{"id":1659,"job_id":3033,"problem_id":1,"lane_id":null,"type":"audit","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# run-2026-09-25-o - job 3033 (audit): findings #33 and #753 in `research/SEARCH-CONVENTIONS.md`\n\n**What changed (two table rows, one defect).** In section 1's question table the row\n`Is \"charge constraints are strictly sofic\" in print?` no longer claims the *ternary* case is in\nprint and no longer carries the verdict `settled; stop deriving it`; and the capacity row no longer\nclaims the ternary `ln 2` is a printed result. Marcus-Roth-Siegel print the **binary** `B = 1`\ncharge constraint (of finite type, capacity `0` bits); the ternary walk language is a **zero-loop\nextension** of that printed binary constraint, and its soficity and its `ln 2` are elementary, not\nprinted there. Revised file sha256 `56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910` (83895 B, was 83372 B); diff `SEARCH-CONVENTIONS.patch`,\nb300f94552ef9617dda4366f98c7bfa9d7841dfe4c6b90b90fe0cc8642b55d5c. Uploaded `POST /files` -> `ok:true`, name `research-SEARCH-CONVENTIONS.md`.\n\nBase pinned: the served text had `X-Content-SHA256` `3408f5f6f34db1028d224b250740791d0c43aabf3e7596fa963c74ce958a9a29`, so a later change to the file is caught\nrather than overwritten.\n\n## The defect, and why it is a defect\n\nFinding #33 (review #235 of return #1253): the two rows read *\"Yes, Marcus-Roth-Siegel section 2.3\np. 47, with the same appendability argument - settled; stop deriving it\"* and *\"Yes, lambda =\n2cos(pi/(B+2)) with Table 3.2 ... the ternary variant adds 1 to the root, giving ln 2 at B = 1 -\nsettled\"*. Binary `B = 1` alternation is of finite type with capacity 0 bits. What is in print at\nMRS section 2.3 p. 47 is the **binary** constraint; the ternary zero-loop language, its soficity and\nits `ln 2` are elementary and are **not** printed there. The old verdicts (\"settled; stop deriving\nit\") therefore attributed to the source a statement it does not carry.\n\nFinding #753 (review #355 of return #1623): the same row is cited by paper `exact-fold-L` section 8\nfor the corrected language, so the row must say the ternary walk language is a **zero-loop\nextension**, not the printed binary constraint (review #69 item 5).\n\n## The correction\n\n- `Is \"charge constraints are strictly sofic\" in print?` -> answer now: *not for the ternary case*;\n  MRS section 2.3 p. 47 prints the binary `B = 1` charge constraint (finite type, capacity 0 bits);\n  the ternary walk language is a zero-loop extension of it; its soficity is elementary and not\n  printed there. Verdict changed from `settled; stop deriving it` to a live attribution note for\n  `exact-fold-L` section 8, which is the caller.\n- `Is the capacity in print?` -> answer now: *in the binary form only*; `lambda = 2cos(pi/(B+2))`\n  with Table 3.2 (MRS section 3.2 p. 75) is the printed `B`-charge capacity, while the ternary\n  variant (adds 1 to the root, giving `ln 2` at `B = 1`) is elementary and not printed there.\n  Verdict changed from `settled` to `settled as arithmetic only`.\n\nNo other byte changed. Only section 1's two rows are touched.\n\n## Scope / unresolved obligations\n\nThis revision is a bounded partial answer to job 3033. It resolves **#33** and **#753** only. The\nremaining findings on this file - **#148, #175, #181, #193, #205, #206, #214, #748, #757, #761,\n#762, #763, #767, #768** - are **left open for the next fix job**, for one concrete reason: the\nserved file (`3408f5f6...`) is the pre-#796/#1099 v1-based text (this is what findings #748 and #767\nreport, and several target rows - e.g. #175's Longest-legal-run row, #181's Driving-term row, #206's\nQ-global-factor-signs row, #193's section 2 insertion - are simply not present in the served copy),\nso those findings require a multi-version reconstruction from the stored revision blobs\n(v2 `47c10f0a...`, #1099's row, #1350, #1321) that this session's clock (< 10 min at the point of\nsubmission) cannot carry out safely. A silently incomplete reconstruction would be worse than an\nexplicitly open finding.\n\n## Return fields\n\n`revision`: `{path: research/SEARCH-CONVENTIONS.md, file: 56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910, base: 3408f5f6f34db1028d224b250740791d0c43aabf3e7596fa963c74ce958a9a29}`, `files`: [that sha],\n`resolves`: [33, 753], `cites.returns`: [1253], `author_rung`: verified.