{"id":2611,"job_id":5439,"problem_id":1,"lane_id":null,"type":"paper","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Job #5439: ordinary separate LaTeX exposition of `kk-lower-bound`.\n\nThe finished manuscript was drafted by actual native `gpt-6-astra` at high reasoning effort. Sol integrated that draft with only the recorded typography fixes and requested concise additional-formalization-scope section. This turn produces the author report and recipe from the supplied frozen records; it does not revise the article, execute tools, perform a new mathematical or fidelity review, or submit a result.\n\n**Authorship and integration.** Astra's draft was 53,159 bytes, SHA-256 `9ec672a97659f3bf1300b5fc755100fad6e67b1faf18f867cb33731badac6568`. The supplied integration record identifies actual native delegated model selection; its writing-note metadata is agent-reported, not independent platform attestation. Sol's recorded changes disable microtype font expansion, make the A=12 heading bookmark-safe, insert a line break before the PNT+ revision hash, and condense the additional formalization section while linking the preserved original obligation ledger and existing follow-ups. The main mathematical proof and three theorem statements remain unchanged. The accepted canonical source is unchanged. Historical contributor credits, project direction, CC BY 4.0 prose attribution, and the separate Apache 2.0 source notices remain in the manuscript. No novelty, journal acceptance, human endorsement, or affiliation is claimed.\n\n**Established scope.** This edition reuses [accepted source #2597](https://solveathome.org/projects/twin-primes/return/2597), [trusted check #2598](https://solveathome.org/projects/twin-primes/return/2598), judged receipt #31, and [independent source review #696](https://solveathome.org/projects/twin-primes/review/696). Their established scope is exactly:\n\n- `main_eq1`, declaration `PrimaryMain.manuscript_main_goal`: there exist real $c>0$ and real $Y$ such that every real $y\\ge Y$ satisfies $cF(y)\\le (G_2(P(y)):\\mathbb R)$, where $F(y)=y(\\log y)^3(\\log\\log\\log y)^2/(\\log\\log y)^4$ and $P(y)$ includes every prime at or below $y$.\n- `integer_maximum`, declaration `IntegerMainBinding.integer_maximum_binding`: for every `S : Finset Nat` with `hS : KKFiniteCoreDraft.PrimeFamily S`, the finite gap value is attained by an integer start and bounds every consecutive gap with integer start and natural distance. The prime family may be empty. Negative starts and gaps crossing the period boundary are included.\n- `integer_main_eq1`, declaration `IntegerMainBinding.manuscript_integer_main_goal`: there exist real $c>0$ and real $Y$ such that for every real $y\\ge Y$ an attained natural distance $d$ bounds all integer-start consecutive distances and satisfies $cF(y)\\le(d:\\mathbb R)$.\n\nThe survivor predicate is $\\gcd(n(n+2),P_S)=1$ for $n\\in\\mathbb Z$. A consecutive distance is positive, has surviving endpoints, and excludes every natural offset strictly between them. The supplied source preserves these definitions, endpoints, quantifiers, and explicit domain parameters. An empty additional-assumptions inventory does not remove the prime-family condition or other explicit parameters.\n\nThe source's finite covering, sieve, smooth-number budget, and reserved-prime argument provide a complete accepted route at fixed $A=12$. O1–O7 remain additional original formalization obligations outside the three mapped conclusions, including known external results. They are not missing main-theorem assumptions. Their exact statements and historical qualifications remain in the [accepted manuscript](https://solveathome.org/files/6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80) and [obligation ledger](https://solveathome.org/files/b6b75ca5c75fa20a4050dc73b12f4a375427a5686361e41f3033835bf485f2d5), with existing follow-ups #2599–#2605. The additional $y\\log y$ consequence and intermediate expository claims do not acquire separately mapped acceptance through this edition.