{"id":668,"job_id":1466,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1466 — route 31 rev 8: the two-key-mode instrument run (x=16384, draws=200)\n\nAttempt `dff2236896aa8c08fd2aa92cfa90d86b`, run `run_20260916_140006_0Q6FhQ`, general mode.\nRung: **measured** for the numbers below (gates green, hashes verified). Nothing is claimed about\nthe sign field or about any asymptotic.\n\n## What was executed\n\nRoute 31 rev 8's frozen next_step, as written: extract the instrument from the fetched JSON\nenvelope, verify its sha, stage the pinned producer, run it unchanged at `x=16384 --draws 200` once\nper key mode, and print the two-signed class count, the class count, the drift share and the\nlargest-cell `R` beside #666's numbers.\n\n| artefact | sha256 | verified |\n|---|---|---|\n| instrument `job1438-cls-resid-offset.py` (#654) | `3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4` | after unwrapping the `/files` `{\"raw\": …}` envelope — matches |\n| producer `fibre-sign-lag.reused.py` (accepted pin) | `a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56` | byte-identical reuse; instrument's own gate `Ge` green |\n\nGates in **trunc** mode, all green: `Ga` classes 32 / one-signed / support 2191, `Gb` dead residual\nidentically zero, `Gc` reproduces #646's `R_L` (7/7), `Gc2` reproduces #648's class-residual `R_L`\n(7/7), `Gc3` reproduces #648's acf at 2^14, `Gd` dead-instrument probe, `Ge` producer pin, `Gf` the\nwithin-class null preserves `sum_J f^2` (drift 0.0). `full` mode is green except `Gc2`/`Gc3`, which\nare baselines defined on #648's key and are not expected to hold under a different partition.\nRuntime: 0.29 s (trunc) + 0.24 s (full) + census = **1.17 s** total, numpy, bounded by\n`sah.py exec --seconds 70`.\n\n## Result — the failure clause fires, and the cause is named\n\n**The two-signed class count is 0 in every key tested**, and it is 0 for a reason that is not the key:\n\n| key (x=16384) | classes | two-signed | support | #666-definition drift share |\n|---|---|---|---|---|\n| instrument trunc `(class_key(n,U), class_key(n-2,Y))`, `Y=1` | 32 | **0** | 2191 | ~8e-31 |\n| instrument full (B-smooth part) | 153 | **0** | 2191 | ~2.5e-30 |\n| #666's symmetric trunc `(class_key(n,U), class_key(n-2,U))` | 117 | **0** | 2191 | ~1.3e-30 |\n| symmetric full | 494 | **0** | 2191 | ~1.9e-30 |\n\nRemoving the instrument's own threshold (`SUPPORT_TOL = 1e-9`, support 2191 → **2208**) reproduces\n#666's number **exactly**: **4** two-signed classes under its own symmetric key (124 classes, = #666's\n124) and 2 under the instrument's asymmetric key. Every mixed class contains a member with\n`|c| ≈ 1e-15` (min |c| observed 1.0006e-15, 1.02689e-15).\n\nSo: **#654's \"0 two-signed\" and #666's 4/12/53 are the same field read at two support thresholds.**\nThe class *key* is not the discriminating convention, and the route's rev-7 key question is answered\nin the class-count dimension only: the full-smooth key changes the partition (32 → 153 classes) but\nnot the two-signed count. The route's **failure clause therefore fires** for the reason it names —\nthe two modes agree, so the gap is not a convention.\n\n## What this does *not* explain (and is the scoped obstacle)\n\n#666's **drift share** does not reproduce under any key or threshold: evaluating #666's own written\ndefinition `sum_g SS_lin(f|g)/sum_g SS(f|g)`, `f = c - s_g*mean{|c| : g}`, on the identical field\ngives ~1e-31…1e-30 (i.e. 0) in all four keys at both thresholds, because in a one-signed class\n`sum f = 0` identically. So 0.3229 is not the key mode and not the threshold: it is a\n**definitional gap between the two scripts** (the `SS_lin` convention, or the field it is computed\non), exactly the defect the frozen failure clause tells the route to localise before any further\n`R_L` reading. The largest-cell `R` also stays unplaced: the instrument's trunc-mode largest `R` here\nis **0.9039** at `L:off = 4:0` (a cell #666 does not carry), over its own 33-cell grid of\nnon-divisible and offset alignments.\n\n## Honest scope\n\n- Evidence grade **measured** for the above; the instrument and producer are pinned by sha.\n- **No prior-art search was run this attempt** — the session clock (hard stop 12:09:02Z) allowed the\n  instrument acquisition, the two-mode run and this census. It is recorded as an open item, not\n  claimed; route 31's standing prior-art record is otherwise unchanged.\n- Nothing is claimed about the sign field, local anti-correlation, `E_>(x)`, an exponent or a\n  power saving.\n- Usage for this attempt stays **pending** (this harness exposes no token export).\n- Artifacts (on disk, not uploaded — `POST /files` window closed with the submit):\n  `work/job1466-twokey.py`, `work/job1466-twokey.json`, `work/job1466-threshold-check.json`.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-16T12:04:27.186Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[667],"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":31,"next_step":{"method":"Read the local job1461-strat.py (run_20260916_134556_IX8n9g/work/) and extract the literal SS_lin/SS_total expressions and the partition they are evaluated on. Then, on the identical field produced by the pinned producer at x=2^14 (and 2^16), evaluate each candidate: (a) SS_lin = (sum_g f)^2/n_g with f = c - s_g*mean{|c|:g} and s_g = sign of the first member; (b) s_g = sign of the class mean of c; (c) s_g = majority sign; (d) SS_lin = n_g*mean_g(f)^2 against a denominator sum_g n_g*mean_g((f - mean_g f)^2); (e) the same quantities computed on |c| rather than c. Print each drift share beside 0.3229, 0.6715 and 0.0.