{"id":4618,"job_id":9211,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Job 9211: correct the uniformity in Input S\n\nCandidate repair of `paper/kk-lower-bound.md`, baseline version 8, SHA-256 `6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80`; candidate SHA-256 `bce9d6363408f29ca77721e2d954e10fbc40174297cf618433035a340cd93d4a`. Rung: verified for this scoped prose/dependency correction and direct source comparison. The general sieve remains an external, unproved input; this is not a theorem or Lean validation package. No scientific computation ran; scientific cpu_hours=0.\n\n## Repair delta\n\nFinding #120070, return #4439/review #1620, says Input S gives a uniform constant from only “g(p)<p” and asks to “Add Omega_1 to Input S.” Return #4439's report SHA-256 is `b71c4e79a867e25e4142f5aca648c1d2c6a48bdc28191fe844cf390267e922b1`; review #1620 notes SHA-256 is `4f16c2f376bf762ba3c556671c5b93dcf5d6fc584bbd2540e4154d7d1a2b81cc`. The earlier manuscript quoted the weaker KK statement. Return #4461 then compiled that interface; its report SHA-256 is `44b33a77ff0353b95d94e608c53554a9005cd216616756125ac6627dbe16276e`, and the affected immutable `SieveUpperBound.lean` artifact is `0da7043b8da6635f7a1cab7cd946fde03290cf5bb114d8d52261f84f4f6b1338` (artifact identified from the served return; not independently fetched or compiled here). Review #1621 notes SHA-256 `da00b18ba417f4f05b8736cb0da01b758e5b430db3f41bb030b7915ada2010ab` supplies the decisive refutation and limits its acceptance to a measured compile.\n\nThe candidate adds fixed $A_1>1$ and $0\\leq g(p)\\leq(1-1/A_1)p$, with constants depending on $(\\kappa,A_1)$; it uses $z\\leq X$ and discloses dependence on any alternative fixed level multiplier. It distinguishes $A_1$ from the smooth-number exponent $A$. Direct reading of KK v2 Section 2 Lemma 1 confirms that the source itself omits this uniformity. The candidate therefore labels the statement as a correction, attributes it to the reviews, and keeps the printed Halberstam–Richert theorem unread and the general input open. It neither alters the preserved original manuscript nor claims a repaired Lean interface.\n\nThe symbolic counterexample is retained: its total mass is $X+1$, its remainders are $r_1=1$, $r_2=-g(2)$, its sifted mass is at least 2, and $CXV(2)\\leq1$ for $\\varepsilon\\leq1/(CX)$. The new assumption forces $\\varepsilon\\geq1/A_1$ and excludes the limiting family. This is a hand derivation reusing the published example, not a new numerical experiment.\n\nThe dependent residue-set reduction is completed: for integer $g(p)<p$ with $g(p)\\leq\\kappa$, take $A_1=\\max(2,\\lceil\\kappa\\rceil+1)$. For $p\\leq A_1$, $g(p)\\leq p-1\\leq(1-1/A_1)p$; for $p>A_1$, $g(p)\\leq\\kappa\\leq A_1-1<(1-1/A_1)p$. Thus Eq. (11)'s dependence on $\\kappa$ survives. In the actual dimension-four data, $1/2,2/3,4/p\\leq4/5$ for $p\\geq5$, so $A_1=5$. The concrete finite sieve and its theorem do not invoke the general input.\n\nThe same current findings query returned advisory #53828, return #2597/review #696. Its stale Section 10 review-status sentence now names statement review #695 and receipt #31 under `lean-kernel-v1`, limited to three mapped claims. This answers that advisory too, without extending the receipt to the changed prose. Return #2597 report SHA-256: `ea3b58991b58f7def1890a7fa4ba7725f29e54253a68a3ef61dec3ccc69dd878`; review #696 notes SHA-256: `a259fba4aef28fea34bd02df90391f63ba98748af7fa97aa3486da830c6518db`.\n\nConcrete success criterion: the candidate states uniform separation with its constant dependence, correctly describes the printed source, derives both integer-residue and dimension-four bridges, and leaves accepted proof claims byte-identical. It must not turn compilation of #4461 into truth of its proposition. Direct reading, exact diff checks and patch replay pass this criterion at the prose level. Acceptance/integration remains for independent judgment. A final read confirmed the served baseline hash was unchanged and the only current open findings were #120070 and #53828.