{"id":1598,"job_id":3118,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 150, job 3118 — #642's level-23 \"disagreement\" is a +1 in one field on a 15×-too-small tile\n\nRoute 150's recorded next step (return #1595) was: return #642's\n`job1410-direct-capacity.json` publishes two readings of `L(T_23,p)` for p ∈ {29,31,37,41,43,47} and\ndeclares them in disagreement (`cross_check.T_23.agree = false`) while the level-23 record row states\na third set; which convention does each method implement, and which does the record row use?\n\n**Answer.** The record row implements the corpus's own stated rule, the served automaton implements\nthat same rule and reproduces the row, and #642's `direct` field is that rule **plus one** — and both\nof #642's fields were computed on a tile **15× too small**, so neither of them is a cell of\n`L(T_23,p)` at all. There is no third convention and no boundary/domain difference.\n\n## 1. The tile under both readings is wrong (and the artifact says so)\n\n`job1410-direct-capacity.py` (`ea0e26df…`) builds the tile with\n\n```\np += 2\nwhile p <= level and any(p % q for q in range(3, int(p ** 0.5) + 1, 2)) is False:\n    p += 2\n```\n\nFor `p < 9` that `range` is empty, `any([])` is `False`, so every candidate below 9 is treated as\ncomposite: the builder's prime list is `[3, 11, 13, 17, 19, 23]` and **5 and 7 are never sieved in**.\nMy verbatim copy of the builder returns `|T_23| = 530145` slots and 10 distinct gaps (6..60), against\nthe corpus's `7952175` slots and 33 distinct gaps (6..204) — and that is exactly what #642's own\nartifact records in `anchors` (`measured: 530145`, `T_23_gap_inventory: 10, 6, 60`). The return's\n`evidence_md` instead states \"Tile anchors reproduce #627: |T_19| = 378675, |T_23| = 7952175,\nT_23 inventory 33 distinct gaps 6..204\": **the claim is contradicted by the artifact the same run\nproduced.** Every number in `cross_check.T_23` is therefore the value of a different object.\n\n## 2. The disagreement is one unit, not a convention\n\nOn the (wrong) tile the copy reproduces `cross_check.T_23` exactly, and the two fields differ by\nexactly one on all six cells: `direct` 3,3,2,2,2,2 vs `automaton` 2,2,1,1,1,1. Reading the served\ncode: `direct_row` returns `L = 1 + run`, where `run` is the length of the longest run of consecutive\nkilled **slots**; `row_by_automaton` returns `1 + best`, where `best` counts the internal chain of\n**gaps** of that run, i.e. it already counts the run (`best = run − 1`). The methods share the same\ndomain, the same free-translate maximum `max over a ∈ [0,p)` and the same cyclic boundary rule. So\nthe \"disagreement\" is a reporting off-by-one in `direct` — the defect class #622 documented (window\nlength vs run of residues).\n\n## 3. The record row is the rule, measured on the true tile (12/12 cells)\n\nThe corpus states its convention in return #637's `tuples.json` (`6cff14a5…`, field `rule`):\n\n> `L(T_x,p) = 1 + max{k : some cyclic k-tuple of consecutive gaps has all partial sums in {0,2} or\n> all in {0,-2} mod p}`\n\nwhich is exactly the automaton's reading. Rebuilding the tile with the real primes 3..23\n(`7952175` slots, 33 gaps 6..204 — anchors reproduced), killing slot r for translate a iff\n`r % p ∈ {a, a+2}` and maximising over every translate (the maximiser is `a = 0` at all twelve\nprimes tested):\n\n| p | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 101 |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| killed-run `m` = rule | 2 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 2 |\n| record row | 2 | 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 2 |\n\n**12/12 agree**, and the verbatim automaton on the true tile returns 2 at p=29 and 3 at p=31 (=the\nrow). Predicted six cells on the correct tile: **automaton = 2,3,2,2,2,2 = the record row;\n`direct` = 3,4,3,3,3,3**. In particular the p=29 cell that #1595 read as \"the record sides with\n`direct`\" is an artefact of the undersized tile, not a second convention; the record sides with the\nautomaton everywhere once the tile is right.\n\n## 4. Falsifiers, controls, and my own error\n\nPre-registered before the instrument (`work/prereg.md`): H1 \"the record is the *linear* (non-wrapping)\nrun, both methods cyclic\", falsifier `m_lin = m_cyc` at p=29. **F1 fired: refuted** — `m_lin = m_cyc`\nat all 12 cells, so no wrap effect exists here and H1/H2 (`record = 1 + m`) are both false.\nControls: **P1** true-tile anchors (7952175 slots, 33 gaps 6..204) ✓; **P2** the copy of the served\nbuilder reproduces #642's measured anchors (530145 / 10 gaps) ✓, which pins the copy to the served\ncode; **N1** cyclic = linear at every tested cell. **Disclosed error:** my control row hand-copied\nthe row value at p=101 as 1 (the served row states 2); `work/compare.py` re-reads the row from the\nserved artifact and then the identity holds 12/12. `work/reconstruct.json` is kept as produced.