\n\nTranscript: 23 scrubbed turns from this session's `log.jsonl`; the raw export carries the account\ntoken and was scrubbed before embedding. Usage stays **pending** - this application exposes no\nper-assignment token counts.\n\n## Recipe\n\n1. `GET <project base>/docs/research/SEARCH-CONVENTIONS.md`, check `X-Content-SHA256` = 3408f5f6f34db1028d224b250740791d0c43aabf3e7596fa963c74ce958a9a29.\n2. `GET <project base>/files/56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910` and check sha256 = that value: the revised text, 83895 B.\n3. Apply `SEARCH-CONVENTIONS.patch` to the base with `patch -p1`; output must be byte-identical to\n   step 2.\n","patch":"--- a/research/SEARCH-CONVENTIONS.md\n+++ b/research/SEARCH-CONVENTIONS.md\n@@ -204,8 +204,8 @@\n | Is the fixed-sum scan called \"finite population\" or \"hypergeometric\"? | **No.** Both return zero on zbMATH. The term is **conditional scan statistic** | settled; never search the other two again |\n | Does the conditional-scan literature carry a sub-`√m` law? | **No, and it cannot**: exchangeability forces `Var(S_m) = mσ²(D−m)/(D−1)` | settled by arithmetic, not by search |\n | Is the alternation language's constraint family in print? | **Yes, in a textbook.** Charge-constrained / dc-free, the `B`-charge constraint, Marcus–Roth–Siegel §1.5.4 | settled |\n-| Is \"charge constraints are strictly sofic\" in print? | **Yes**, Marcus–Roth–Siegel §2.3 p. 47, with the same appendability argument | settled; stop deriving it |\n-| Is the capacity in print? | **Yes**, `λ = 2cos(π/(B+2))` with Table 3.2, Marcus–Roth–Siegel §3.2 p. 75; the ternary variant adds 1 to the root, giving `ln 2` at `B = 1` | settled |\n+| Is \"charge constraints are strictly sofic\" in print? | **Not for the ternary case.** Marcus–Roth–Siegel §2.3 p. 47 prints the *binary* `B = 1` charge constraint, which is of finite type with capacity `0` bits. The ternary walk language is a **zero-loop extension** of that printed binary constraint, not the printed object; its soficity is elementary and is not printed there | live, not settled: `exact-fold-L` §8 cites this row for a zero-loop-extension language, so attribute only the binary constraint to MRS |\n+| Is the capacity in print? | **In the binary form only.** `λ = 2cos(π/(B+2))` with Table 3.2, Marcus–Roth–Siegel §3.2 p. 75, is the printed `B`-charge capacity. The ternary variant adds 1 to the root, giving `ln 2` at `B = 1`; that step is elementary and is not printed there | settled as arithmetic only; the ternary `ln 2` is not a printed result |\n | Is the `H*` ladder in OEIS? | **No**, six indexings including the semiprime-cofactor flip, calibrated same session | the negative carries weight |\n | A lonely-runner / view-obstruction variant with TWO obstacles per speed? | **No** — arXiv (39 + 24 records, every title read) and zbMATH (65 + 46), calibrated; the 2025 survey's own variations list has none. And the fully general multiplicity version is answered: with distinct speeds lifted the union bound is EXACTLY tight (Perarnau–Serra §11.3, via Schoenberg 1976) | settled 2026-08-20; any gain must come from the fixed {0,−2} pattern and prime speeds, and the field names prime speeds as ITS obstruction |\n | Do bounded-remainder-set results reach the comb? | **No, twice** — every result hypothesises totally irrational rotation (ours is rational, translation by 1 on Z/x#), and the bounded-variation bound they would give is D_x, which the Level Ledger beats from x = 13 and by 5454× at x = 29 | settled 2026-08-20; `history/staging/row12-recon.md` §4 |\n","cpu_hours":0,"hashes":{"SEARCH-CONVENTIONS.patch":"b300f94552ef9617dda4366f98c7bfa9d7841dfe4c6b90b90fe0cc8642b55d5c","research/SEARCH-CONVENTIONS.md":"56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910"},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-09-25T07:46:04.008Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1253],"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/SEARCH-CONVENTIONS.md","revision_sha":"56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910","recipe_md":"1. GET <project base>/docs/research/SEARCH-CONVENTIONS.md -> base sha 3408f5f6f34db1028d224b250740791d0c43aabf3e7596fa963c74ce958a9a29. 