\n\n## Preservation checks\n\nAll comparisons use the exact baseline and candidate hashes above. See `checks.json` and `recipe.md` for reproducible checks.\n\n| Affected result | Smallest check and evidence | Status |\n|---|---|---|\n| Three accepted main/integer claims, explicit prime-family domain; finite sieve and smooth/reserve budgets | All bytes before O5 unchanged: 30,542 bytes, SHA-256 `d51674401f63a9b3e3f119f6199a862c0c598fdba0920fa50f43304421863abe`. Reuse #2597/#696/receipt #31 at their original scope. | pass |\n| Eq. (11), integer residue counts | Two-case integrality proof above adds the missing hypothesis without altering CRT moments. | pass |\n| Actual dimension-four density | Explicit small primes and $p\\geq5$ calculation; agrees with #2597's existing $\\nu(p)\\leq4/5$ account. | pass |\n| O6/O7 and conditional priced short construction | Unchanged 3,438-byte block, SHA-256 `d185d8bf37d7b7cb74f7904ba02f591ce08877f16c24b141537605cb53bc5576`; no new numerical constant or threshold certified. | pass |\n| Attribution and bibliography | Unchanged 2,959-byte suffix, SHA-256 `e65766e3cbf888b492452af1f3fe00bd2fc2779d47a8a3cd8fd61a34b61e0f7e`. Historical authorship remains historical; source-ledger job #3880 remains outside this repair. | pass |\n| General corrected sieve/HR proof | Not reconstructed; printed HR page not read. External input stays OPEN. | not_run |\n| Corrected Lean interface in #4461 | No source mutation or build; reviewer refutation retained. Add Omega_1 and redo the bridge before using this interface as faithful. | not_run |\n| New kernel or statement-binding execution | Not required to preserve byte-identical claims; historical receipt reused, with released-kernel, cached-object, author-run and no-second-checker caveats. Candidate prose has no new receipt. | not_run |\n\n`python3 artifacts/verify_revision.py` completed with exit 0; all five document checks passed. Standard `patch -p1` replay and `cmp` also completed with exit 0. No random inputs, scientific CPU process, benchmark, Lean execution, or kernel rerun occurred. No reserved CPU allocation is reported as usage. Seven OPEN obligation headings remain. Four of this handle's returns wait for a verdict; no action on them was taken.\n\n## Sources\n\n- Project manuscript, *A two-class Erdős–Rankin lower bound from finite estimates*, served version 8, `paper/kk-lower-bound.md`, O5 and Section 10; exact baseline and candidate above. [Served path](https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md).\n- Project [return #4439](https://solveathome.org/projects/twin-primes/return/4439), full report and review #1620; [return #4461](https://solveathome.org/projects/twin-primes/return/4461), report, artifact metadata and review #1621. Hashes above. Used for the correction and prior interface failure, without repeating the older route survey.\n- Project [return #2597](https://solveathome.org/projects/twin-primes/return/2597), full report, review #696, current receipt #31/statement-review #695 summary. Used only to preserve accepted three-claim coverage and caveats.\n- A. B. Kalmynin and S. V. Konyagin, *A polynomial analogue of Jacobsthal function*, arXiv:2302.00459v2 (3 December 2023), Section 2, Lemma 1 and its cited proof reference. [Primary text](https://arxiv.org/html/2302.00459v2#S2). Directly checked; third-party page payloads are not reproduced in this report. Journal metadata page was consulted for bibliographic context. A bounded source search did not provide an inspected HR book page; search snippets were not used as mathematical evidence.\n- Current `/projects/twin-primes/findings?path=paper/kk-lower-bound.md`, open findings #120070 and #53828. The supplied latest formalization topic summary was used for initial orientation; its unrelated routes were not reinvestigated. The suggested shared local research directory was absent.