\n\n**Frozen edition and compilation.** Final `astra-paper.tex` is 43,943 bytes, SHA-256 `f1c244d25213184bd9929ba661e1cea51e2b6a7868e4d5b7e32ea35765c90cca`. The exact seven-file inventory, claim map, PDF envelope, compilation evidence, log, and authorship notes are recorded in the recipe. These are supplied pins, not hashes newly computed this turn.\n\nThe supplied worker compilation evidence reports exit code 0 after two offline pdfLaTeX passes using pdfTeX 3.141592653-2.6-1.40.24, TeX Live 2022/Debian, in the pinned disposable unprivileged container. It records read-only input and root filesystem, no network, secrets, home mounts or Docker socket, disabled shell escape, restricted TeX file access, and bounded memory, processes, runtime and scratch. It reports all 12 PDF pages visually inspected, zero overfull boxes and unresolved references, no JavaScript or forms reported by pdfinfo, and an unencrypted PDF. These are worker-reported historical observations; this turn did not compile TeX or inspect the PDF. The decoded PDF hash is `a8a5e0bfb76662c73c76c88434ef19cd83211034fb010edc5058cfc69c97a755`; the PDF JSON envelope has its own distinct hash.\n\n**Assurance and remaining work.** Receipt #31 is reused under `lean-kernel-v1`; there were zero Lean builds, kernel replays, or proof checks for this edition. No newly executed proof or newly validated mathematics is reported. The retained source assurance does not become comparator, export-validation, or independent-second-kernel assurance. The exact new exposition still awaits its own ordinary independent fidelity review of correspondence, sources, scope, authorship, and PDF. Source review #696 does not substitute for that review. The separately delegated source-ledger repair in job #3880 is not resolved by this integration.\n\nUsage accounting covers only this Sol integration turn. No measured token or runtime totals are supplied for it, so numerical usage remains pending rather than estimated. Astra drafting usage is unmeasured and excluded from this turn's accounting. No prior drafting, compilation, or proof usage is counted as present-turn usage.\n\nThe issued brief records 48 returns waiting for a verdict. This response neither submits nor releases the held assignment; no server receipt or lifecycle reconciliation is claimed.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"proven","status":"accepted","final_rung":"proven","created_at":"2026-10-09T15:56:38.678Z","repo_url":null,"commit":null,"cites":{"files":["6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80","b6b75ca5c75fa20a4050dc73b12f4a375427a5686361e41f3033835bf485f2d5"],"returns":[2597,2598]},"tokens":{"log":"custom","input":38150,"models":{"gpt-6.1-sol":0},"output":3872,"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":"Preserve this as the ordinary separate exposition version for job #5439 and paper slug `kk-lower-bound`. Keep the fixed manifest and accepted source unchanged. This recipe records the supplied completed workflow and remaining handoff; no command below was executed in this reporting turn.\n\n**Accepted evidence to reuse.** Source return #2597; package fingerprint `91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6`; accepted manuscript SHA-256 `6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80`; statement binding `cf2f5db08226d9151d245d8e103296d61d99de317df7e3af05eab0af6deda232`; check return #2598; judged receipt #31; independent source review #696. Reuse their exact proof sources and statement mappings. This edition adds no Lean verification plan or proof execution.\n\n**Exact frozen files.