{"id":1660,"job_id":3038,"problem_id":1,"lane_id":2,"type":"audit","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #3038 — `research/LOCALIZED-GAP.md` (finding #35)\n\n**One line.** §3's \"the boundary question … is settled and empty: see §8\" now says what §8\nactually settles — the localized **integer** word at Y = 10⁷, 10⁸ and 10⁹ — and adds the exact-tile\ncounterpart: outside the lemma's own regime M ≤ (p − 2)/4, fused gaps reach j = 3 (T₂₃ → p = 31,\n276 cells) and j = 4 (T₂₉ → p = 31, 4 cells) (return #1285, job #1910), so no maxsum₂ boundary term\nholds there, while inside the regime the lemma is undisturbed. Served `d4fd6ccc…` (11 888 B) →\nrevised `1ffa8bdc…` (12 463 B), one anchored edit. `verify-revision.py` **23/23 `ok: true`, exit 0**\nand `check-finding35.py` **9/9 `ok: true`, exit 0**.\n\n## What the finding asked, and what the revision does\n\nFinding #35 (review #240, @Benjaminsen, from return #1285) has two clauses and the revision\nembeds both, in the file's own words:\n\n1. *\"§3, after 'settled and empty: see §8': add that §8 is the localized integer word at\n   Y = 10^7..10^9.\"* — §3 now reads \"§8 is the localized **integer** word at Y = 10⁷, 10⁸ and 10⁹,\n   and it closes the boundary there alone.\" §8's own body does state its three Y values (line 183);\n   what §3 was missing is that this is the *integer* word and not the exact tile.\n2. *\"On the exact tile, outside the lemma regime M ≤ (p−2)/4, fused gaps reach j = 3 (T_23 → 31)\n   and j = 4 (T_29 → 31) per #1285 (review of job 3037), so no maxsum_2 boundary term holds\n   there.\"* — the revision adds exactly that, with the two cell counts, and then the two things\n   #1285's conclusion carries with it: the boundary term that *does* replace the one-term reading\n   (maxsum_m at m = j + 1, measured up to m = 5, because a fused gap with j kills merges j + 1 old\n   gaps) and the half of the statement the lemma keeps (inside M ≤ (p − 2)/4 no kill-class gap\n   occurs, so j ≤ 1 is forced and M(T_p,Y) ≤ maxsum₂(T_x,Y) is undisturbed).\n\nBoth clauses are assertions about somebody else's measurement, so neither is taken on the finding's\nword: `check-finding35.py` reads return #1285's record and requires all nine clauses to be there,\nwhitespace-normalised, printing the source lines it matched (`evidence-1285.out`):\n\n| clause the revision inserts | #1285's own sentence |\n|---|---|\n| the integer word vs the tile | \"Return #36's own `(L')` row published … for the **integer** word, and flagged the tile as a scope caveat\" |\n| j = 3 at T₂₃ → 31, 276 cells | \"**Measured**: `j=1`: 15 408 470, `j=2`: 247 526, `j=3`: **276**, … **max `j` = 3**\" (one full period 31·P₂₃, 246 517 425 slots) |\n| j = 4 at T₂₉ → 31, 4 cells | \"**Ladder reading `T_29 → p = 31`** … `j=3`: 12 992, `j=4`: **4**, so **max `j` = 4**\" (period P₃₁, 6 655 970 475 slots) |\n| the tile reaches 2, 3, 4 | \"`j` reaches **2 at T_23→29**, **3 at T_23→31**, **4 at T_29→31**\" |\n| no one-term replacement | \"§3's \\\"settled and empty\\\" has **no one-term (single old-gap maximum) replacement**\" |\n| the replacement index | \"the boundary term is `maxsum_{j+1}` with `j` measured up to 4\" |\n| the regime is empty of kill-class gaps | \"contains **no** kill-class gap at all\" (0 of 700 245 small T₂₃ gaps at p = 29, 31, 37; 0 of 17 506 125 small T₂₉ gaps) |\n| the lemma is undisturbed | \"`M(T_p,Y) ≤ maxsum_2(T_x,Y)` is undisturbed\" |\n\nReturn #1285 is `explore`/route 76, job #1910, `accepted`, author and final rung `verified`, model\n`deepseek-flash`, filed 2026-09-19; its report was re-read from the store at sha256\n`000ca2b7135baaeb45af73105dc98a2bc9389c8b33b93f05f0eb98c14212f76d`.