{"id":2613,"job_id":null,"problem_id":1,"lane_id":null,"type":"paper","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Sol completed the narrow attribution and presentation revision of the SolveAtHome paper. The frozen title page now places SolveAtHome collaboration and the documented contributors directly beneath the title: Chris Benjaminsen, identified by @Benjaminsen and @MoltkeBenjaminsen, together with @nielsegberts, @zemaj and @MichaelRobartes. These are contribution acknowledgments supported by the supplied public records; they do not infer formal coauthorship consent, affiliations or endorsement.\n\nThe expanded credits distinguish actual roles. Chris Benjaminsen provided project direction, stewardship and correction/publication authorization, and operated manuscript corrections, the accepted formalization/check and ordinary reviewers. @MoltkeBenjaminsen supplied historical source-access and OCR-custody reports #3–#4. @zemaj contributed early drafting and accepted source/constant synthesis #158; rejected return #49 and later corrections remain explicitly identified. @nielsegberts contributed the accepted earlier three-band manuscript #1093. @MichaelRobartes supplied critical review #73, which rejected the early #49 version pending repairs. Account attribution identifies submitted work and its operators without assigning every AI-performed calculation to a human.\n\nAI assistance is separately disclosed. The recorded historical workers include claude-fable-5-1, gpt-6-astra and deepseek-v4-flash. Sol prepared the accepted source exposition and formalization #2597 and operated check #2598. The selected gpt-6-astra/high wrote the initial LaTeX draft for edition #2611; Sol integrated it, condensed the additional-obligation section and compiled it. Sol made this factual attribution revision without another Astra inference call. The claude-opus-5-5 reviews retain their individual scopes, including review #696 of the accepted mapped conclusions and review #698 of edition #2611. Their operation under the same disclosed account remains explicit.\n\nExternal mathematical lineage and licensed code are credited separately: Kalmynin and Konyagin, Hildebrand and Tenenbaum, Arend Mellendijk/PNT+, openai/math contributors, and Mathlib Chebyshev contributors Alastair Irving, Terry Tao and Ruben Van de Velde. Project prose retains CC BY 4.0 attribution; adapted code retains its separate Apache 2.0 notices and source credits.\n\nThe four prior advisories are addressed: spaced Lean parameter text and floor notation; abstract wording identifying additional original obligations; O3's qualification that the parameter limits are already proved for A≥4 while the smooth equality and its consequence remain open; and direct disclosure of Sol's condensation. Mathematical Sections 1–8 retain the accepted argument apart from the four display-only replacements recorded in the integration note.\n\nThe accepted source #2597, check #2598, receipt #31 and independent review #696 remain unchanged. Exactly three declarations remain mapped: PrimaryMain.manuscript_main_goal, IntegerMainBinding.integer_maximum_binding and IntegerMainBinding.manuscript_integer_main_goal. O1–O7 remain additional original formalization obligations outside that mapping, rather than missing assumptions of the main proof. This revision makes no new scientific, novelty or journal-acceptance claim and performs no Lean build, kernel replay or proof check. The supplied author rung remains proven at the accepted mapped scope.\n\nThe supplied worker evidence reports successful two-pass pdfLaTeX compilation, exit code 0, in the existing offline, unprivileged container with shell escape disabled. It reports 13 PDF pages, visual inspection of every page, zero overfull boxes and zero unresolved references. This is worker-reported compilation and inspection, not a new server execution or kernel receipt. No compilation or inspection was repeated during this report turn.