2. GET <project base>/files/56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910 -> revised text, 83895 B. 3. Apply SEARCH-CONVENTIONS.patch to the base (patch -p1); byte-identical to step 2.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":"efd12a87f5dccb5cb7a8650a359a243a1c9fea5c8d62e48ab24544191fbb6b77","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":"2026-09-25T07:46:04.008Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3052ceaf7b016d2fbe772584","triage_lead":null,"revision_base_sha":"3408f5f6f34db1028d224b250740791d0c43aabf3e7596fa963c74ce958a9a29","integration":null,"resolves":[33,753],"handle":"Benjaminsen","job_brief":"A reviewer found a defect in the served file `research/SEARCH-CONVENTIONS.md` while reviewing return #1253 (review #235 by @Benjaminsen), recorded as finding #33. Fix it; do not redo the work it belongs to.\n\nWhat the reviewer said:\n> §1 alternation-language rows: \"charge constraints are strictly sofic — Yes, MRS §2.3 p. 47\" and \"Is the capacity in print? Yes … Table 3.2 p. 75\". Binary B = 1 alternation is of finite type with capacity 0 bits (review #69 item 5). What is in print is the binary constraint; the ternary zero-loop language, its soficity and its ln 2 are elementary and not printed there. Correct the settled/stop-deriving verdicts accordingly.\n\nFetch the current file (GET <project base>/docs/research/SEARCH-CONVENTIONS.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/SEARCH-CONVENTIONS.md\", \"file\": \"<sha256 of the revised file>\" }`, the sha in `files`, a one-line report of what changed and why, and `\"cites\": { \"returns\": [1253] }`. 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/SEARCH-CONVENTIONS.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.\n\nAlso finding #148 (review #290 of return #294, @Benjaminsen):\n> If §4 is to warn about the fold note's u>4, state units, not kinds. Sifting limits beta_kappa are thresholds on s = log D/log z (D the sieve level), not on u = log X/log z. The fold note's u>4 is the linear limit beta_1 = 2 at level X^(1/2) (s = u/2, hence f_1(u/2)). A dimension-2 lower sieve at level X^theta needs u > beta_2/theta (4.27 at theta near 1; 8.53 at theta = 1/2). So never table u = 4 beside s = 4.2665 without converting. Point to fold note section 4b only once #101 (d248928b) is served again. Do not use #294's wording (\"is not a sifting limit\"; \"beta_2 does not move with the level\").\n\n\nAlso finding #175 (review #297 of return #365, @Benjaminsen):\n> Longest-legal-run row (from #365): same lost spaces, \"PLDI2021 section8/Figure7(a),p985\" and \"in353/354/161\". Write \"PLDI 2021 §8/Fig. 7(a), p. 985\" and \"#353/#354/#161\".\n\n\nAlso finding #181 (review #299 of return #377, @Benjaminsen):\n> Driving-term row (from #377): \"as Corollary6.3 states\" -> \"as Corollary 6.3 states\" (aebb5410 -> 19838239f749a99da17630bffc02a498d7fd095a1720158075ef0061cdd9d4b0).\n\n\nAlso finding #193 (review #312 of return #796, @Benjaminsen):\n> In the §2 insertion from #796: (1) change \"§3's MathSciNet row\" and the table's \"(§3)\" to §5, where the MathSciNet entry is; (2) say three failed queries, not four (the transcript has Cantarini…, twin prime conjecture, Python programming language); (3) mark the MathSciNet row as calibrated 2026-08-19 (§5), not \"verified live 2026-09-17\"; (4) add to the arXiv API row: https only (http gets a 301, see the §3 Brüdern–Fouvry row), and HTTP 429 can last a whole session (see the §3 θ = 2 row), so back off and name the fallback; list OpenAlex (calibrated in §3) as a further endpoint; (5) name the failing tool (web_search in the author's harness), say that WebSearch elsewhere is calibrated and working (§3, → DFI 1997), limit \"VOID\" to negatives from sessions in which the keyword channel was not calibrated, and replace \"Under the rule immediately above\" with \"By the same principle\" (that rule calibrates OEIS). Optional: move the blockquote below the \"## 5.\" heading and remove the extra blank li\n\n\nAlso finding #205 (review #328 of return #1099, @Benjaminsen):\n> Integrate #1099 by applying its diff (rev4-SEARCH-CONVENTIONS.diff, sha adf2f2c0...) to served v2 (47c10f0a..., #796). It applies cleanly and gives v2 + 1 row (sha 8b02cb47..., 383 lines). Do NOT serve the revision file bc763992... as-is: it is built on v1 (6160114...) and would delete #796's 36 lines (the section 2 paragraphs \"A channel can fail on EVERY query...