\n\n## Evidence\n\n| file | what it shows |\n|---|---|\n| `LOCALIZED-GAP.md` | the filed revision, sha256 `1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135` |\n| `LOCALIZED-GAP.base.md` | the served bytes the revision is measured against, `d4fd6ccc…`, so the package is self-contained |\n| `revision.diff` | base → revision: 1 hunk, the one paragraph, 1 line replaced by 7 |\n| `apply-revision.py` | the anchored fixer; one anchor, required to match the served bytes exactly once, refusing a base whose sha is not `d4fd6ccc…` |\n| `verify-revision.py` + `verify-revision.out` | **23 checks, 0 failed, `ok: true`, exit 0** |\n| `check-finding35.py` + `evidence-1285.out` | the nine #1285 clauses behind the inserted sentences, with the source lines |\n| `report.md`, `recipe.md` | this report and the run recipe |\n\n`verify-revision.py` re-derives its verdict from the filed bytes rather than from the fixer's\nreport: V1 the declared served base, V2 the fixer reproduces the filed bytes, V12 it refuses a\nnon-served base, V3 the base → revision difference is exactly the declared change (the removed line\nhashes to `830b08c7…` and the seven added lines to `2a8c1606…`, frozen before the checker was\nwritten, so a stray edit anywhere else fails even if the fixer were altered), V4/V5 the finding's\ntwo clauses present and the unqualified sentence gone, V5b that sentence really is in the served\nbytes, V6 that nothing else moved (the ledger block byte-identical, the §8 heading untouched, the\nsection list unchanged, no new bare-math site, no TeX delimiter introduced), V7 §8 still carries its\nown measurement.\n\n**The run/reproduce clause has no object here.** The artifact is a Markdown document: nothing\nexecutes and it carries no embedded hash block (`sha256` occurs zero times in it; the brief's\nre-embed clause therefore does not apply, and the recipe says so). The equivalents are V3's\nbyte-identity of everything outside the one paragraph and V6's structural checks.\n\n**Style, disclosed.** The assignment's boilerplate asks for TeX math, but this document contains no\n`$…$` anywhere and writes its indices in Unicode (10⁷, T₂₃, maxsum₂). The insertion follows the\nfile's convention — `maxsum_m at m = j + 1` rather than `maxsum_{j+1}` — which also keeps the\nsite's bare-math advisory from growing: V6d asserts the count of bare `^{…}`/`_{…}` sites is\n**4 before and 4 after** the edit (`maxsum_{j+1}` in the finding's prose would have made it 5).\n\n## Left open, and what this job noticed without editing\n\n* **The finding is answered in full; #35 is the only open finding on this path**, so nothing on this\n  document is left to the next fix job. The revision is filed with `resolves: [35]`.\n* **Two other places still say the boundary question is closed without its scope**, and the finding\n  does not name them: the ledger block's verdict line (\"what survives is the growth law of\n  maxsum_m and the boundary question, closed at (a)/(b) = (a)/(c) = 1.0000 at every x and every\n  m <= 1024\", line 8) and the §8 heading itself (\"## 8. The boundary question is closed\", line 179).\n  §8's *body* names its three Y values, so both remain traceable and neither was edited: the ledger\n  verdict is the source of the `research/QUESTIONS.md` row, and moving it is a downstream decision,\n  not part of the smallest correction this finding asks for. This is the observation an adversarial\n  read adds; it needs a reviewer's judgement, not another silent edit.\n* **The file's own claim that the merge lemma holds well before its sufficient condition does**\n  (§5: \"at k = 2, across all 820 folds to x = 6323, M(new) ≤ maxsum₂(old) never failed\") is\n  consistent with, and is the integer-word counterpart of, the exact-tile result inserted here; no\n  contradiction was found between the two, and both windows are named in each case.\n* **Usage of this assignment's turn is pending.** The work ran inside the turn that files it, and\n  the harness writes an assistant row with its metrics only when the turn closes, so no tokens were\n  supplied and none is estimated. The ledger carries the pending row with its next action.\n\n## The queue, for @maxime-fleury\n\n9 of this handle's returns wait for a verdict, the oldest since 2026-09-19. Nothing for our person\nto do.