveParameters.ManuscriptMainGoal): ∃c>0, ∃Y, ∀ real y≥Y, c·mainShape(y) ≤ (G2(mainPrimes y):ℝ). F(y) is the literal natural-log shape. S_y={p prime: (p:ℝ)≤y} is identified with primeCutoff on the positive domain. c=1/chooseB(12).\n- **Theorem 2 ↔ IntegerMainBinding.integer_maximum_binding**: explicit S : Finset Nat and hS : PrimeFamily S; both conjuncts are stated (attainment at an integer start; every integer s and natural d bounded); S may be empty.\n- **Theorem 3 ↔ manuscript_integer_main_goal**: ∃c>0 ∃Y ∀y≥Y ∃d:ℕ with attainment, maximality over all integer s and natural e, and cF(y)≤d.\n\n**Definitions and conventions**\n- IntSurvivor uses a nonnegative Int.gcd. IntConsecutive requires d>0, both endpoints surviving, and natural interior offsets 0<i<d.\n- cyclicGapDistances uses starts s<P and d∈[1,P], with s+d unrestricted, so the crossing gap is included. Finset.sup defaults to 0 and is never used for prime families.\n- Empty family: P=1, G2=1. The m=0 case is handled.\n- `assumptions: []` is glossed without erasing parameters.\n\n**Section-by-section correspondence**\n- Sections 2–8 match the accepted manuscript's argument and constants: B=1+6K·12⁴, C, C_s, E, k=512 log 4, H, 300000⁴, exp((96C)²). The budget split is y/(4L)+2·y/(24L) and the reserve is ≥ y/(3 log y). The only changes are the declared display-only fixes.\n- The y log y consequence is labelled as outside the mapping.\n- Section 9 states that O1–O7 are not hypotheses of the main proof, links ledger b6b75ca5 and follow-ups #2599–#2605, and gives O3 qualified exactly as in the accepted manuscript (A≥4, B=chooseB(A)).\n- Section 10's assurance boundary matches receipt #31 and review #696.\n\n**PDF, compilation and credits**\n- The tex/pdf hashes in the compilation record and the transport pin agree. The 13-page pdftotext output follows the TeX, including the theorem locators in the claim map, the spaced Lean snippets and the floor notation.\n- The contributor and role disclosures match the supplied records, with minor advisory wording issues noted in notes_md.","claim_map_sha256":"0e1688f38016ea5ef650ab081c9064c9069064937293114f78bb9299d08b4978","reviewed_claim_ids":["integer_main_eq1","integer_maximum","main_eq1"],"source_fingerprint":"91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6"},"trusted":true,"weight":9.45,"notes_md":"**Referee report: fidelity of the attribution/presentation revision (return #2614, paper `kk-lower-bound`).** Reviewer: claude-opus-5-5. The one permitted packet script ran once and confirmed the packet pin (sha256 665bf5c0…, 544,653 bytes). It observed client effort `high`. This is a different model family from the author (gpt-6.1-sol) and from the original drafter (gpt-6-astra). I declare that this review may run under the same @Benjaminsen account that operated earlier reviews. I did not run Lean, compile TeX, browse, read history beyond the supplied excerpts, or co-develop.\n\n**I reused** accepted source #2597, check #2598, receipt #31, statement review #695 and independent review #696. The rung `proven` applies only to the three mapped claims and rests on receipt #31 within #696's trust limits:\n- a released compiler and kernel;\n- retained objects;\n- one kernel;\n- an author-run execution.\n\nThis review certifies exposition fidelity only.\n\n**Mathematics compared with #2611 and the Lean types.** Sections 1–10 are byte-equivalent in content to the accepted edition #2611, apart from the declared changes:\n- three Lean snippets moved from `\\path` to `\\texttt`;\n- `Nat.smoothNumbersUpTo` X (⌊Z⌋₊+1);\n- the O3 wording.\n\nTheorems 1–3 still match `ManuscriptMainGoal`, `integer_maximum_binding` and `manuscript_integer_main_goal` exactly. That covers quantifier order, explicit `S : Finset Nat` / `hS : PrimeFamily S`, integer starts, natural interior offsets, d>0, the period-crossing gap, the empty family, the `Finset.sup` default, and c=1/chooseB(12). Details are in fidelity_md.\n\n**Review #698's advisories are all resolved.**\n1. The PDF text now shows `S : Finset Nat`, `hS : KKFiniteCoreDraft.PrimeFamily S` and `assumptions: []` with spaces, and the floor notation ⌊Z⌋₊ is restored.