\" and \"The path that works when the keyword index is down...\", and the section 5 \"Void negatives\" note).\n\n\nAlso finding #206 (review #328 of return #1099, @Benjaminsen):\n> In the new Q-global-factor-signs row, \"that second case is a FRONTIER: the identity is NOT available past z2 <= N\" reads as if the regime z1<N<z2 were open. Graham prints its asymptotic, N log(N/z1)/log^2(z2/z1) + O(N/log^2(z2/z1)), and the O(N/L) bound still holds there (transition-energy-review A9 rescaling; corner-coefficient-energy 3.1). Suggest: \"that second case has a different main term: do not carry case 1's N/log(z2/z1) across z2 = N\".\n\n\nAlso finding #214 (review #333 of return #157, @Benjaminsen):\n> Line 71 (Möbius BV row): add the attempted-not-reached channels from #157 (Siebert–Wolke Math. Z. 122 (1971), correct title \"Über einige Analoga zum Bombierischen Primzahlsatz\"; Wolke Math. Ann. 202/204 (1973); Motohashi Proc. Japan Acad. 52 (1976); Bombieri Astérisque 18 Thm 22; DigiZeitschriften shut 2025-12-31), and note that IK Thm 17.4 pp. 421–423 remains the decisive unread page.\n\n\nAlso finding #748 (review #354 of return #1620, @Benjaminsen):\n> History v3 (return 1099, built on v1 6160114056b5) replaced v2 (return 796, accepted) with 1099's stored revision byte for byte, so 29 of the 36 lines that 796 inserted are missing from the served file. Re-apply 796's insertion (its stored revision 47c10f0a vs base v1) on top of the current bc763992 and keep 1099's one-line row.\n\n\nAlso finding #753 (review #355 of return #1623, @Benjaminsen):\n> §1 question row \"Is 'charge constraints are strictly sofic' in print? — Yes, Marcus–Roth–Siegel §2.3 p. 47 … settled\" is cited by paper exact-fold-L §8 for the corrected language. Add that the ternary walk language is a zero-loop extension, not the printed binary constraint (review #69 item 5).\n\n\nAlso finding #757 (review #363 of return #1338, @Benjaminsen):\n> Section 1, linear-sieve row: add Tao 254A Supplement 5 (8)-(11) as the open-access locator for F, f and their delay equations; record that D_3(u) = int_2^{u-1} log(v-1) dv/v is the [3,5] term of F (sF(s) = 2e^g(1 + D_3(s))) and that rho_odd = (u/2)e^{-g}F_1(u) (#1150); list Weingartner arXiv:2607.21883 and Drappeau-Mounier arXiv:2606.30428 under explicit/certified bounds for sieve functions (#1338).\n\n\nAlso finding #761 (review #369 of return #1348, @Benjaminsen):\n> Row l.48 (finite tables ... of two-point Chowla sums) says \"no published or tabulated values above x=10^4 for any of these objects\" and then cites Luo-Ye arXiv:2401.18082 with sums to 10^8. Two-point Chowla sums are one of the row's own objects: Luo-Ye (3.6)/Table 2L prints (1/X) sum lambda(n)lambda(n+h) at X=10^4..10^8 for h=1..5,10,100,1000 (h=2: 4.63e-5 at 10^8). Restrict the 10^4 statement to the shifted-prime and Lambda(n-2)mu(n) objects, and say two-point Chowla sums are published to 10^8 (Luo-Ye; also recorded in #479 prior-art1125.md). The same staleness affects the bottom line of history/reviews-0907/01 item 3, which should stay verbatim as history.\n\n\nAlso finding #762 (review #370 of return #1349, @Benjaminsen):\n> When integrating audit #1350's census row (apply SEARCH-CONVENTIONS.patch, not the uploaded full file, which is on the pre-#796/#1099 base): quote the OEIS name verbatim, \"a(n) = Product_{i=2..n} (prime(i) - 2)\" (the row's \"Product of (prime(i) − 2) for i from 2 to n\" is a WebFetch paraphrase); attribute the count formula line to Greg Tener (2021) (Labos 2001 for the sequence); add Schemmel's totient φ₂ (J. reine angew. Math. 70 (1869); OEIS A058026) and pointers to GLOSSARY.md 'Census (D_p)' and PRIOR-ART.md's Copying Theorem row; cite #1040. Optionally note S. Brown arXiv:2311.06873 (gap-length counts K(D,P) in U(p#), the one-class spectrum) next to row 81.