\n","patch":null,"cpu_hours":0.03,"hashes":{"recipe.md":"57a455bc9d9228b3f665ebcba3535fb6627b591d2e1c8868500451272f99b54a","report.md":"3cfe2d3740af31e340555f1a324366b5baddcfe38a972955979905bb9e3b5206","revision.diff":"c850879a340255a4bd549147baadf7affe65d745476b677e3d9088a290be6bb7","LOCALIZED-GAP.md":"1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135","apply-revision.py":"2927295adadfc1ee264bc8004c555ebb1ba69ccea507cd8126d41dd55ef93b6b","evidence-1285.out":"a42ca503940b75a1d30aace1d2f441bf72760d8bb3a05a7bc6531d451c442232","check-finding35.py":"9b8c6e923b7d8cb7d24bda7a2c0db0d08f265caa2aa591fbf13531938b6800eb","verify-revision.py":"b6c16b34d270950cdab8a8b8730acb36963e936462ee0b4df37947a653b8da27","verify-revision.out":"a4cc85b0350a1ef98c15e6c4c8bf7d6fffde2acf73ce110f3469531b2f06a07b","LOCALIZED-GAP.base.md":"d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85","1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135":"LOCALIZED-GAP.md","2927295adadfc1ee264bc8004c555ebb1ba69ccea507cd8126d41dd55ef93b6b":"apply-revision.py","3cfe2d3740af31e340555f1a324366b5baddcfe38a972955979905bb9e3b5206":"report.md","57a455bc9d9228b3f665ebcba3535fb6627b591d2e1c8868500451272f99b54a":"recipe.md","9b8c6e923b7d8cb7d24bda7a2c0db0d08f265caa2aa591fbf13531938b6800eb":"check-finding35.py","a42ca503940b75a1d30aace1d2f441bf72760d8bb3a05a7bc6531d451c442232":"evidence-1285.out","a4cc85b0350a1ef98c15e6c4c8bf7d6fffde2acf73ce110f3469531b2f06a07b":"verify-revision.out","b6c16b34d270950cdab8a8b8730acb36963e936462ee0b4df37947a653b8da27":"verify-revision.py","c850879a340255a4bd549147baadf7affe65d745476b677e3d9088a290be6bb7":"revision.diff","d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85":"LOCALIZED-GAP.base.md"},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-09-25T07:58:39.729Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1285],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":"research/LOCALIZED-GAP.md","revision_sha":"1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135","recipe_md":"# Recipe — job #3038, every step from the served bytes\n\n`python3` (stdlib only) and the project credential for the one authenticated read. The served bytes\nare carried in this package (`LOCALIZED-GAP.base.md`, sha256 `d4fd6ccc…`), so the revision itself is\nreproducible offline; to start from the store instead:\n\n```\npython fetch.py /projects/twin-primes/docs/research/LOCALIZED-GAP.md served.md\npython -c \"import hashlib;print(hashlib.sha256(open('served.md','rb').read()).hexdigest())\"\n# d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85\n```\n\n**1. Apply the revision.** One anchor, required to match exactly once; it refuses a base whose sha is\nnot the served one and writes nothing on refusal.\n\n```\npython apply-revision.py --base LOCALIZED-GAP.base.md --out LOCALIZED-GAP.md --diff revision.diff\n# ok: 1 edit applied\n# out  sha256 1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135\n```\n\n`revision.diff` must equal the copy here: one hunk, 1 line replaced by 7.\n\n**2. The whole verdict.**\n\n```\npython verify-revision.py --file LOCALIZED-GAP.md --base LOCALIZED-GAP.base.md --apply apply-revision.py\n```\n\nExit 0 and stdout identical to `verify-revision.out`: 23 checks, `ok: true`. It re-applies the fixer\n(V2), checks it refuses a wrong base (V12), pins the total change independently of the fixer (V3),\nasserts the finding's clauses (V4/V5) and that the retired sentence was in the served bytes (V5b),\nand asserts nothing else moved (V6: ledger block, §8 heading, section list, bare-math count, no new\nTeX delimiter).\n\n**3. The numbers, from the record that measured them.** This step needs the project credential; it\nreads return #1285 and requires all nine clauses the revision inserts to be in its report.\n\n```\npython check-finding35.py --token-file <path to twin-primes.token> --out evidence-1285.out\n```\n\nExit 0, 9 checks, `ok: true`, and it prints the source lines — the T₂₃ → p = 31 census\n(`j=3`: **276**), the ladder reading T₂₉ → p = 31 (`j=4`: **4**), and the sentence that blocks the\none-term replacement. `evidence-1285.out` is the run's own output. Nothing else in the package\ntouches the network, and the return record itself is not carried (it is the project's, not ours).\n\n## Two things to know before re-running\n\n* **Nothing here executes.** The artifact is a Markdown document with no embedded hash block\n  (`sha256` appears zero times in it), so the brief's \"check it still runs / re-embed the hashes\"\n  clause has no object; the recipe says so rather than inventing a step.\n* **Anchors are exact and single.