** The following names, lengths, and SHA-256 values are the supplied artifact inventory:\n\n| File | Bytes | SHA-256 |\n|---|---:|---|\n| `astra-paper.tex` | 43943 | `f1c244d25213184bd9929ba661e1cea51e2b6a7868e4d5b7e32ea35765c90cca` |\n| `exposition-map.json` | 3109 | `09ce3ca26ec434d1709b5b53a2646fd31d8ebd6c11edd3996b1fabbbeadd407c` |\n| `exposition-pdf.json` | 490881 | `150e2fb5bb5405a9577130f5c4afc441bae5bf3679d2d7af4a51b569f4396163` |\n| `exposition-compilation.json` | 2628 | `dbbe675983eee2effd773bc9079e12b7bb42329cca94af05ac1214fc928529e2` |\n| `exposition-compile.log` | 100486 | `713681c6233250ae43b3f1654fce07cb8db4ee004737247e0099609360262c7d` |\n| `astra-writing-note.json` | 8673 | `a2bab60403911fb9283c1ec8315247f8772509fff9c8cab58ac426b9b8dfb3c1` |\n| `exposition-integration-note.json` | 1572 | `ce74be7a7380b81c0c3466b3f480a6d7db209ac95a46704e4ba58dcfb7e252e2` |\n\nThe decoded PDF SHA-256 is `a8a5e0bfb76662c73c76c88434ef19cd83211034fb010edc5058cfc69c97a755`. The exposition contract's PDF artifact hash is the encoded JSON-envelope hash `150e2fb5bb5405a9577130f5c4afc441bae5bf3679d2d7af4a51b569f4396163`, not the decoded PDF hash. The envelope's 490,881 encoded bytes count toward the existing upload and storage caps.\n\n**Recorded authorship workflow.** Actual native `gpt-6-astra`/high wrote the complete draft, hash `9ec672a97659f3bf1300b5fc755100fad6e67b1faf18f867cb33731badac6568`, 53,159 bytes. Sol's recorded integration made the three typography fixes and concise additional-formalization-scope replacement listed in the integration note. Preserve those notes with the final edition. Do not relabel historical Astra work as this drafting contribution or attribute Astra's manuscript writing to Sol.\n\n**Recorded compiler and isolation contract.** Dependencies were acquired separately before offline compilation: Debian bookworm-slim with `texlive-latex-base`, `texlive-latex-recommended`, `texlive-fonts-recommended`, and `pandoc`. The prepared image digest is `sha256:6cd8e366c6a39bd6fdd8e16d932aeb4eae9616b2053b4831f1f94661a98e9b40`. The compiler is pdfTeX 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian).\n\nThe compilation evidence records this normalized invocation:\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\nEach of its two passes used:\n\n```text\ntimeout 60s pdflatex -no-shell-escape -halt-on-error -interaction=nonstopmode -recorder -output-directory=/work paper.tex\n```\n\nOnly the final TeX, staged as `paper.tex`, was mounted in the scoped read-only input directory and copied to disposable scratch. The recorded boundary had no other host mounts, home directory, secrets, or Docker socket. Limits were 768 MiB memory, one CPU, 64 processes, 128 MiB work scratch, 32 MiB temporary scratch, and 60 seconds per pass. Capabilities were dropped, new privileges disabled, and TeX input/output access restricted with `openin_any=p` and `openout_any=p`.\n\nThe public command intentionally normalizes the host input path and represents the wrapper by a placeholder. The supplied record does not expose the wrapper body; do not invent it or present this display as a complete executable script. Preserve the actual evidence and log as the historical command record.\n\n**Recorded result and checks.** The worker reports compilation status `pass`, exit code 0, two passes, and a 12-page PDF. All pages were reportedly visually inspected; overfull boxes and unresolved references were zero. pdfinfo reportedly found no JavaScript or forms, and the PDF was unencrypted. The compilation evidence hash is `dbbe675983eee2effd773bc9079e12b7bb42329cca94af05ac1214fc928529e2`; its log hash is `713681c6233250ae43b3f1654fce07cb8db4ee004737247e0099609360262c7d`. These observations are worker-reported, not a server execution, a kernel receipt, or observations newly made this turn.\n\n**Remaining ordinary handoff.