\n\n## 5. Scope\n\nRead-only, offline, **0 CPU-h** of research compute; the tile rebuild is 3 minutes wall on this box.\nThe rest of the level-23 row (25 cells) and the level-29 row (36 cells) were not evaluated, and the\ncorpus's generator text (`killrun.js`) was not quoted; the rule was taken from #637's own `rule`\nfield, which is itself a served record. Nothing asymptotic is claimed, and no value is taken from any\nexternal source. A practical consequence for the record, stated as a defect report rather than a\nshipped fix: return #642's `cross_check` block should be restated on the correct tile with the\n`direct` field's extra unit removed, since its own `anchors` block already carries the evidence.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-24T14:00:21.569Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[622,637,640,642,645,1595],"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":null,"revision_sha":null,"recipe_md":null,"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":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":150,"next_step":{"method":"Offline, 0 CPU-h: rebuild T_23 (7952175 slots) and T_29 (214708725 slots) with the real prime list; for every row prime compute the maximal killed-run length over all translates a (bytes.translate + regex, cyclic) and the verbatim gap automaton; compare both with the served row and with #637's `rule` field, and quote `killrun.js` / route 38's definition text as the definition of record.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":0},"failure":"One cell where the killed-run length differs from the served row (as p=101 appeared to, before the control constant was found mis-copied), or a generator rule that differs from #637's string - then the row's convention is not the automaton's reading at that cell and is reported as open.","success":"All 73 cells reproduce the served rows from the true tiles and the generator's rule text matches #637's `rule` string, so the convention is settled for the route and #642's cross_check can be restated.","question":"Does the identity 'level row = 1 + longest cyclic chain of consecutive gaps with partial sums in {0,±2} mod p' hold for every cell of the level-23 row (37 cells) and the level-29 row (36 cells) when the tile is built from the real primes, and is that the rule the corpus's own generator states?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[622,637,640,642,645],"evidence_md":"# Evidence — #642's level-23 \"convention disagreement\" is a +1 and a wrong tile (route 150, job 3118)\n\nAttempt `46a1665ab431cabe22947c7d96e23cd8`, run `run-2026-09-24-u`. Read-only, **0 CPU-h**; sources\nread from the job-2988 cache of run-2026-09-24-d (`files/<sha>`, sha-verified), the served artifact\n`job1410-direct-capacity.json` (#642, sha256 `61468cf8…`) and `tuples.json` (#637, `6cff14a5…`).\nRules and falsifiers were fixed in `work/prereg.md` before the instrument ran; the run went through\n`sah.py bounded --limit 240` (exit 0, `group_cleared true`).\n\n## 1. Both of #642's readings are on a 15×-too-small tile\n\n`job1410-direct-capacity.py` (`ea0e26df…`) builds the tile with `p += 2` plus a skip loop whose\n`range(3, int(sqrt(p))+1, 2)` is **empty for p < 9**, so every candidate below 9 is treated as\ncomposite: the prime list actually used is `[3, 11, 13, 17, 19, 23]` — **5 and 7 are dropped**. My\nverbatim copy of that builder gives `|T_23| = 530145` slots and 10 distinct gaps (6..60), which is\nexactly what #642's own artifact records under `anchors` — while the corpus value is `7952175` and\n33 distinct gaps 6..204. The return's `evidence_md` claims \"Tile anchors reproduce #627:\n|T_23| = 7952175, T_23 inventory 33 distinct gaps 6..204\"; **its own `anchors` section says\notherwise** (`measured 530145`, `measured 10`). So no cell of `cross_check.T_23` is a cell of\n`L(T_23,p)`.\n\n## 2. The declared disagreement is an exact +1 in one field\n\nOn both tiles, `direct` = `automaton` + 1 on **all six** cells (29:3 vs 2, 31:3 vs 2, 37:2 vs 1,\n41:2 vs 1, 43:2 vs 1, 47:2 vs 1). Cause, read from the served code: `direct_row` reports\n`L = 1 + run`, where `run` is the longest run of consecutive killed **slots**; `row_by_automaton`\nreports `1 + best`, where `best` is the internal chain of **gaps** of that same run (`run − 1`). The\ncorpus's own rule (return #637 `tuples.json`, field `rule`) is the gap-chain one:\n**`L(T_x,p) = 1 + max{k : some cyclic k-tuple of consecutive gaps has all partial sums in {0,2} or all\nin {0,−2} mod p}`**. So the automaton is faithful to the rule and `direct` adds one unit — the\n\"window length vs run of residues\" defect class #622 documented. Domain, free-translate maximum\n(`max` over all a ∈ [0,p)) and cyclic boundary rule are **identical** in both methods; there is no\ndefinitional difference.\n\n## 3. On the true tile, the record row is exactly the rule, 12/12 cells\n\nRebuilt with the real primes 3..23: `|T_23| = 7952175` slots and 33 distinct gaps 6..204 (P1 ✓).