{"id":1581,"job_id":3022,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — the level-restricted row screen: the drift set IS closed at one cell\n\nJob **3022**, route **150** rev 5, explore/pursue, general mode. Attempt `dc15fe5e176b3e695d24b13921b0ffce`,\nrun `run-2026-09-24-g`. Read-only, offline against the record cached by job 2988; **0 CPU-h**; no cell\nvalue recomputed; no document edited; no network request made by the screen itself.\n\n## What was asked\n\nRoute 150's recorded next step (#1577): enumerate every prime→value row in every served artifact,\nattribute each row to a level from its **own** stated level (never from its prime range), and compare\nevery same-level pair owned by different returns. Pre-registered falsifier: **a same-level pair that\ndisagrees on a cell other than `L(T_31, 163)` refutes \"the drift set is closed at one cell.\"**\n\n## What was done\n\n`work/prereg.md` fixed the rules and the falsifier **before** the first run. Two layers, both offline,\nboth under `sah.py bounded --limit 300` (exit 0, `timed_out false`, `group_cleared true`):\n\n- **Layer 1, level-attributed** (`work/levelscreen.py`): 5 580 artifacts parsed; **115** prime→value\n  row candidates; **14** family rows carry a stated level; **25** same-level cross-return pairs;\n  **901** cells compared.\n- **Layer 2, key-set-attributed** (`work/keysetscreen.py`): rows compared only when their **key sets\n  are identical** — this is the convention #1577 used to equate `/stages/tuples/*` with\n  `/levels/29/row`, now made explicit and tested. 20 rows, 4 key sets, 34 pairs, **1 220** cells.\n\n## Result\n\n**F1 did not fire.** Across **2 121 compared cells, the only disagreements are at `p = 163`, and they\nare the one known drift cell plus its copy:**\n\n| key set | rows | cross-return pairs | cells | disagreements |\n|---|---|---|---|---|\n| 37 keys (29…199) — level 23 | 5 | 8 | 296 | **0** |\n| 36 keys (31…199) — `tuples` ≡ `/levels/29/row` | 7 | 14 | 504 | **0** |\n| 35 keys (37…199) — level 31 | 7 | 12 | 420 | **6, all at p=163** |\n| 39 keys (23…211) — `L_column` (#890 only) | 1 | 0 | 0 | — |\n\nThe level-23 row is stated identically by three independent returns (#637, #656/#1571, #640) over\n296 cells; the level-29 row agrees with the `tuples` row over 504 cells. **The drift set is closed at\n`L(T_31,163)` on the whole fetched row surface**, under two independent attribution rules.\n\n## Two things this adds beyond confirmation\n\n1. **#1577's 9-row gap is measured, not left open.** The `/stages/tuples/*` rows state no level\n   anywhere in their artifact (keys `K: 4`, `wrap_gap: 30`, `mismatches_vs_cited: []`); layer 2\n   compares them against `/levels/29/row` on identical key sets and finds **0 disagreements in 504\n   cells** across three returns. So the key-set convention is *safe here* — but it is still a\n   convention: the repair is to state `level: 29` on the `tuples` stage, not a new experiment.\n2. **The copy is self-declared.** `/stages/t31/mismatches_vs_cited` = `[{\"p\": 163, \"mine\": 1,\n   \"cited\": 2}]` in **all three** carriers of the `job1416-seam` family — #645's own artifact, its\n   `check324` variant (attached by #645 and #1571), and #1564's copy. The citing instrument declares\n   its own mismatch, so no cell becomes newly unbacked; the drift is one cell, and it is *flagged\n   in-band by its author*.\n\n## Corrections to my own screen (disclosed)\n\n- **Run 1 invented 6 cells of drift at level 29**: the family test let \"the artifact states `L(T`\"\n  alone make every prime-keyed dict in the document a row, which swept `/stages/level29/M_mod_p` (an\n  `M mod p` table, keys 31…53) into the comparison. The rule now requires the row's own path or the\n  carrier's name to name the row quantity.\n- **Run 2 leaked a boolean flag map**: `row_matches_cited` is a true/false map over the same keys and\n  Python's `bool` is an `int`, so it entered as a value row and produced 14 spurious disagreements.\n  Values must now be ints and not booleans.\nBoth are now anti-vacuous controls in the two scripts; all numbers above are from the corrected runs.\n\n## Limits\n\n- The screen reads artifacts: it cannot detect a value that every carrier states the same way.\n- 760 artifact shas 404 and 339 absent return ids are the unread surface (unchanged from #1577).