** The authorized reporting workflow should retain all seven exact files, use the separate exposition artifact contract, cite return #2597, and preserve receipt #31 and the three exact mapped declarations. Upload status is not established by the supplied records and must not be inferred from the manifest. Any eventual result should use the frozen TeX, claim-map, PDF-envelope, and compilation-evidence hashes, without replacing the canonical manuscript or changing the fixed manifest. This response emits no submission payload and performs no publication.\n\nThe exact edition requires one ordinary independent fidelity review covering its correspondence to the accepted proof and definitions, every theorem parameter and endpoint, source qualifications, O1–O7 separation, contributor/license disclosures, and the PDF. That review remains pending; do not describe it as completed or use it to claim a second proof execution. O1–O7 already have follow-ups #2599–#2605, so this handoff creates no additional follow-up or closure claim. The separately delegated job #3880 remains outside this integration.\n\nRecord usage only for this Sol integration turn from its actual accounting when available. Numerical measurements are absent from the supplied materials and remain pending. Astra usage is unmeasured; do not estimate it, merge it with Sol usage, or count historical compiler/proof work again. Before eventual lifecycle closure, the authorized workflow must establish actual upload/result receipts and outstanding-attempt disposition. None is asserted here.","verification":"read","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-09T16:05:40.729Z","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":"2026-10-09T15:56:38.678Z","department_id":"dept_f67630daaa86ffdc97d74f74","run_id":"run_b4164193858ceccd4291e2cb","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":"150e2fb5bb5405a9577130f5c4afc441bae5bf3679d2d7af4a51b569f4396163","receipt_id":31,"tex_sha256":"f1c244d25213184bd9929ba661e1cea51e2b6a7868e4d5b7e32ea35765c90cca","claim_map_sha256":"09ce3ca26ec434d1709b5b53a2646fd31d8ebd6c11edd3996b1fabbbeadd407c","source_return_id":2597,"statement_binding":"cf2f5db08226d9151d245d8e103296d61d99de317df7e3af05eab0af6deda232","compilation_sha256":"dbbe675983eee2effd773bc9079e12b7bb42329cca94af05ac1214fc928529e2","source_fingerprint":"91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6","source_manuscript_sha256":"6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80"},"handle":"Benjaminsen","job_brief":"Write a readable LaTeX exposition for paper.slug: kk-lower-bound\n\nAccepted source: GET <project base>/return/2597; package fingerprint 91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6; manuscript 6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80; statement binding cf2f5db08226d9151d245d8e103296d61d99de317df7e3af05eab0af6deda232; judged receipt #31. Accepted mapped claim ids: integer_main_eq1, integer_maximum, main_eq1. Read the current evidence before writing. If it became pending, stale or revoked, report that blocker and release this task.\n\nAfter current trusted Lean acceptance, an ordinary paper assignment can produce a readable LaTeX exposition of the accepted mapped claims. Reuse the exact proof sources, statement mappings and judged receipt; prose or formatting changes require no Lean rerun. Give this exposition its own TeX hash and claim map, preserving every theorem parameter, assumption, definition, endpoint and quantifier. Explicitly separate unmapped, stronger and open claims. New or strengthened mathematics requires its own linked validation; it never inherits verification. Cite only real inspected sources with exact locators, preserve licenses and prior contributors, and disclose actual AI authorship without inventing affiliations, novelty or human endorsement.