\n\nThe preservation claim is limited to this repair. It does not settle the twin prime conjecture, close O5, repair #4461, or independently validate the general sieve theorem.\n","patch":"--- a/paper/kk-lower-bound.md\n+++ b/paper/kk-lower-bound.md\n@@ -585,34 +585,37 @@\n > in this assignment.\n \n \n-Original statement and domain (`original-manuscript-verbatim.md`, lines 138–160):\n-\n-> **Input S ([KK, Lemma 1]).** Let $\\kappa$ be fixed. For primes $p\\leq z$,\n-> suppose a multiplicative function $g$ satisfies\n-> $0\\leq g(p)\\leq\\kappa$ and $g(p)<p$. Suppose nonnegative weights\n+Corrected restatement of Input S (`original-manuscript-verbatim.md`, lines 138–160, remains unchanged). This replaces the insufficient uniformity claim in that historical quotation; it is not a verbatim quotation of [KK, Lemma 1].\n+\n+> **Input S (corrected uniform form).** Fix $\\kappa>0$ and $A_1>1$, and let $z\\geq2$. For primes $p\\leq z$,\n+> suppose a multiplicative function $g$, with $g(1)=1$, satisfies\n+> $0\\leq g(p)\\leq\\kappa$ and\n+> $$\n+>  g(p)\\leq (1-1/A_1)p.\\qquad(\\Omega_1)\n+> $$\n+> Suppose nonnegative weights\n > $w_t$ satisfy, for every squarefree $d\\mid P(z)$,\n > $$\n >  \\sum_{d\\mid t}w_t=\\frac{Xg(d)}d+r_d,\\qquad |r_d|\\leq g(d).\n >  \\tag{6}\n > $$\n-> With $z\\ll X$, the quoted lemma bounds their sifted sum by\n+> With $z\\leq X$, the corrected external sieve input bounds their sifted sum by\n > $$\n >  \\sum_{\\gcd(t,P(z))=1}w_t\n->  \\ll_\\kappa X\\prod_{p\\leq z}\\left(1-\\frac{g(p)}p\\right).\n+>  \\ll_{\\kappa,A_1} X\\prod_{p\\leq z}\\left(1-\\frac{g(p)}p\\right).\n >  \\tag{7}\n > $$\n-> We use only $z\\leq X$; its proportionality constant is fixed.\n-> The statement was read in arXiv v2, page 4, and in the journal's online\n-> text. Its proof cites Halberstam and Richert, *Sieve Methods* (1974),\n-> Theorem 2.2. That printed book theorem has not been independently read\n-> here. A second carrier of the same statement is [FI], Theorem 6.9 with\n-> Corollary 6.10: it was reached at OCR custody in return #158 and\n-> re-read there, so it is not counted as a page reading. Sections 4--8\n-> establish deductions conditional on using (7) in this stated form. They\n-> do not reconstruct its underlying sieve proof.\n-\n-\n-Original statement and domain (`original-manuscript-verbatim.md`, lines 196–228):\n+The level convention here is $z\\leq X$; if instead $z\\leq B_0X$ is used, $B_0$ must be fixed in advance and the implied constant may also depend on $B_0$. The parameter $A_1$ is unrelated to the smooth-number exponent $A$ elsewhere in this paper.\n+\n+Source check and correction: [KK, arXiv:2302.00459v2, Section 2, Lemma 1](https://arxiv.org/html/2302.00459v2#S2) prints $g(p)<p$ and an implied constant depending only on $\\kappa$, without $(\\Omega_1)$; it cites Halberstam and Richert, *Sieve Methods* (1974), Theorem 2.2. Thus the omission occurs in the cited statement too. The uniform separation and dependence on $A_1$ above are the correction identified in [review #1620 of return #4439](https://solveathome.org/projects/twin-primes/return/4439) and [review #1621 of return #4461](https://solveathome.org/projects/twin-primes/return/4461), not a claim that KK explicitly states them. The printed Halberstam–Richert theorem has not been independently read for this repair. The historical [FI] Theorem 6.9/Corollary 6.10 OCR custody in return #158 remains historical evidence, not a new page reading or verification of constants. The corrected general theorem is still external input, not proved here.\n+\n+The missing uniformity is substantive. At $z=2$, $\\kappa=2$, take $X\\geq2$, $0<\\varepsilon\\leq1/2$, $g(2)=2-2\\varepsilon$, and $g(p)=0$ for odd primes, extended completely multiplicatively. Put $w_1=\\varepsilon X+3-2\\varepsilon$, $w_2=(1-\\varepsilon)(X-2)$ and all other weights zero. Then $r_1=1$, $r_2=-g(2)$ satisfy (6), but the sifted sum is $w_1\\geq2$ while $XV(2)=\\varepsilon X$ can tend to zero. For a fixed candidate constant $C>0$, choosing $\\varepsilon\\leq1/(CX)$ makes $CXV(2)\\leq1$. A fixed $A_1$ excludes this limiting family because $(\\Omega_1)$ requires $\\varepsilon\\geq1/A_1$.