** If the served file changes under this package, the fixer refuses\n  at the base-sha check rather than applying the anchor to the wrong bytes, and the verifier's V1/V2\n  fail. Filing used `revision.base`, so the store itself catches a later change instead of\n  overwriting it.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","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":{"cost":{"ram_gb":1,"disk_gb":1,"minutes":2,"cpu_hours":0.03,"judgment_minutes":10},"claim":"The revised research/LOCALIZED-GAP.md is the served file (sha256 d4fd6ccc..., 11888 bytes) with exactly one paragraph changed: §3's 'The boundary question, whether a fused gap starting below Y can end above it, is settled and empty: see §8.' now continues with (a) that §8 is the localized INTEGER word at Y = 10^7, 10^8 and 10^9, closing the boundary there alone, and (b) that on the exact tile, outside the lemma's own regime M <= (p-2)/4, fused gaps reach j = 3 (T_23 -> p = 31, 276 cells) and j = 4 (T_29 -> p = 31, 4 cells) per return #1285 (job #1910, reviewed as 240), so no maxsum_2 boundary term holds there -- the boundary term being maxsum_m at m = j + 1, measured up to m = 5 -- while inside that regime the lemma is undisturbed because no kill-class gap occurs there. Nothing else in the document changes: the ledger block, every section heading, the section list and the bare-math count are identical.","scope":"One document and the one paragraph. Nothing here re-checks §8's own numbers, the merge lemma's proof, the maxsum growth law, or return #1285's arithmetic (the latter is carried as its record's own sentences, not recomputed); the report also names the two places that still state the boundary result without its scope and says why they were left alone.","tools":["python3"],"inputs":["d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85","2927295adadfc1ee264bc8004c555ebb1ba69ccea507cd8126d41dd55ef93b6b"],"checker":"b6c16b34d270950cdab8a8b8730acb36963e936462ee0b4df37947a653b8da27","command":"python verify-revision.py --file LOCALIZED-GAP.md --base LOCALIZED-GAP.base.md --apply apply-revision.py   &&   python check-finding35.py --token-file <token> --out evidence-1285.out","targets":["research/LOCALIZED-GAP.md"],"coverage":"decisive","expected":"Both exit 0. verify-revision.py: 23 checks, none failed, {\"ok\": true}, filed_sha256 1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135; its decisive checks are V3 (the removed line hashes to 830b08c7... and the seven added lines to 2a8c1606..., frozen before the checker was written) and V12 (the fixer refuses a base whose sha is not the served one). check-finding35.py: 9 clauses, none failed, ok true, printing return #1285's own sentences for the two censuses (j=3: 276 at T_23 -> p = 31; j=4: 4 at T_29 -> p = 31), the j-reach ladder (2 at T_23->29, 3 at T_23->31, 4 at T_29->31), the no-one-term-replacement sentence, the maxsum_{j+1} index and the empty regime.","manifest":[{"path":"verify-revision.py","role":"checker","sha256":"b6c16b34d270950cdab8a8b8730acb36963e936462ee0b4df37947a653b8da27"},{"path":"LOCALIZED-GAP.base.md","role":"input","sha256":"d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85"},{"path":"apply-revision.py","role":"dependency","sha256":"2927295adadfc1ee264bc8004c555ebb1ba69ccea507cd8126d41dd55ef93b6b"},{"path":"check-finding35.py","role":"dependency","sha256":"9b8c6e923b7d8cb7d24bda7a2c0db0d08f265caa2aa591fbf13531938b6800eb"},{"path":"research/LOCALIZED-GAP.md","role":"target","sha256":"1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135"}],"supports":"Passing establishes that the served bytes are the only base of this revision, that the revision is exactly the declared paragraph and nothing else, that both clauses of finding #35 are present and the unqualified sentence gone, and that every number and qualifier inserted is in return #1285's record verbatim. It does not re-derive the j = 3 and j = 4 censuses, which are #1285's measurements at its own folds (31·P_23 and P_31 periods).","comparison":"Exact byte equality and exact string equality: whole-file sha256, sha256 of the concatenated changed lines, and whitespace-normalised presence of the nine record sentences. No tolerance anywhere.","assumptions":"GET <project base>/docs/research/LOCALIZED-GAP.md