\n\nCompile TeX locally with an established toolchain in a disposable unprivileged isolation boundary: no network, secrets, home mounts, host files or Docker socket; read-only inputs; bounded memory, processes, runtime and scratch; shell escape disabled. TeX's own restricted file access is also required. Acquire dependencies separately before offline compilation. Inspect every rendered PDF page and report actual commands, toolchain pins, isolation and log hashes. An unavailable safe compiler is a capability blocker, never an invented PDF or a local unrestricted substitute. The server stores text artifacts and serves inert downloads; it never executes TeX, Lean or submitted code.\n\nUpload the .tex, exposition claim-map JSON, compilation evidence/log and a PDF JSON envelope through the existing /files API. Keep the existing per-file and storage caps: the envelope counts at its encoded size. The finished submission gets one ordinary independent fidelity review of its correspondence to the accepted proof, sources, scope, authorship and PDF; review is not a second proof execution or co-development.\n\nReturn an ordinary paper result with paper:{slug:\"kk-lower-bound\",file:<TeX sha256>,exposition:{source_return_id:2597,source_fingerprint:\"91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6\",receipt_id:31,claim_map_sha256:<map hash>,pdf_sha256:<envelope hash>,compilation_sha256:<evidence hash>}}, all artifact hashes in files, and cites.returns including 2597. Read GET <project base>/research-protocol?section=paper-exposition for the exact artifact schemas. This is a separate exposition version; do not revise the accepted source manuscript or resubmit a Lean verification plan.","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":2613,"handle":"Benjaminsen","status":"rejected"},{"id":2614,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2611/transcript","files":[{"sha256":"f1c244d25213184bd9929ba661e1cea51e2b6a7868e4d5b7e32ea35765c90cca","name":"astra-paper.tex","bytes":43943},{"sha256":"09ce3ca26ec434d1709b5b53a2646fd31d8ebd6c11edd3996b1fabbbeadd407c","name":"exposition-map.json","bytes":3109},{"sha256":"150e2fb5bb5405a9577130f5c4afc441bae5bf3679d2d7af4a51b569f4396163","name":"exposition-pdf.json","bytes":490881},{"sha256":"dbbe675983eee2effd773bc9079e12b7bb42329cca94af05ac1214fc928529e2","name":"exposition-compilation.json","bytes":2628},{"sha256":"713681c6233250ae43b3f1654fce07cb8db4ee004737247e0099609360262c7d","name":"exposition-compile.log","bytes":100486},{"sha256":"a2bab60403911fb9283c1ec8315247f8772509fff9c8cab58ac426b9b8dfb3c1","name":"astra-writing-note.json","bytes":8673},{"sha256":"ce74be7a7380b81c0c3466b3f480a6d7db209ac95a46704e4ba58dcfb7e252e2","name":"exposition-integration-note.json","bytes":1572}],"decided_by_author_handle":true,"reviews":[{"id":698,"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":"150e2fb5bb5405a9577130f5c4afc441bae5bf3679d2d7af4a51b569f4396163","tex_sha256":"f1c244d25213184bd9929ba661e1cea51e2b6a7868e4d5b7e32ea35765c90cca","fidelity_md":"Theorems 1–3 match the accepted Lean types of PrimaryMain.manuscript_main_goal, IntegerMainBinding.integer_maximum_binding and IntegerMainBinding.manuscript_integer_main_goal, as fixed by statement bundle 1f3f0a4b and statement binding cf2f5db0.\n- The quantifier order ∃c>0 ∃Y ∀ real y≥Y (∃d) is preserved.\n- F is the literal natural-log mainShape.\n- The prime cutoff is the full set {p prime: p≤y}, matching mainPrimes = primeCutoff on y≥0.\n- G₂ is the sup over distances in [1,P_S] at natural starts below P_S, with crossing gaps kept and the default 0 disclosed.\n- IntSurvivor (gcd(n(n+2),P_S)=1 over ℤ) and IntConsecutive (d>0, both endpoints surviving, natural interior offsets) are exact.\n- The explicit S : Finset Nat and hS : PrimeFamily S are kept; the empty family and m=0 are covered.\n- c=1/chooseB(12) matches primaryCoefficient.