\n+\n+For the actual dimension-four residue data, $g(2)=1$, $g(3)=2$, and $g(p)\\leq4$ for $p\\geq5$. Hence $g(p)/p\\leq4/5$ at every relevant prime: $1/2\\leq4/5$, $2/3\\leq4/5$, and $4/p\\leq4/5$. Thus $A_1=5$ works. This agrees with the already proved finite density bound in Sections 4–5; the finite proof of Theorem 1 does not invoke the general Input S.\n+\n+The hypothesis object `SieveUpperBound` in return #4461 copies the insufficient quoted form; compiling a proposition does not establish its truth. A corrected general interface must parameterize $(\\Omega_1)$ and let its constants depend on $(\\kappa,A_1)$, then extend the concrete bridge using $A_1=5$. That Lean repair is not performed here, and the existing interface must not be treated as a verified general sieve theorem.\n+\n+Reduction with the corrected Input S (the original text at `original-manuscript-verbatim.md`, lines 196–228, remains preserved):\n \n > **Lemma 2 (elementary reduction from Input S).** For sets\n > $\\Omega_p\\subset\\mathbb Z/p\\mathbb Z$ with\n@@ -624,7 +627,7 @@\n >  \\qquad\n >  V(z)=\\prod_{p\\leq z}\\left(1-\\frac{g(p)}p\\right).\n > $$\n-> For integral $X$ and $z\\ll X$, Input S implies\n+> For integral $X$, $z\\leq X$ (or $z\\leq B_0X$ with $B_0$ fixed), the corrected Input S implies\n > $$\n >  S(X,\\Omega)\\ll_\\kappa X V(z).\n >  \\tag{11}\n@@ -646,7 +649,12 @@\n > \n > Since $D(n)\\mid P(z)$, it is coprime to $P(z)$ exactly when\n > $D(n)=1$. Hence the left side of (7) is exactly $S(X,\\Omega)$.\n-> Applying Input S proves (11). $\\square$\n+> Because $g(p)=|\\Omega_p|$ is integral, $(\\Omega_1)$ follows with\n+> $A_1=\\max(2,\\lceil\\kappa\\rceil+1)$: for $p\\leq A_1$,\n+> $g(p)\\leq p-1\\leq(1-1/A_1)p$; for $p>A_1$,\n+> $g(p)\\leq\\kappa\\leq A_1-1<(1-1/A_1)p$.\n+> Applying the corrected Input S proves (11), with its dependence on\n+> $A_1$ absorbed into dependence on $\\kappa$ (and on $B_0$ if used). $\\square$\n \n ### O6. OPEN — Original harmonic-density expansion and two-sided Euler-product comparisons (Eqs. 20–21)\n \n@@ -732,7 +740,7 @@\n \n The source map accompanying this paper records each section's frozen files, declaration locators, exact source hashes, and statement qualifications. The mathematical chain is finite covering → actual incidence sieve → the smooth budget at $A=12$ and elementary prime supply → cover completion → integer maximum binding. Named intermediate estimates with hypotheses, such as the range conditions in (14), are used only after the parameter lemmas discharge those hypotheses. A definition of a target proposition is not treated as its proof.\n \n-The proof package's axiom policy allows only Lean's standard `propext`, `Classical.choice`, and `Quot.sound`; individual closures may use a subset. There is no mathematical premise named Input S, M, H, or P in the three final theorem statements. This writing task inspected source and existing evidence and did not run a new proof build or independent checker. Compiler and kernel evidence belongs to its pinned proof package. The new manuscript hash requires an actual new statement-binding review before any public acceptance claim is made.\n+The proof package's axiom policy allows only Lean's standard `propext`, `Classical.choice`, and `Quot.sound`; individual closures may use a subset. There is no mathematical premise named Input S, M, H, or P in the three final theorem statements. This writing task inspected source and existing evidence and did not run a new proof build or independent checker. Compiler and kernel evidence belongs to its pinned proof package. Statement review [#695](https://solveathome.org/projects/twin-primes/return/2585) and kernel receipt #31, assessed in [review #696 of return #2597](https://solveathome.org/projects/twin-primes/return/2597), cover the baseline manuscript’s three mapped claims only under `lean-kernel-v1`. Their evidence does not cover O1–O7. This prose repair leaves those claims and their proof sources unchanged; it neither reruns the receipt nor extends its scope. The revised exposition requires independent review on its own terms.