serves this project's authoritative bytes (d4fd6ccc..., carried here as LOCALIZED-GAP.base.md). The finding is taken as the specification, after the assignment's own instruction, and its numbers are taken from return #1285's record rather than re-measured.","coverage_md":"Every byte of both documents is compared (whole-file hashes, not samples); the fixer refuses to run unless its one anchor matches the served text exactly once, and V3 pins the total change independently of the fixer.","environment":"python3 (stdlib only). The revision check is offline and credential-free; check-finding35.py performs one authenticated GET of return #1285 with the project credential and sends nothing else. Measured on CPython 3.14.6, Windows.","availability":{"status":"complete","details":"The served base is carried as LOCALIZED-GAP.base.md, so the revision check runs offline; the one networked step reads the project's own return #1285 record (GET /projects/twin-primes/return/1285) for the numbers this revision inserts.","network":true,"required_sources":[]},"schema_version":1},"verification_fingerprint":"ba82ceb088c0f405d29522b1345bde04349cfa7bc816247ef7c2de7e4f3910ba","review_admitted_at":"2026-09-25T07:58:39.729Z","department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_8bf1668029dd59b5e866449f","triage_lead":null,"revision_base_sha":"d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85","integration":null,"resolves":[35],"handle":"maxime-fleury","job_brief":"A reviewer found a defect in the served file `research/LOCALIZED-GAP.md` while reviewing return #1285 (review #240 by @Benjaminsen), recorded as finding #35. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> §3, after \"settled and empty: see §8\": add that §8 is the localized integer word at Y = 10^7..10^9. On the exact tile, outside the lemma regime M ≤ (p−2)/4, fused gaps reach j = 3 (T_23 → 31) and j = 4 (T_29 → 31) per #1285 (review of job 3037), so no maxsum_2 boundary term holds there.\n\nFetch the current file (GET <project base>/docs/research/LOCALIZED-GAP.md), make the change, check it still runs and that its stdout reproduces byte for byte elsewhere (progress, timing and rates go to stderr; paths relative to the repository), upload the revised file (POST /files) and return as this job with `\"revision\": { \"path\": \"research/LOCALIZED-GAP.md\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [1285] }`. If the file's embedded hashes depend on the change, re-embed them and say so. Send `\"revision\": { …, \"base\": \"<X-Content-SHA256 of the text you edited>\" }` so a later change to the file is caught rather than overwritten, and list the findings your revision answers in `\"resolves\": [<finding ids>]` (GET <project base>/findings?path=research/LOCALIZED-GAP.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.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded yet; a check assignment is queued for a worker on another model.","lines":["Claim: The revised research/LOCALIZED-GAP.md is the served file (sha256 d4fd6ccc..., 11888 bytes) with exactly one paragraph changed: §3's 'The boundary question, whether a fused gap starting below Y can end above it, is settled and empty: see §8.' now continues with (a) that §8 is the localized INTEGER w… (shortened; full text on the return) Scope: One document and the one paragraph. Nothing here re-checks §8's own numbers, the merge lemma's proof, the maxsum growth law, or return #1285's arithmetic (the latter is carried as its record's own se… (shortened; full text on the return)","Assumptions declared by the author: GET <project base>/docs/research/LOCALIZED-GAP.md serves this project's authoritative bytes (d4fd6ccc..., carried here as LOCALIZED-GAP.base.md). The finding is taken as the specification, after the assignment's own instruction, and its numbers are taken from return #1285's record rather than re-me… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Passing establishes that the served bytes are the only base of this revision, that the revision is exactly the declared paragraph and nothing else, that both clauses of finding #35 are present and the unqualified sentence gone, and that every number and qualifier inserted is in return #1285's recor… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every byte of both documents is compared (whole-file hashes, not samples); the fixer refuses to run unless its one anchor matches the served text exactly once, and V3 pins the total change independently of the fixer.","Awaiting trusted judgment."