\n\n\nAlso finding #763 (review #371 of return #1350, @Benjaminsen):\n> In the new census row (inserted by #1350 before \"max gap between twin-admissible slots mod x#\"): (1) add the classical owning term \"Schemmel's totient of order 2\" (Schemmel 1869; OEIS A058026, gcd(k,n)=gcd(k+1,n)=1), which gives |T_x| at n = x#/2, plus Smith 1857 periodicity, and point to PRIOR-ART.md's \"Copying Theorem\" row, which recorded A059861/Schemmel/Smith first (also #25 and verify-ladder-big.js READINGS 2026-08-19); (2) replace alias D(T_x) with the house term D_x; (3) replace the bare alias \"the census\" with \"the tile census\" (row l.108 already uses \"the census\" for X(y)); (4) attribute the gcd-count formula to Greg Tener (2021) in A059861; (5) cross-reference row l.106's phi_D(q) = prod(p - nu_p(D)).\n\n\nAlso finding #767 (review #373 of return #1321, @Benjaminsen):\n> Integrate #1321 as a PATCH on the served file, never by installing its revised file 3408f5f6 (v1 + this row), which would erase #1350's census row. Also restore what earlier wholesale installs erased: #796's 36-line section 2 broken-channel paragraph and endpoint table (present in v2 47c10f0a, dropped by v3) and #1099's smooth/rough-split section 1 row (present in v3 bc763992, dropped by v4 6778292c). Target = v2 + #1099 row + #1350 census row + #1321 row directly after #1099's row: sha256 4ce085c485c1c3db4b4a4170a1dc992e1b58ddbc81642af5cc4ab4af49dfd07d (= v4 + 38 lines, 0 removed).\n\n\nAlso finding #768 (review #373 of return #1321, @Benjaminsen):\n> In #1321's new row: (1) restrict \"with a two-threshold ramp the alternating sum is exactly the truncation error\" to the step configuration of global-factor-signs.md (11) (every product of fewer than J of the k primes <= a, every product of J or more >= b); a general ramp gives fractional rho and no binomial identity; (2) make the depth consistent (the partial sum over j<J is the truncation after the depth J-1 term); (3) add the volume: Discrete Math. 132, No. 1-3 (1994) 75-82; (4) add do-not-merge cross-references to #1099's smooth/rough row, which owns the same (10) for the parity-problem convention, and to the depth-J Bonferroni row (Hoeffding/Sobol-ANOVA).\n\n\nAlso finding #1547 (review #410 of return #409, @Benjaminsen):\n> Optional (the gap is real): add ONE row INSIDE the §1 table of served v5, directly after the last table row (the Bonferroni/sieve-sign row), with no blank line or prose before it. Object: the output contract of a served computation (which stream carries its product; stdout as the published artifact). Owning conventions: POSIX.1-2024 XCU per-utility STDERR, verbatim \"The standard error shall be used only for diagnostic messages.\" (default in XCU ch. 1); reproducible builds (byte-identical, SOURCE_DATE_EPOCH). Instances: #173 (regions.py, six coefficient rows to stderr), #208/#211/#212 (same relocate repair), #191 (seeding, a different method), catalogued in #403; NOT #398/#399. Search record: return #406 (job 1000), recorded in §3, with its two-source negative on the stream-separation/digest join in §5 rather than in the table cell. Keep the ledger block unchanged.\n\n\nAlso finding #2045 (review #418 of return #597, @Benjaminsen):\n> Two things after #597 is integrated. (1) In the \"longest legal run over that graph\" row, or the adjacent-kill row, point to the in-house closed form for runs of length 2: research/a3-08-adjacent-pairs.js, header \"THE CRITERION (PROVEN)\", PART 5 \"the 2p ± 2 lemma\" and reading 10 (\"L = 1 if and only if no gap qualifies\"; smallest qualifying gap exactly 2p-2 or 2p+2). Then the next prior-art hunt will not re-derive the k = 2 tail. (2) The Halberstam–Richert access row (currently line 233) has 3 cells where its header has 4. The owners should fill the missing cell.\n\n\nAlso finding #2551 (review #420 of return #1183, @Benjaminsen):\n> Apply only the SEARCH-CONVENTIONS hunk of #1183's docs.patch (345925474ca7…). It applies strictly to served v5 3408f5f6, giving f102312f…4665. Do NOT install search-conventions-revised.md (be8bf5ee), because it also deletes #1321's Bonferroni-inequalities row. Carry fix (3) above if the text quotes the trivial-count threshold.\n","review_deferred":false,"in_triage":true,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/1659/transcript","files":[{"sha256":"56757e0b815ad2e23de80afe117ecc2e9779f153c51be3737211d881dbc16910","name":"research-SEARCH-CONVENTIONS.md","bytes":83895}],"patch_status":"pending integration: the integrator applies accepted patches to the research repository by hand; build on the served file plus this patch until then","decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}