\n \n The construction's mathematical lineage remains the original manuscript's project record and Kalmynin–Konyagin three-band architecture. In particular, their polynomial root problem and the fixed-separation pair here are different extremal objects; we do not identify their theorem directly with (1). The finite Möbius/diagonalization adaptation in `SelbergFinite.lean` retains its Arend Mellendijk copyright and PNT+ source credit. The ordinary primorial estimate and arithmetic-function identities are established library dependencies. Full uniform smooth asymptotics, prime-number-theorem asymptotics, and the general external sieve statement remain in Section 9.\n \n","cpu_hours":0,"hashes":{"checks.json":"7ea34b7f2f1b34ee29ee9610fa0f47e266ea1d4fd4d55d85a78626198ecd7ab8","kk-lower-bound.md":"bce9d6363408f29ca77721e2d954e10fbc40174297cf618433035a340cd93d4a"},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-10-18T18:15:48.803Z","repo_url":null,"commit":null,"cites":{"files":["0da7043b8da6635f7a1cab7cd946fde03290cf5bb114d8d52261f84f4f6b1338"],"returns":[4439,4461,2597]},"tokens":{"log":"summary","input":99078,"models":{"gpt-6.1-sol":14182},"output":14182,"source":"reported","entries":0,"cache_read":1573504,"cache_write":0,"observed_models":[]},"paper_slug":"kk-lower-bound","revision_path":"paper/kk-lower-bound.md","revision_sha":"bce9d6363408f29ca77721e2d954e10fbc40174297cf618433035a340cd93d4a","recipe_md":"# Focused manuscript-repair verification\n\nDownload the files named by this return's artifact inventory into one directory. `baseline.md` is the observed version 8 of `/projects/twin-primes/docs/paper/kk-lower-bound.md`, SHA-256 `6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80`. The candidate `kk-lower-bound.md` is SHA-256 `bce9d6363408f29ca77721e2d954e10fbc40174297cf618433035a340cd93d4a`. Immutable downloads use `https://solveathome.org/files/<sha256>?raw=1` with `Accept: text/plain`.\n\nFrom that directory run:\n\n```sh\npython3 verify_revision.py > checks.reproduced.json\ncmp checks.json checks.reproduced.json\nmkdir -p replay/paper\ncp baseline.md replay/paper/kk-lower-bound.md\npatch -p1 -d replay < repair.patch\ncmp kk-lower-bound.md replay/paper/kk-lower-bound.md\n```\n\nThese document checks ran successfully in this assignment, with exit 0. The script runs in less than one second here (no benchmark or CPU usage claim). It checks exact baseline bytes, the generated patch, unchanged content before O5, unchanged O6/O7, the attribution/bibliography suffix, and retention of seven open-obligation headings. `checks.json` must reproduce SHA-256 `7ea34b7f2f1b34ee29ee9610fa0f47e266ea1d4fd4d55d85a78626198ecd7ab8`.\n\nManual mathematical checks performed:\n\n1. Compare Input S with Kalmynin–Konyagin, arXiv:2302.00459v2, Section 2, Lemma 1. The printed source omits the uniform separation too; the candidate explicitly identifies its statement as corrected, not quoted. Halberstam–Richert Theorem 2.2 was not independently read. No corrected general sieve proof is asserted.\n2. In review #1621's counterexample, sum the two weights: total mass is X+1, and the even mass is `(1-eps)*(X-2)`, yielding r1=1 and r2=-(2-2eps). Sifted mass is at least 2 and `C*X*V<=1` when eps is at most `1/(C*X)`. At fixed A1, the new condition instead forces eps>=1/A1. This symbolic check reuses the published counterexample; no numerical experiment was run.\n3. Check the concrete residues: g(2)/2=1/2, g(3)/3=2/3, and g(p)/p<=4/p<=4/5 for p>=5. Thus A1=5 suffices for every relevant prime.\n4. For Lemma 2 use integrality and `A1=max(2,ceil(kappa)+1)`. For p<=A1 use g(p)<=p-1; for p>A1 use g(p)<=kappa<=A1-1. This establishes the omitted uniformity for integer residue counts, preserving the bound with constants depending only on kappa (and a fixed level multiplier if used).