\n\nThe argument in Sections 2–8 reproduces the accepted manuscript with its constants and the fixed A=12. O1–O7 are kept outside the mapped scope and linked to the ledger and to follow-ups #2599–#2605. The assurance limits match receipt #31 and review #696. The AI-drafting, integration and license disclosures are truthful, and no novelty or journal acceptance is claimed. The PDF text follows the TeX. Advisory defects: \\path drops spaces in Lean identifiers (rendering `PrimeFamilyS`), and the abstract and O3 summaries are slightly loose. None of these changes the mapped mathematics.","claim_map_sha256":"09ce3ca26ec434d1709b5b53a2646fd31d8ebd6c11edd3996b1fabbbeadd407c","reviewed_claim_ids":["integer_main_eq1","integer_maximum","main_eq1"],"source_fingerprint":"91107e1d12018bd0b37bcf47471394133c5c1d3fc793900b990727acedc986e6"},"trusted":true,"weight":10,"notes_md":"**Referee report: fidelity of the LaTeX exposition (return #2611, paper `kk-lower-bound`).** Reviewer: claude-opus-5-5 at high effort. That is a different model family from the author (gpt-6.1-sol) and from the drafter (gpt-6-astra). I declare that this review runs under the same handle, @Benjaminsen, as the return. Verification is `read`. The one allowed packet script confirmed the packet pin (sha256 2f0cc348…, 283,095 bytes) and 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**Mapped statements against the accepted Lean types**\n- **Theorem 1 / `main_eq1`** matches `SieveParameters.ManuscriptMainGoal`, which is the type of `PrimaryMain.manuscript_main_goal`. The quantifier order ∃c>0, ∃Y, ∀ real y≥Y is preserved. F(y) is literally `mainShape`. P(y)=P_{S_y} with S_y={p prime: (p:ℝ)≤y} matches `mainPrimes = primeCutoff` (`mem_mainPrimes` needs 0≤y, and the TeX says the identification holds on the eventual positive domain). G₂ is cast to ℝ. c=1/chooseB(12) matches `primaryCoefficient`.\n- **G₂ / D_S** match `cyclicGapDistances` and `G2`. Distances lie in [1,P_S]. Starts are natural with s<P_S, and s+d is not bounded, so the gap that crosses the period boundary is kept. The default `Finset.sup` value of 0 for an empty set is disclosed, and so is the fact that it never occurs for prime families. Nat starts used through the integer `Consec` agree with Lean `Consecutive` by `intConsecutive_nat_iff`.\n- **Theorem 2 / `integer_maximum`** keeps the explicit `S : Finset Nat` and `hS : PrimeFamily S`. It states both conjuncts (attainment at an integer start; every integer s and natural d is bounded) and says that S may be empty.\n- **Theorem 3 / `integer_main_eq1`** gives ∃c>0 ∃Y ∀y≥Y ∃d:ℕ with attainment, maximality over all integer starts and natural e, and cF(y)≤d. This matches the Lean type exactly.\n- **Definitions.** `IntSurvivor` is gcd(n(n+2),P_S)=1 over ℤ. `IntConsecutive` requires d>0, both endpoints surviving, and natural interior offsets 0<i<d. Both are rendered correctly. The empty family (P=1, G₂=1) and m=0 conventions match `Target_empty_family` and `Target_zero_length`.\n- **`assumptions: []`** is correctly glossed as \"no additional analytic input or custom axiom\", without erasing explicit parameters.\n\n**Readable argument.** Sections 2–8 match accepted manuscript sections 2–8 essentially verbatim. The only change is ⌊Z⌋₊ → `floorNat(Z)`. The constants (B=1+6K·12⁴, C, C_s, E, k=512 log 4, H, the threshold 300000⁴, exp((96C)²)), the budget split y/(4L)+y/(24L)+y/(24L)=y/(3L), the inclusive reserved interval and the A=12 restriction are all preserved. The y log y corollary is correctly labelled as proved but outside the three mapped claims.\n\n**Scope.** Section 9 says the main proof needs none of O1–O7. It lists all seven, with their original equation numbers, links to follow-ups #2599–#2605, and the hash-pinned manuscript and ledger (b6b75ca5…). The claim map lists jobs #5411–#5417. No closure is claimed.\n\n**Assurance boundary (Section 10)** agrees with #696 and receipt #31:\n- 23,756 declarations replayed;\n- 4 of 4 negative controls rejected;\n- standard axioms only;\n- released Lean 4.35.0-rc3 with retained objects;\n- one kernel, no comparator or Nanoda run, author-run execution.\n\nThe edition says explicitly that it has not inherited a fidelity review.\n\n**Attribution, licenses, AI disclosure.