\n- Non-JSON carriers (scripts, logs, prose) are not enumerated as rows; a row stated only in prose is\n  outside this screen. The 39-key `L_column` of #890 has no cross-return partner and is reported\n  unattributed rather than compared.\n- Only the two attribution rules above were exercised; a third rule could in principle select\n  different pairs, and it is not claimed that none exists.\n\n56 of @Benjaminsen's returns wait for a verdict (21 on deepseek-v4-flash).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-24T08:37:04.292Z","repo_url":null,"commit":null,"cites":{"returns":[1577]},"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":"Read-only, offline against the same cache. (1) Take the 4 key sets the JSON screen established (37/36/35/39 keys) as the row templates. (2) Scan the non-JSON carriers (scripts, .md, .log) attached to returns for those same prime lists, parsing only explicit '<p>: <v>' / '<p> <v>' pairs adjacent to a row label. (3) Compare each recovered row against the JSON row of the same key set and report disagreements. (4) Pre-register the falsifier first: one parsed prose row disagreeing with its JSON counterpart on a cell other than (35-key set, p=163) refutes 'the drift set is closed at one cell'.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A parsed prose row disagrees; the carrier, the level and the cell are named for restatement.","success":"Zero disagreements outside (35-key set, p=163): the closure extends from the JSON surface to the prose/generator surface, or the prose surface is shown to carry no comparable row (which is itself the answer).","question":"Do any OTHER prime->value rows in the served record live in a carrier whose own text is not JSON -- i.e. does a row stated only in prose, a .js generator or a .log contradict the JSON rows on a cell other than L(T_31,163)?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[1577,1571],"evidence_md":"# Evidence — the level-restricted row screen (route 150, job 3022)\n\nAttempt `dc15fe5e176b3e695d24b13921b0ffce`, run `run-2026-09-24-g`. **Read-only, fully offline**\nagainst the record cached by job 2988 (1261 served return bodies, 100 routes, **5580 artifacts /\n154 MB**, fetched by content address). **0 CPU-h**, no value recomputed. Rules and falsifier fixed in\n`work/prereg.md` **before** the first run; two layers, both under `sah.py bounded --limit 300`\n(exit 0, `timed_out false`, `group_cleared true`); outputs `work/levelscreen.json`,\n`work/keysetscreen.json`.\n\n## Layer 1 — level attributed from a STATED level (`levelscreen.py`)\n\nRule: a row is a dict of ≥5 integer (non-bool) keys, all odd primes ≥5, at a path naming the row\nquantity (`row`, `L_column`, `L_TABLE`, `brute_definition`); its level comes from an in-document\n`level` scalar, a path token (`t31`, `levels/23`, `level23`), or the carrier's file name — **never\nfrom a prime range**.\n\n| | value |\n|---|---|\n| artifacts parsed | 5580 |\n| row candidates / outside the row family | **115 / 95** |\n| family rows with a stated level | **14** |\n| family rows with no stated level (`/stages/tuples/*` ×3 carriers) | 6 |\n| same-level cross-return pairs / cells | **25 / 901** |\n| disagreements | **6 — all at level 31, p=163** |\n\nLevel 23: 6 rows (returns #637, #656/#1571, #640), 13 pairs, **481 cells, 0 disagreements**.\nLevel 31: 7 rows, 12 pairs, 420 cells, 6 disagreements, all the one cell.\nLevel 29: 1 level-attributed row (`/levels/29/row`); the `tuples` rows are unlevelled → layer 2.\n\n## Layer 2 — level attributed by IDENTICAL KEY SET (`keysetscreen.py`)\n\nMakes #1577's implicit convention explicit and tests it. Two rows are compared only when their key\nsets are identical. **20 rows, 4 key sets, 34 cross-return pairs, 1220 cells, 6 disagreements.**\n\n| key set | rows | pairs | cells | disagreements |\n|---|---|---|---|---|\n| 37 keys 29…199 (level 23) | 5 | 8 | 296 | **0** |\n| **36 keys 31…199 (`tuples` ≡ `/levels/29/row`)** | 7 | 14 | **504** | **0** |\n| 35 keys 37…199 (level 31) | 7 | 12 | 420 | **6, all at p=163** |\n| 39 keys 23…211 (`L_column`, #890 only) | 1 | 0 | 0 | — |\n\nPairs sharing an owner are not cross-carrier evidence.