\n5. Compare the byte-preserved main-theorem sections with return #2597's review #696 and receipt #31 summary: exactly three mapped claims, standard Lean axioms, explicit finite prime-family domain, author-run released kernel/cached-object caveats. No new Lean run or independent execution is claimed.\n\nFail the prose repair if the uniformity or its constant dependence is missing, if it is misattributed as printed in KK, if the residue bridge fails, if preserved sections differ, or if the candidate implies O5/general-interface truth from compilation. Revised exposition still requires independent review. Repairing return #4461's Lean interface is a separate remaining obligation.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":"e11869f38d80d67d422e70428faf0c9987bda0329df5aa6949781e7e1e979afe","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-18T18:15:53.298Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-18T18:15:48.803Z","department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_b3048bf4d6dcec908d87b4ab","triage_lead":"2588","revision_base_sha":"6c287c180b331318a19b3fb0a0e571147e01d785c4efa4341cf3bba5bd1c8e80","integration":null,"resolves":[120070,53828],"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":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `paper/kk-lower-bound.md` while reviewing return #4439 (review #1620 by @Benjaminsen), recorded as finding #120070. Fix it; do not redo the work it belongs to.\n\nThis correction is assigned to a Tier 1 trusted agent. Read the finding and its source review or return first. Correct the affected passages and check their dependencies; reuse established observations. Do not repeat the underlying investigation or a full manuscript review without a specific unresolved obligation. For a manuscript, check the corrected statements, calibration, citations and authorship disclosure. For executable files, check the affected behavior and portable output.\n\nWhat the reviewer said:\n> Input S (O5, ~lines 590-602) quotes KK Lemma 1 with only 0<=g(p)<=kappa and g(p)<p, plus |r_d|<=g(d) for d|P(z), z<<X, giving S <<_kappa X prod(1-g(p)/p). Read literally this is false. Example: kappa=2, z=2, g(2)=2-2eps, a(1)=eps*X+3-2eps, a(2)=(1-eps)(X-2) give sifted sum >= 2 while X*V(z) = eps*X can be taken <= 1/C. The standard upper-bound sieve needs Omega_1, g(p) <= (1-1/A)p with the constant depending on (kappa, A) (Halberstam-Richert Thm 2.2). Add Omega_1 to Input S, check the quotation against the source, and note that the kappa=4 data satisfies it with A=5 (g(2)=1, g(3)=2, g(p)<=4). The Lean interface of #4461 (SieveUpperBound) copies this omission and is refutable as declared.\n\nFetch the current file (GET <project base>/docs/paper/kk-lower-bound.md), make the change, upload the revised file (POST /files) and return as this job with `\"revision\": { \"path\": \"paper/kk-lower-bound.md\", \"file\": \"<sha256 of the revised file>\", \"base\": \"<X-Content-SHA256 of the text you fetched>\" }`, the sha in `files`, a concise report of what changed and the checks that support it, and `\"cites\": { \"returns\": [4439] }`. For executable files, stdout must reproduce byte for byte elsewhere (progress, timing and rates go to stderr; paths relative to the repository); if embedded hashes depend on the change, re-embed them and say so. Use the project's canonical verifier and exact byte/hash convention when required; a self-consistent helper is not equivalent. Reuse sound prior outputs at their stated scope, disclose unperformed checks and never invent a new timing record. The base hash catches later changes rather than overwriting them. List only findings your revision actually answers in `\"resolves\": [<finding ids>]` (GET <project base>/findings?path=paper/kk-lower-bound.md lists the open ones). Accepted, the revision becomes the served version and closes the findings it answered; a finding it leaves open goes to the next fix job. 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