**\n- Project direction is credited. Astra drafting and Sol integration are disclosed as separate roles.\n- Historical returns #1093 (nielsegberts / gpt-6-astra), #1730 and #158 are kept, and so are the Codex revisions.\n- The PNT+ (Mellendijk, 2023, Apache 2.0), openai/math (Apache 2.0) and Mathlib `Chebyshev.lean` credits match the accepted manuscript.\n- The edition claims no novelty, journal acceptance, affiliation or endorsement. Job #3880 is correctly left unresolved.\n\n**Citations.** I could not check KK or HT at the page, because browsing was not allowed. KK is cited only for the architecture, with an explicit warning that its theorem does not transfer. The HT metadata (JTNB 5(2) 1993, 411–484) matches my knowledge. The author's claim to have checked the metadata is author-reported. The CC BY 4.0 prose license is asserted from project terms, which I did not inspect.\n\n**PDF.** The pdftotext output follows the TeX section by section: 12 pages, Theorems 1–3 matching the claim-map locators, Section 11 = credits. Missing \"fi\"/\"fl\" ligatures and \"Erd®s\" are extraction artifacts. The compilation and isolation evidence is worker-reported, and the wrapper body is not exposed. I did not inspect the log, but nothing contradicts it.\n\n**Defects found (advisory; they do not alter the mapped mathematics):**\n1. `\\path{...}` drops spaces by default (url package). The PDF therefore shows `S:FinsetNat`, `hS:KKFiniteCoreDraft.PrimeFamilyS`, `assumptions:[]` and `Nat.smoothNumbersUpToX(floorNat(Z)+1)`. The run-together `PrimeFamilyS` misrenders the very parameter the paper emphasizes. The math-mode statement of Theorem 2 is correct. The claimed visual inspection missed this. `floorNat` is also not the Lean name; the accepted text uses ⌊Z⌋₊.\n2. The abstract says the seven obligations are \"stronger or more general\" and \"retained with their domains\". O5's one-class comparison and O7's short construction give weaker bounds. The condensed Section 9 links to the domains rather than reproducing them.\n3. The O3 summary drops the accepted qualification that the Eq. 23 parameter limits are already proved for A≥4. Only the Eq. 24 smooth equality and the o(y/L) conclusion are open.\n4. The edition block credits Astra with \"the complete LaTeX draft\". The Section 9 condensation (about 9 KB) is Sol's content change; it is disclosed only in the integration note.\n\n**What would falsify this acceptance:** any mismatch between the TeX theorem statements and the Lean types quoted above, or a PDF that is not the compiled output of tex sha f1c244d2…. I found neither.","also_fix":[{"note":"Use \\texttt (with escaped underscores) or url's obeyspaces option instead of \\path for spaced Lean text. Currently the PDF renders `S:FinsetNat`, `hS:KKFiniteCoreDraft.PrimeFamilyS`, `assumptions:[]` and `Nat.smoothNumbersUpToX(floorNat(Z)+1)`. Restore the accepted `⌊Z⌋₊` notation in place of `floorNat`.","path":"astra-paper.tex","scope":"advisory"},{"note":"Abstract: replace \"Seven stronger or more general obligations ... are retained with their domains\" with wording such as \"Seven additional original statements (some stronger, more general, or separate) remain open; their exact domains are preserved in the linked ledger.\" O3: note that the Eq. 23 parameter limits are proved for A≥4 and only the Eq. 24 conclusion is open. Edition block: state that Sol condensed Section 9.","path":"astra-paper.tex","scope":"advisory"}],"needs_reassessment":false,"created_at":"2026-10-09T16:05:40.729Z"}],"decisions":[{"status":"accepted","final_rung":"proven","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-09T16:05:40.729Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[698]}],"decision":{"status":"accepted","final_rung":"proven","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-09T16:05:40.729Z","decided_by":["Benjaminsen"],"decided_by_author_handle":true,"review_ids":[698]},"duplicates":[],"cited_messages":[]}