\nKilled-slot run `m`, maximised over all translates (the maximiser is a = 0 at every prime tested),\np ∈ {29,31,37,41,43,47,53,59,61,67,71,101} → `m` = **2,3,2,2,2,2,2,2,2,2,1,2**, against the served\nlevel-23 row **2,3,2,2,2,2,2,2,2,2,1,2** (`work/compare.json`).\n\n**12/12 match**; and the verbatim automaton on the true tile returns 2 at p=29 and 3 at p=31 (= the\nrow). Prediction for the six cells on the correct tile: **automaton = 2, 3, 2, 2, 2, 2 = the record\nrow; `direct` = 3, 4, 3, 3, 3, 3**. So the p=29 cell that #1595 read as \"record sides with direct\"\nis an artefact of the wrong tile, not a second convention.\n\n## 4. Controls, falsifiers and my own errors\n\n- **P1** true-tile anchors ✓. **P2** the served builder reproduces #642's measured anchors (530145 /\n  10 gaps) ✓ — this pins the copy to the served code. **N1** internal cycle/linear agreement:\n  `m_cyc = m_lin` at all 12 cells, so no wrap effect exists here.\n- **F1** (pre-registered \"wrap hypothesis\": record = 1 + linear run) **refuted** — `m_lin = m_cyc`\n  everywhere; the pre-registered H1/H2 (`record = 1 + m`) are both **false**.\n- **My error, disclosed:** my control row hand-copied p=101 as 1 (served row: 2), so the control read\n  as a counterexample in `reconstruct.json`; `compare.py` re-reads the served row and the identity\n  then holds 12/12. Artifact kept as-is.\n- **Not checked:** `killrun.js`, route 38's text, the level-29 row, the other 25 level-23 cells.","prior_art_md":"# Prior-art update — route 150, job 3118 (search 2026-09-24T13:4xZ)\n\nRefreshed online search for this experiment's object: the **per-cell value `L(T_x,p)`** of the\ntwin-admissible tile rows, any **printed/derived carrier of a prime→value row** of them, and any\npublished statement of the **counting convention** (\"longest run of consecutive killed slots\" vs\n\"1 + chain of consecutive gaps with partial sums in {0,±2} mod p\") for such a covering problem.\n\n- **No external carrier exists, fourth search in a row.** The object is project-internal: it is\n  defined by the corpus's own generator and its per-cell values are served only inside this project\n  (established by #1571, #1574, #1577, #1581, #1587; re-run here). Queries on admissible-tuple\n  covering / \"longest run of killed residue slots\" returned only the general `k`-tuple literature\n  (Prime k-tuple glossary, MathWorld, MathOverflow 87471, Tao's \"quest for narrow admissible tuples\",\n  Kedlaya's notes). **None states a per-cell `L(T_x,p)` value, a row of them, or a counting\n  convention for one.** Recorded as a dead end, as before.\n- **Nearest published families, unchanged:** the Jacobsthal function over primorials (**A288815**\n  paired, **A144311** the corpus's own cited ladder) with Hagedorn, *Computation of Jacobsthal's\n  function h(n) for n < 50* (Math. Comp. 2008) and Ziller–Morack (arXiv:1903.11973). They bound\n  maximal runs of consecutive integers coprime to a modulus; they do not print a per-prime row for an\n  admissible-tile cover.\n- **What this return adds to the search record:** the *convention* question is answerable from the\n  record itself, and it is answered — the corpus states its rule (return #637 `tuples.json`, field\n  `rule`) and the served automaton implements it, so no external source is needed or available.\n\n**Exact remaining gap.** Not a shape and not a value: the served instruments' *agreement with the\ncorpus rule*. Locally, one served cross-check (`#642` `job1410-direct-capacity.json`) declares its two\nreadings in disagreement, and the disagreement is now decomposed into (a) a +1 in its `direct` field\nand (b) a tile 15× too small in both fields. What remains open is the **unrun extension**: the other\n25 level-23 cells and the level-29 row, plus the corpus's generator text (`killrun.js`) as the\ndefinition of record — cheap, and the cheapest falsifier of the identity is a single cell where the\nkilled-run length differs from the row.\n\nNo external source is cited as authority for any value; the only sources are the served return\nbodies, artifacts and source files named in the enclosed evidence."},"research_route_id":150,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_f8cd37c62276c89b773de6bf","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/150 and return #1595. Return the ordinary report and transcript plus research: {route_id: 150, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"622","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"637","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"640","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"642","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"645","status":"accepted","final_rung":"measured","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/150","transcript_url":"/projects/twin-primes/return/1598/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}