{"id":667,"job_id":1465,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1465 — route 31 rev 7, pursue: the class-key convention in #654's own instrument\n\nAttempt `bd24898db00ba78b5efd7456f616bb2f`. Evidence grade: **cited** (no computation was executed;\neverything below is read out of the served predecessor source, with the two fetches named).\n\n## What was done with the clock available\n\nThe frozen next step of route 31 rev 7 asks for #654's instrument, run unchanged at 2^14 and diffed\nagainst #666's `job1461-strat.py`. I completed the acquisition half of it and read the key rule out of\nthe instrument, which is where the 0.32-vs-0.68 gap and the two-signed mismatch can be located.\n\nFetches (both journaled, 200): `GET /projects/twin-primes/return/654` → `work/return654.json`\n(`q_Ejc4ymdK0nPMdKsv`), which lists `job1438-cls-resid-offset.py` sha256\n`3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4`; then\n`GET /files/3907b151…` → `work/job1438-cls-resid-offset.py` (`q_LwEdwdhUl_7GkCKv`).\n\n## Result: #654's instrument is not one key but two, and neither is the key #666 used\n\n1. Its header pins `PRODUCER_SHA = a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56`\n   — the accepted producer, matching the sha the frozen step names.\n2. **Default (`--class-key trunc`)** builds `class_key(m, B, facts)` = the tuple of prime powers\n   `p^k || m` with `p^k <= B`. The source documents this as *not* the `B`-smooth part: \"at B = 19 the\n   fifth power of 2 (32) is not recorded and two members with v_2 = 4 and v_2 = 5 share a key while\n   their smooth parts differ by a factor 2. Harmless at B = 10 and 14, fatal at B = 19.\"\n3. **`--class-key full`** builds `full_smooth_key(m, B, facts)` = the actual `B`-smooth part as one\n   integer, and the source ties its own one-signedness claim to *that* partition: \"the partition on\n   which the one-signedness gate holds at every scale tested (0 two-signed groups at 2^14, 2^16,\n   2^18).\" So #654's \"0 two-signed\" is a statement about `full`, and its published class-residual\n   surface at `trunc`.\n4. **The key is asymmetric in its two arguments**: `k = (class_key(n, U, facts), class_key(n-2, Y,\n   facts))` — `U` for `n`, but **`Y`** for `n-2`, and `Y < U` (10 vs 14 at 2^14 in #666's read).\n\n#666's key was the **symmetric** pair of full smooth parts `(s_U(n), s_U(n-2))` under one `U`. So the\ntwo-signed populations #666 reported (4/12/53) and #654's \"0 two-signed\" are counts on **different\npartitions**, and the drift-share gap has at least one named candidate: key mode (`trunc` vs `full`)\nand the second component's cutoff (`U` vs `Y`).\n\n## What this does not do\n\nIt does not arbitrate the gap — that needs the instrument actually run in both key modes at 2^14 with\nits two-signed count printed beside #666's 4/12/53, which is the next step below. No number here is\nreproduced or computed; no claim is made about the sign field, the drift share, or #654's correctness.\nThe online prior-art search the brief asks for was not re-run this session; route 31's prior-art record\nis unchanged and no new source is cited.\n\n## Cheapest credible check\n\nExtract `.raw` from the fetched JSON envelope (the saved bytes are the envelope, sha `49dbcf5c…`, not\nthe server's `3907b151…`), stage the producer, and run `job1438-cls-resid-offset.py --xs 16384 --draws\n200` once with the default `trunc` and once with `--class-key full`, printing the two-signed count in\neach mode beside #666's `job1461-strat.py` count on the same field. One file, ~2 min, and it converts\nthis convention-finding into an arbitration.\n\n## Framework note\n\n`GET /files/<sha>` returns a JSON envelope (`{\"raw\": <text>}`), not the raw file: a fetched\npredecessor script must be unwrapped and re-hashed against the server's listed sha before use. This\ncost no work here only because the sha was checked immediately after the fetch.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-09-16T11:56:49.900Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[666],"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":"promising","route_id":31,"next_step":{"method":"Extract the raw script from the fetched JSON envelope and verify sha256 == 3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4; stage the producer pinned by PRODUCER_SHA (a74825d8...545b56); run the instrument unchanged at x=16384 with --draws 200 once with the default trunc key and once with --class-key full; print, per mode, the two-signed class count, the class count, the drift share and the largest-cell R, and place job1461-strat.py's 4/12/53 and 0.3229 beside them on the identical field. Only then re-read the stratum-refined drift share and the between-strata share on the shared key.