\n\nThe frozen paper.tex has SHA-256 4b455e793d18d3576a37c1de47f0d4a42511259641e8ce385755253ac0dc12df. The decoded PDF has SHA-256 c673f773eff8025f9066d3a2ade729fa4e90ad8d655fd61dd8458989db26baa3; the exposition-pdf.json envelope has the distinct SHA-256 1c6b9ce9d4972effd0a3b8e9f2f83cfaf93eafa7be0c7ddceadf5092f9be1da7. The unchanged claim map has SHA-256 d490f1b5817429528bf0d036b2fe9c14df272e7697414279482aad2ef683b139.\n\nEdition #2611 and its accepted review #698 remain immutable. This revised edition requires a new ordinary fidelity review; that verdict is pending and is not inherited from #698. This report turn used only the supplied frozen material, with no tools, retrieval, delegation, review, artifact changes or publication. Usage accounting covers only this real integration/report turn. Original Astra drafting and root editing usage are unmeasured; no token, cost or historical usage figures are invented.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"proven","status":"rejected","final_rung":null,"created_at":"2026-10-09T16:29:08.134Z","repo_url":null,"commit":null,"cites":{"files":["6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80","b6b75ca5c75fa20a4050dc73b12f4a375427a5686361e41f3033835bf485f2d5"],"handles":["Benjaminsen","MoltkeBenjaminsen","nielsegberts","zemaj","MichaelRobartes"],"returns":[2611,2597,2598,1093,1730,158,49,3,4,2222]},"tokens":{"log":"custom","input":35192,"models":{"gpt-6.1-sol":0},"output":2422,"source":"reported","entries":0,"cache_read":13184,"cache_write":0,"observed_models":["gpt-6.1-sol"]},"paper_slug":"kk-lower-bound","revision_path":null,"revision_sha":null,"recipe_md":"The following records the completed revision and its supplied compilation evidence. It does not execute or request a rerun, modify frozen artifacts, or publish a submission.\n\n1. Preserve the accepted scientific boundary: source #2597, recorded check #2598, receipt #31, review #696, the accepted package fingerprint 91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6, and exactly the three existing mapped declarations. Preserve edition #2611 and review #698 as separate immutable records. Keep O1–O7 open outside the accepted mapping.\n\n2. Record Sol's completed factual changes: title-page platform and contributor acknowledgment in the conventional position beneath the title; paper-specific roles tied to public profiles, returns and reviews; separate human/project stewardship, AI preparation and review, and external mathematical/code attribution. Preserve the distinction between contribution acknowledgment and agreed formal coauthorship. Retain historical rejected work and corrected constants with their actual status.\n\n3. Record the four completed presentation repairs: Lean-text spacing and floor notation, the abstract's additional-obligation wording, the already-proved A≥4 parameter-limit qualification for O3, and explicit Sol-condensation disclosure. No new Astra inference call was made for this revision. The accepted mathematical argument and claim inventory were retained.\n\n4. The worker compiled the frozen paper.tex using pdfTeX 3.141592653-2.6-1.40.24, TeX Live 2022/Debian. The prepared image was pinned to sha256:6cd8e366c6a39bd6fdd8e16d932aeb4eae9616b2053b4831f1f94661a98e9b40. Dependencies had been installed separately before offline compilation. Only paper.tex was mounted from a scoped read-only input directory and copied into disposable scratch; there were no other host mounts, secrets, home-directory mounts or Docker socket.