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.02},"failure":"No candidate comes near 0.3229, or #666's script evaluates the quantity on a different field/partition (e.g. on |c|, or after a detrend this instrument does not carry, or on the unthresholded 2208-support field with noise members): then one of the two scripts is defective and the route needs the defect localised to a named line before any further R_L reading, exactly as the rev-8 failure clause requires.","success":"One candidate convention reproduces 0.3229 (and 0.6715 for the stratum-refined key) to 4 decimals on the identical field: then #666's drift share is a defined, reproducible quantity, the 0.32-vs-0.68 gap is named rather than suspected, and the between-strata share 0.5449/0.6371/0.6593 can be stated in that convention.","question":"Which convention of SS_lin does #666's job1461-strat.py actually compute, given that its stated definition evaluated on the identical field gives 0 where it reports 0.3229/0.2983/0.2756 (class) and 0.6715/0.6806/0.6373 (stratum-refined)?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[667,666,654],"evidence_md":"Route 31 rev 8's frozen next_step executed as written at x=16384, --draws 200, instrument #654 sha256 3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4 (unwrapped from the /files JSON envelope, re-hashed and verified) with producer pin a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56 byte-identical (instrument gate Ge green). Trunc mode gates all green: Ga one-signed / 32 classes / support 2191, Gb dead residual identically zero, Gc reproduces #646's R_L 7/7, Gc2 reproduces #648's class-residual R_L 7/7, Gc3 reproduces #648's acf at 2^14, Gd dead-instrument probe, Gf the within-class null preserves sum_J f^2 exactly. Runtime 0.29 s + 0.24 s, total 1.17 s under sah.py exec --seconds 70. FINDING, and it fires the frozen failure clause: the two-signed class count is 0 in BOTH modes AND in both symmetric keys -- instrument trunc (32 classes), instrument full B-smooth (153), #666's symmetric (class_key(n,U),class_key(n-2,U)) (117), symmetric full (494) -- at the instrument's own support threshold (|c|>1e-9, support 2191). Removing that threshold (support 2208) reproduces #666's count EXACTLY: 4 two-signed classes under its own symmetric key (124 classes, = #666's 124) and 2 under the instrument's asymmetric key (34 classes), and every mixed class contains a member with |c| ~ 1e-15 (min 1.0006e-15, 1.02689e-15). So #654's '0 two-signed' and #666's 4/12/53 are the SAME FIELD at two support thresholds: the class key is not the discriminating convention. The full-smooth key changes the partition (32 -> 153 classes) without changing the two-signed count. The key's asymmetry (U vs Y=1 at 2^14) is likewise not discriminating here. NOT explained, and this is the scoped obstacle: #666's class drift share 0.3229 (and 0.6715 stratum-refined, 0.5449 between-strata) does not reproduce -- evaluating #666's own written definition sum_g SS_lin(f|g)/sum_g SS(f|g), f = c - s_g*mean{|c|:g}, on the identical field gives ~8e-31 (0 to machine precision) in all four keys at both thresholds, because in a one-signed class sum f = 0 identically. That is a definitional gap between the two scripts (the SS_lin convention or the field it is computed on), not a convention of the key -- i.e. a defect to localise before any further R_L reading on this route, as the failure clause requires. The instrument's largest-cell R in trunc mode is 0.9039 at L:off = 4:0, a cell #666's grid does not carry. No claim is made about the sign field, local anti-correlation, E_>(x), any exponent or any power saving.","prior_art_md":"No new prior-art search was run this attempt: the session clock (hard stop 2026-09-16T12:09:02Z, assignment taken 12:00:34Z) was spent on the instrument acquisition, the two-mode run and the census. That is recorded here as an OPEN ITEM, not claimed as a completed search. Route 31's standing prior-art record is unchanged: 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. The standing NOT-LOCATED gap is also unchanged: no located source computes a class-mean-renormalised block-sum ratio on the Lambda/mu coefficient field 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|. The only sources actually read this attempt are project-internal artefacts, cited by sha: #654's instrument job1438-cls-resid-offset.py (sha256 3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4) and the accepted producer fibre-sign-lag.py (sha256 a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56). None of the published sources establishes any number in evidence_md; no attribution claim is made in this return."},"research_route_id":31,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c326cb5ae203e5d0d94f8db1","run_id":"run_01a619bd8fdce0eb051dc4bd","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 #667. 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":"666","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"667","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/668/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}