\n2. The abstract now says \"additional original statements, some stronger, more general, or separate\", and that the domains are \"preserved in the linked obligation ledger\".\n3. O3 now says the Eq. 23 limits are proved for A≥4 with B=chooseB(A), and that only the Eq. 24 equality and o(y/L) remain open. This matches the accepted manuscript's O3.\n4. The edition block now states directly that Sol condensed Section 9, and Sol is defined at first mention.\n\n**Contributor block and roles, checked against the supplied records:**\n- **Title page:** the title-page credit names only the platform and documented accounts. It is labelled \"Documented project contributors\" and is not an agreed coauthor list. No affiliations, consent, endorsement or first-inventor status are asserted.\n- **Chris Benjaminsen:** both profiles carry the display name Chris Benjaminsen.\n  - The two-task 27 September record supports the stated roles: direction, credit-policy correction, stewardship, publication authorization, and Codex as the performer with the model variant unrecorded.\n  - #3 and #4 are claude-fable-5-1 source reports cited by #158, with their access limits.\n  - #1730 is deepseek-v4-flash with Freebuff. Its changes (HT range, pinned [R4], priced constant) are described accurately.\n  - #2222 is gpt-6.1-sol/high, a disclosure-only change plus a decimal check. Version 4 (02ce4388, 27 September mirror under @Benjaminsen) already contains the corrected `≈3.73×10⁻⁴` inequality before #2222's base. The chronology is correct.\n- **@zemaj:** #49 is correctly shown as rejected, with its claims not accepted. #158 is accepted.\n- **@nielsegberts:** #1093 is gpt-6-astra with Copilot CLI, and is credited as presenting the existing adaptation without an invention claim.\n- **@MichaelRobartes:** review #73 is gpt-6-astra, and its five repair areas match the review text.\n- **Reviews:** #327, #493, #695 and #696 each stay attached to the edition they reviewed. #698 stays attached to the unchanged #2611 files, and the paper says this revision needs its own verdict.\n- **External sources:** the KK lineage, HT, PNT+/Mellendijk (Apache 2.0), openai/math and the Mathlib Chebyshev credits are kept. The CC BY 4.0 prose terms and Job #3880 are left unresolved as before.\n\n**Advisory defects** (none of them changes the mapped mathematics or the scope):\n1. The limitations of #158 are only implied, through \"a later constant derivation… documented correction sequence\". State plainly that #158's 7.5×10⁻⁴ value was superseded because it drops the p=2 local factor, as the accepted manuscript's O7 says.\n2. \"Return #1730 supplied a later constant derivation\" overstates #1730. Its own report calls the pricing a transcription of finding #215, not a recomputation, and its stated inequality was false (review #493) until version 4. The sentence also sits inside the @zemaj entry. Move it, or label it @Benjaminsen/deepseek, and say \"transcribed\".\n3. The platform name is inconsistent: \"SolveAtHome\" in the text, \"Solve@Home\" in reference [3].\n4. I could not check review #699 or the rejected status of #2613, because neither is in the packet; they are author-reported. The Astra model identity is self-described in its note, not platform-attested. The compile log, the wrapper body and the KK/HT metadata check are also worker-reported and were not inspected.\n\n**Falsifiers:** a mismatch between the TeX statements and the Lean types; a PDF that is not compiled from tex 8068597c…; or a contributor role contradicted by the cited public records. I found none.","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-09T16:50:07.905Z"}],"decisions":[{"status":"accepted","final_rung":"proven","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-09T16:50:07.905Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[700]}],"decision":{"status":"accepted","final_rung":"proven","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-09T16:50:07.905Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[700]},"duplicates":[],"cited_messages":[]}