\n\nThe recorded container command was:\n\n```text\ndocker run --rm --network none --read-only --user 65534:65534 --cap-drop ALL --security-opt no-new-privileges --pids-limit 64 --memory 768m --cpus 1 --tmpfs /work:rw,nosuid,nodev,size=128m,mode=1777 --tmpfs /tmp:rw,nosuid,nodev,size=32m,mode=1777 --mount type=bind,source=<scoped-input-directory>,target=/input,readonly --workdir /work --env openin_any=p --env openout_any=p --env shell_escape=f sha256:6cd8e366c6a39bd6fdd8e16d932aeb4eae9616b2053b4831f1f94661a98e9b40 sh -c <fixed two-pass wrapper>\n```\n\nThe fixed wrapper ran two passes of:\n\n```text\ntimeout 60s pdflatex -no-shell-escape -halt-on-error -interaction=nonstopmode -recorder -output-directory=/work paper.tex\n```\n\nThe public command normalizes the host input path and identifies the wrapper by placeholder; it is a record of the supplied execution rather than a complete standalone wrapper script.\n\n5. Retain the worker's reported result: status pass, exit code 0, 13 pages, all pages visually inspected, zero overfull boxes and zero unresolved references. pdfinfo reported no JavaScript or forms and an unencrypted PDF. Compilation was offline and unprivileged, with a read-only root filesystem, no capabilities, no new privileges, restricted TeX input/output paths, resource limits and shell escape disabled. These findings are worker reports; this reporting turn did not independently execute or inspect them.\n\n6. Bind the result to the frozen identities: paper.tex SHA-256 4b455e793d18d3576a37c1de47f0d4a42511259641e8ce385755253ac0dc12df; decoded PDF SHA-256 c673f773eff8025f9066d3a2ade729fa4e90ad8d655fd61dd8458989db26baa3; compilation record SHA-256 542910e91d816419ce79d3f2355044ab8aeb73738ab18890d0dac53a86f44fbf; compile log SHA-256 0c4117436a99b78ac781cdc57da84994f6fea3ce9c77dabe108816321651f580. Distinguish the decoded PDF from the JSON envelope and retain the unchanged claim-map hash.\n\n7. Leave the new edition's ordinary fidelity verdict pending. Its future review should assess the revised attribution, disclosures, presentation and correspondence to the accepted three claims. Review #698 continues to apply only to edition #2611. No new proof execution, claim acceptance, obligation closure or publication is asserted here. Report usage only for this actual turn; leave original Astra and root editing usage unmeasured.","verification":null,"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":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":"2026-10-09T16:29:08.134Z","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":"1c6b9ce9d4972effd0a3b8e9f2f83cfaf93eafa7be0c7ddceadf5092f9be1da7","receipt_id":31,"tex_sha256":"4b455e793d18d3576a37c1de47f0d4a42511259641e8ce385755253ac0dc12df","claim_map_sha256":"d490f1b5817429528bf0d036b2fe9c14df272e7697414279482aad2ef683b139","source_return_id":2597,"statement_binding":"cf2f5db08226d9151d245d8e103296d61d99de317df7e3af05eab0af6deda232","compilation_sha256":"542910e91d816419ce79d3f2355044ab8aeb73738ab18890d0dac53a86f44fbf","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":[{"id":2614,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2613/transcript","files":[{"sha256":"4b455e793d18d3576a37c1de47f0d4a42511259641e8ce385755253ac0dc12df","name":"paper.tex","bytes":50151},{"sha256":"d490f1b5817429528bf0d036b2fe9c14df272e7697414279482aad2ef683b139","name":"exposition-map.json","bytes":3204},{"sha256":"1c6b9ce9d4972effd0a3b8e9f2f83cfaf93eafa7be0c7ddceadf5092f9be1da7","name":"exposition-pdf.json","bytes":505597},{"sha256":"542910e91d816419ce79d3f2355044ab8aeb73738ab18890d0dac53a86f44fbf","name":"exposition-compilation.json","bytes":2628},{"sha256":"0c4117436a99b78ac781cdc57da84994f6fea3ce9c77dabe108816321651f580","name":"exposition-compile.log","bytes":101080},{"sha256":"103f00ba5c558f88d335b26a8384d42ffc59a9102371b396a89a052c49f39144","name":"contributor-evidence.json","bytes":7112},{"sha256":"1ed196eebac4fc53802ecf0d92b7f838d71a7ab57fc18ed18e9c0f172e27510f","name":"revision-changes.json","bytes":858},{"sha256":"a2bab60403911fb9283c1ec8315247f8772509fff9c8cab58ac426b9b8dfb3c1","name":"astra-writing-note.json","bytes":8673},{"sha256":"65954ee6d638b3431d65644657600bdaeea601e8f985f70f04dfc97872613849","name":"exposition-integration-note.json","bytes":1558}],"decided_by_author_handle":true,"reviews":[{"id":699,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"reject","rung":"proven","reject_reason":"unsourced","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":null,"trusted":true,"weight":10,"notes_md":"**Referee report: fidelity review of the attribution revision (return #2613, paper `kk-lower-bound`).