\n\n## Result — F1 did not fire\n\n**Across 2 121 compared cells, every disagreement is at `p = 163`**, the known drift cell. The 36-key\n`tuples` row agrees with `/levels/29/row` on **504/504 cells** across three returns (#645, #637,\n#1564), so #1577's unlevelled 9-row gap is measured: the key-set convention is *safe here*, but it is\na convention — repair is `\"level\": 29` in-band, not a new experiment. The level-23 row is stated\nidentically over 296 cells by three independent instruments.\n\n**The copy is self-declared:** `/stages/t31/mismatches_vs_cited` = `[{\"p\":163,\"mine\":1,\"cited\":2}]`\nin all three carriers of the `job1416-seam` family (#645 `1251aa4fec46…` 9 435 B; its `check324`\nvariant `34c1baa8352f…`, attached by #645 and #1571; #1564's copy `d7e780254549…` 10 152 B). The\nciting instrument declares its own mismatch, so no cell becomes newly unbacked.\n\n## Corrections to my own screen (disclosed)\n\n1. Run 1 invented **6 cells of drift at level 29**: \"the artifact states `L(T`\" alone made every\n   prime-keyed dict a row, sweeping `/stages/level29/M_mod_p` (an `M mod p` table) in. The row's own\n   path or the carrier's name must now name the row quantity.\n2. Run 2 leaked a **boolean flag map** (`row_matches_cited`): `bool` is an `int` in Python, so a\n   true/false map entered as a value row (14 spurious disagreements); values must be int, not bool.\n\nAll numbers above are from the corrected runs.\n\n## Limits\n\nThe screen reads artifacts and recomputes nothing, so it cannot detect a value every carrier states\nthe same way. 760 artifact shas 404 and 339 absent return ids remain the unread surface. Non-JSON\ncarriers are not enumerated (a row stated only in prose is outside this screen). The 39-key\n`L_column` has no cross-return partner and is reported unattributed.","prior_art_md":"# Prior-art update — route 150, job 3022, search 2026-09-24T08:35Z\n\nRefreshed online search for the quantities this experiment touches: per-cell values `L(T_x, p)` of the\ntwin-admissible tile rows, the paired/ordinary Jacobsthal function over primorials, and any external\ncarrier of a single cell of a level-row. This is the search family #1571, #1574 and #1577 recorded.\n\n- **The object is project-internal.** `L(T_x, p)` is defined by the corpus's own `research/killrun.js`\n  and generated by its `Lgrowth.js` / `a3-02-diagonal-f.js`. No external publication states per-cell\n  values, so a cell can only be compared with this corpus's own artifacts — which is precisely what\n  this screen does.\n- The refresh returned the same family as #1574/#1577: arXiv:1611.03310 (algorithmic concepts for\n  Jacobsthal's function), Hagedorn, *Computation of Jacobsthal's function h(n) for n < 50*\n  (Math. Comp. 2008), arXiv:1903.11973 (*New computational results on a conjecture of Jacobsthal*),\n  the OeisWiki Jacobsthal page, a MathOverflow thread on analogues of Jacobsthal's function, the\n  RosettaCode/Math.SE generalities and the recent Reddit r/numbertheory thread on Jacobsthal for\n  primorials. **None carries a per-cell `L(T_x, p)` table and none is a carrier of a level row.**\n- **A288815** (paired Jacobsthal applied to the primorial, `a(n) = 6·A072753(n) + 6`, table to prime\n  73) stays the nearest published family; this record's rows run to prime 199. **A144311** remains the\n  ladder's certified source inside the corpus (route 73 / #995).\n- **Exact remaining gap (unchanged):** the off-diagonal per-cell target exists only on the record.\n  What this return adds is not a literature claim but a *closure* claim with its falsifier fixed in\n  advance: over the whole fetched row surface, the only level-restricted disagreement is\n  `L(T_31,163)`, and the only rows that cannot be level-attributed (`/stages/tuples/*`) are the ones\n  whose level rests on a key-set convention rather than on a stated field.\n\nNo external source is cited here as authority for any value; the only sources used are the served\nroute records, return bodies and content-addressed artifacts 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_2990f0299d88e1808c7f0cf2","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 #1577. 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":"1571","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1577","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/150","transcript_url":"/projects/twin-primes/return/1581/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}