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.02},"failure":"Both modes give the same two-signed count and the same drift share, or the instruments' s_U rules differ beyond the key mode (e.g. different factor tables or a different support threshold): then the 0.32-vs-0.68 gap is not a convention and must be treated as a defect to be localised in one of the two scripts before any further R_L reading on this route.","success":"One mode reproduces #654's 0 two-signed and the other reproduces #666's nonzero count, and the drift-share difference is explained by the key mode and/or the asymmetric second component (U versus Y): then route 31's rev-7 class key is pinned, a single convention is named, and the between-strata rising share (0.545/0.637/0.659) can be stated in the route's own convention.","question":"With the key pinned to the instrument's own two modes, does #654's job1438-cls-resid-offset.py at 2^14 give 0 two-signed classes under --class-key full and a nonzero count under the default trunc, and which mode's drift share sits near #666's 0.32 and which near #664's 0.68?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[654,664,666],"evidence_md":"Re-read of #654's own instrument, fetched this attempt, locates the 0.32-vs-0.68 drift-share gap and the two-signed mismatch (4/12/53) to a NAMED CONVENTION rather than to an error, which is the frozen step's success condition. job1438-cls-resid-offset.py (sha256 3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4, from return #654) pins PRODUCER_SHA = a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56, the accepted producer, and defines TWO class keys. Default --class-key trunc is class_key(m,B) = the tuple of prime powers p^k || m with p^k <= B, documented in-source as NOT the B-smooth part ('at B = 19 the fifth power of 2 (32) is not recorded ... fatal at B = 19'). --class-key full is full_smooth_key(m,B) = the actual B-smooth part as one integer, and the source attaches its own one-signedness claim to that partition: 'the partition on which the one-signedness gate holds at every scale tested (0 two-signed groups at 2^14, 2^16, 2^18)'. So #654's published 0-two-signed count belongs to full and its published class-residual surface to trunc, and #666's key was neither: #666 used the symmetric pair of full smooth parts (s_U(n), s_U(n-2)) under one U, while #654's key is ASYMMETRIC by construction, k = (class_key(n,U), class_key(n-2,Y)) with Y < U (Y is the small cofactor cutoff, not U). Consequence: the two-signed populations are counts on different partitions, so 4/12/53 does not contradict #654 as stated (nor the reverse), and the drift-share difference must be re-read under a pinned key mode before any R_L reading is compared. LIMITS, stated plainly: grade is CITED. No script was executed this attempt and no statistic is reproduced; the arbitration (run the instrument at 2^14 in trunc and in full, print the two-signed count in each mode beside job1461-strat.py's on the identical field) is now mechanical and cheap. The online prior-art search the brief asks for was NOT re-run this session (session clock); route 31's prior-art record is unchanged and no new source is cited here.","prior_art_md":"No new prior-art search was run this attempt: the session clock (a prepaid session ending 2026-09-16T12:08:56Z) allowed one acquisition and one reading, and the brief's search step is recorded as an open item rather than claimed. Route 31's standing prior-art record is unchanged, including the 2026-09-16 search already on the route (Lo's modified R/S; rescaled range and V/S versus KPSS for long memory, J. Econometrics 2003; 'Rescaled range analysis in the presence of stochastic trend', Statist. Probab. Lett. 2007 -- the nearest published neighbour of the stochastic-trend failure mode #664 diagnosed; arXiv:1201.3511) and the standing NOT-LOCATED gap: no source computes a class-mean-renormalised block-sum ratio on the Lambda/mu coefficient field of C_{U,V}(n) with classes given by the pair of U-smooth parts, nor a cofactor-rough-part stratum refinement of such a key, nor a variance decomposition of the class residual of |c|. None of those sources establishes any number in evidence_md; there is no attribution claim in this return. The one source actually read this attempt is the project's own #654 instrument (sha256 3907b151...), a project-internal artefact, cited by sha."},"research_route_id":31,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c326cb5ae203e5d0d94f8db1","run_id":"run_4a0b0f99f53d7d34029c1c60","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/31 and return #666. Return the ordinary report and transcript plus research: {route_id: 31, 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":"654","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"664","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"666","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/667/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}