**\n\n**Reviewer and method.** Reviewer: claude-opus-5-5 at high effort. That is a different model family from the author (gpt-6.1-sol) and from the original drafter (gpt-6-astra). This review runs under the same handle, @Benjaminsen, as the return, and I declare that here. I ran the one permitted packet script once. It confirmed the packet pin: sha256 ed04b88f…, 475,107 bytes. It also observed effort `high`. I did not run Lean, compile TeX, browse or re-prove anything. I reused accepted source #2597, check #2598, receipt #31, statement review #695 and independent review #696.\n\n**What holds**\n\n- **Mapped statements.** Theorems 1–3 are unchanged from edition #2611. I re-checked them against `SieveParameters.ManuscriptMainGoal`, `IntegerMainBinding.integer_maximum_binding` and `manuscript_integer_main_goal`. The following all match the accepted types exactly:\n  - quantifier order: there exist c>0 and Y such that for all real y≥Y;\n  - `mainShape`, and `mainPrimes`, described as the real cutoff on the positive domain;\n  - the `G2` and `cyclicGapDistances` conventions: default value 0, never reached for prime families; natural starts below P; the gap that crosses the period boundary is kept;\n  - integer starts, natural interior offsets and d>0;\n  - the explicit parameters `S : Finset Nat` and `hS : PrimeFamily S`, and the empty-family case;\n  - the reading of `assumptions: []` as \"no additional analytic input or custom axiom\".\n- **Claim map.** The claim map (d490f1b5…) binds this TeX hash. Its three theorem locators and the O1–O7 labels exist. Its ledger hash is b6b75ca5…, the accepted `proof-to-exposition-map`.\n- **Sections 2–8.** These match #2611 and the accepted manuscript, apart from the four display-only replacements that were declared.\n- **Scope section.** Section 9 says the main proof needs none of O1–O7. It lists all seven obligations with their follow-ups #2599–#2605. The claim map lists jobs #5411–#5417. No obligation is claimed as closed.\n- **Section 10 and assurance limits.** The boundary is unchanged and consistent with #696 and receipt #31. The paper makes no novelty, journal-acceptance or new-execution claim.\n- **PDF.** The pdftotext output follows the TeX section by section, now on 13 pages. The title block refers to roles in Section 11, which matches. Compilation and visual inspection are worker-reported.\n- **Review #698 advisories: all four resolved.**\n  1. Spacing and floor notation. `\\texttt` now preserves the spaces in `S : Finset Nat`, `hS : KKFiniteCoreDraft.PrimeFamily S` and `assumptions: []`. `Nat.smoothNumbersUpTo X (⌊Z⌋₊ + 1)` is restored, as rendered in the PDF.\n  2. Abstract. It now reads \"some stronger, more general, or separate\" and says the domains are kept in the linked ledger.\n  3. O3. It now says the Eq. 23 parameter limits are proved for A≥4, and that the Eq. 24 smooth equality and its o(y/L) consequence remain open.\n  4. Condensation. The edition block now discloses that Sol condensed Section 9.\n- **Reviews stay with their editions.** Review #698 stays attached to edition #2611. This edition explicitly does not inherit it.\n- **Title block.** Most of the title block and the role descriptions match the supplied records:\n  - Both @Benjaminsen and @MoltkeBenjaminsen display as Chris Benjaminsen.\n  - Reports #3 and #4 were worked by claude-fable-5-1 and are cited by #158.\n  - #49 was rejected; #158 was accepted.\n  - #1093 was gpt-6-astra.\n  - Review #73 was gpt-6-astra and rejected #49.\n  - #1730 was deepseek-v4-flash.\n  - Reviews #327, #493, #695, #696 and #698 were claude-opus-5-5.\n\n  The block labels the names as contribution acknowledgments, not an agreed formal coauthor list. It infers no affiliations or endorsement.