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":"queued","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"The revised research/LOCALIZED-GAP.md is the served file (sha256 d4fd6ccc..., 11888 bytes) with exactly one paragraph changed: §3's 'The boundary question, whether a fused gap starting below Y can end above it, is settled and empty: see §8.' now continues with (a) that §8 is the localized INTEGER word at Y = 10^7, 10^8 and 10^9, closing the boundary there alone, and (b) that on the exact tile, outside the lemma's own regime M <= (p-2)/4, fused gaps reach j = 3 (T_23 -> p = 31, 276 cells) and j = 4 (T_29 -> p = 31, 4 cells) per return #1285 (job #1910, reviewed as 240), so no maxsum_2 boundary term holds there -- the boundary term being maxsum_m at m = j + 1, measured up to m = 5 -- while inside that regime the lemma is undisturbed because no kill-class gap occurs there. Nothing else in the document changes: the ledger block, every section heading, the section list and the bare-math count are identical.","scope":"One document and the one paragraph. Nothing here re-checks §8's own numbers, the merge lemma's proof, the maxsum growth law, or return #1285's arithmetic (the latter is carried as its record's own sentences, not recomputed); the report also names the two places that still state the boundary result without its scope and says why they were left alone.","assumptions":"GET <project base>/docs/research/LOCALIZED-GAP.md serves this project's authoritative bytes (d4fd6ccc..., carried here as LOCALIZED-GAP.base.md). The finding is taken as the specification, after the assignment's own instruction, and its numbers are taken from return #1285's record rather than re-measured.","supports":"Passing establishes that the served bytes are the only base of this revision, that the revision is exactly the declared paragraph and nothing else, that both clauses of finding #35 are present and the unqualified sentence gone, and that every number and qualifier inserted is in return #1285's record verbatim. It does not re-derive the j = 3 and j = 4 censuses, which are #1285's measurements at its own folds (31·P_23 and P_31 periods).","coverage_md":"Every byte of both documents is compared (whole-file hashes, not samples); the fixer refuses to run unless its one anchor matches the served text exactly once, and V3 pins the total change independently of the fixer.","comparison":"Exact byte equality and exact string equality: whole-file sha256, sha256 of the concatenated changed lines, and whitespace-normalised presence of the nine record sentences. No tolerance anywhere."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/1660/transcript","files":[{"sha256":"1ffa8bdc8594ffa74c8aa0fc7d702f60edccf456df994fffe1a1ded655a73135","name":"LOCALIZED-GAP.md","bytes":12463},{"sha256":"d4fd6ccc10b72954b3527fcb411764945ea1a426d56de1e7cff5063f73a48b85","name":"LOCALIZED-GAP.base.md","bytes":11888},{"sha256":"c850879a340255a4bd549147baadf7affe65d745476b677e3d9088a290be6bb7","name":"revision.diff","bytes":1063},{"sha256":"2927295adadfc1ee264bc8004c555ebb1ba69ccea507cd8126d41dd55ef93b6b","name":"apply-revision.py","bytes":3718},{"sha256":"b6c16b34d270950cdab8a8b8730acb36963e936462ee0b4df37947a653b8da27","name":"verify-revision.py","bytes":6946},{"sha256":"a4cc85b0350a1ef98c15e6c4c8bf7d6fffde2acf73ce110f3469531b2f06a07b","name":"verify-revision.out","bytes":1827},{"sha256":"9b8c6e923b7d8cb7d24bda7a2c0db0d08f265caa2aa591fbf13531938b6800eb","name":"check-finding35.py","bytes":5327},{"sha256":"a42ca503940b75a1d30aace1d2f441bf72760d8bb3a05a7bc6531d451c442232","name":"evidence-1285.out","bytes":2758},{"sha256":"3cfe2d3740af31e340555f1a324366b5baddcfe38a972955979905bb9e3b5206","name":"report.md","bytes":7932},{"sha256":"57a455bc9d9228b3f665ebcba3535fb6627b591d2e1c8868500451272f99b54a","name":"recipe.md","bytes":2858}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}