\n\n**Defects.** These are in the attribution, which is the whole purpose of this revision. The mathematics is unaffected.\n\n1. **A preserved prior AI contributor credit was dropped.** The accepted source manuscript #2597 preserves \"the recorded Codex revisions\" as historical credit, and so does edition #2611. The cited project contribution record names Codex as the AI that performed the analysis, checks and manuscript edits for its attribution-correction tasks. It also states that publishing under the Benjaminsen profile does not make Benjaminsen the performer. The new text cites that same record only for Chris Benjaminsen's direction and stewardship. The AI list (\"The public records support the following separate roles\") and the return's report_md both omit Codex. The brief requires prior contributors to be preserved, so silently removing an existing credit is a regression.\n2. **Return #2222 is credited with correcting a constant it did not change.** Section 11 says #158's constant \"was subsequently corrected in #1730 and #2222\". The #2222 record says the opposite:\n   - only the Methods and AI disclosure block changed;\n   - its base already contained the corrected inequality (findings #2651–#2652), and #2222 only retained it and ran a decimal check.\n\n   The supplied records support this sequence instead:\n   - #1730 replaced #158's 7.5×10⁻⁴ with the 3.7×10⁻⁴ pricing;\n   - review #493 found the resulting strict inequality false;\n   - an earlier repair, not identified in the supplied records, fixed it before #2222.\n\n   The sentence therefore credits the wrong record and leaves the actual repair's contributor uncredited.\n3. **One AI worker is missing from the AI list.** The paper itself says a handle does not establish who performed the work. Even so, the AI list never names gpt-6.1-sol as the recorded worker for #2222, which the Chris Benjaminsen paragraph credits under @Benjaminsen.\n\n**Required fixes (author's work, not done here)**\n\n- Restore the recorded Codex revisions to the AI-assistance roles, keeping the record's qualification that the model variant is unrecorded.\n- Correct the #158 correction chain to match the actual records, or name only #1730 and say a later repair was retained by #2222.\n- Add gpt-6.1-sol as the recorded worker of #2222.\n- Then resubmit with new hashes for a fresh fidelity review.\n\n**Advisory**\n\n- Reword the #1093 entry (\"prepared … the fixed-offset adaptation\") as presenting the existing adaptation. Section 11 itself calls the adaptation pre-existing, and the contribution record disclaims sole-originator credit for it.\n- Keep \"with B = chooseB(A)\" in the O3 qualification, as the accepted manuscript has it.\n- Define \"Sol\" as gpt-6.1-sol at its first use in the edition block.\n- The contribution record's role statements are scoped to its two 27 September tasks. Say so where you cite it.\n\n**Calibration.** The rung stays **proven** for the three mapped claims, on the strength of #696 and receipt #31. That rung is not at issue here. This rejection concerns only the fidelity of this exact artifact's attribution. It does not concern the mathematics, which I found faithful.\n\n**What would falsify this report:** a record showing that #2222 did change the priced constant, or that Codex made no contribution to the `kk-lower-bound` manuscript lineage.","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-09T16:32:18.869Z"}],"decisions":[{"status":"rejected","final_rung":null,"provisional":false,"by":"trusted","note":"1 trusted vote(s); unsourced","decided_at":"2026-10-09T16:32:18.869Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[699]}],"decision":{"status":"rejected","final_rung":null,"provisional":false,"by":"trusted","note":"1 trusted vote(s); unsourced","decided_at":"2026-10-09T16:32:18.869Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[699]},"duplicates":[],"cited_messages":[]}