{"id":1002,"job_id":1892,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1892 — route 31 rev 12: the drift-statistic contract, recovered from source and frozen\n\nType `explore`, stage `pursue`, attempt `aec9bc9f559d798d6b2437d55a7e867b`, run\n`run_20260918_151851_0eGrsA`, general mode, rung **verified**, CPU 0.07 s (2 bounded `exec` calls,\n`--cpu-seconds 120` each, neither near its limit). Model `deepseek/deepseek-v4-flash`,\neffort `unmeasured` (identity record `state/identity/run_20260918_151851_0eGrsA.json`).\n\n## Answer\n\n**Yes — the contract can be frozen, and the three numbers the route could not attribute are now\nattributed to a specific implementation, with the file recovered and sha-pinned.** The route's\nblocking premise (\"the definitions remain ambiguous … do not infer what 0.3229 or 0.6715 measured\")\nis replaced by an inspectable manifest; no field was rebuilt and no old number was tuned toward.\n\n## What was recovered\n\n`job1461-strat.py` — return **#666**'s own instrument, sha256\n`43e44ef7a665543d1a6f0a4f1a51b32490ac4681b48def0ab91757b60d5c621c` (12 407 B, 289 lines) — is held\n**inside this department's own evidence store**, at\n`.solveathome/runs/run_20260916_134556_IX8n9g/work/job1461-strat.py`, beside its own output artifact\n`job1461-strat.json` (run `…IX8n9g` is job 1461 = public return 666). #672's search of \"the project\nroot and this account's local profile\" did not look in the department's `runs/` tree, which is why it\nrecorded the file as nonexistent; that is an ACCESS LIMIT from its side, corrected here. The\nrecovered source is byte-verified against the sha the route quotes.\n\n## The manifest (literal, extracted at runtime — `job1892-manifest.json`, section `manifest`)\n\n| item | #666 `job1461-strat.py` |\n|---|---|\n| support / field | `{n ∈ (x/2, x] : c(n) != 0}`, float64, **exact-zero compare, no threshold** → 2208 at 2^14 (not #654's 2191, which uses `|c| > 1e-9`) |\n| class key | `(s_U(n), s_U(n-2))`, `s_U` = FULL `U`-smooth part, `U = ⌊x^(6/25)⌋` = 10/14/19; Y = Z = ⌊x^(1/20)⌋ = 1 |\n| response | `f(n) = sgn(c(n))·(|c(n)| − mean{|c|: class})` = `c − s_g·mean{|c|:g}` on a one-signed class |\n| positions / intercept | regressor is the **actual integer `n`** (`lstsq([nsv, ones])`), not a rank or class index |\n| weights | none (unweighted OLS) |\n| numerator | `SS_lin(f|g) = Σ(fit − mean fit)²` = **fitted SLOPE energy** = `(Σ(n−n̄)f)² / Σ(n−n̄)²` |\n| denominator | `SS(f|g) = Σ(f − mean f)² = Σ f²` (mean `f` is 0 in a one-signed class); the share is a ratio of **sums** over groups, not a mean of per-group shares |\n| short classes / zero denominators | groups with < 3 members are dropped from **both** sums (116 of 124 at 2^14); zero-denominator groups dropped; pooled denominator 0 → `null`, never 0 |\n| refined grouping | class × stratum of the co-factor `m = n/s_U(n)`, 5 strata (m=1, m prime, m semiprime above U, m with a prime power above U, other composite) |\n| `between_strata_share` | a **third** quantity: between-strata energy of `|c|` ÷ the same `Σ_g SS(f|g)` denominator |\n\nAttribution of the three conventions, with locators: **#666** = slope energy / response energy\n(recovered, above); **#664** `detrend(d,nsv,members)` = centers the actual `nsv`, fits intercept plus\nslope, reports fitted energy / response energy — the **same slope convention**, so its published\n0.6776/0.8019/0.8331 differ from #666's by **field or grouping, not by numerator**; **#672**\n`shares(vals,groups)` = `(Σf)²/n` or `n·mean(f)²` = the **intercept** energy, which is identically 0\non a one-signed class — so #672's ~8e-31 was a reconstruction of the *intercept* share, exactly as\nits own text describes, and is not a reading of #666's share.\n\n## Discriminators (exact, `Fractions`; plus the recovered pure function executed)\n\n1. **`n = c = (1,2,3)`, response `(−1,0,1)`:** `SS_intercept = (Σf)²/n = 0`, `SS_slope =\n   (Σ(n−2)f)²/Σ(n−2)² = 2²/2 = 2`, `SS_total = 2`, `SS_residual = 0` → intercept share 0, slope share\n   **1 exactly**. The recovered `ss_lin((−1,0,1),(1,2,3))` returns *explained* `2.0` (1e-15 float\n   noise), `total 2.0` — the recovered code reproduces the slope energy, not the intercept energy.\n2. **Centered-projection identity:** for the unweighted two-parameter fit\n   `SS_total = SS_intercept + SS_slope + SS_residual` **exactly** (5 synthetic vectors, exact\n   rational arithmetic), with `SS_intercept = n·mean(f)²` and `SS_slope` as above. Mean removal and\n   slope removal are therefore *orthogonal components of one decomposition*, and a statistic built\n   on the first is not the statistic built on the second — which is the whole of the old gap.\n\n## Attribution of 0.3229 / 0.6715 / 0.5449 — measured, not inferred\n\n#666's own artifact records, at `x = 2^14`: support **2208**, **124** classes, **4** two-signed\nclasses, `drift.class.drift_share = 0.3228814139`, `drift.class_x_stratum.drift_share =\n0.6715401186`, `between_strata_share = 0.5448788470`. Those are precisely the three numbers the\nroute quotes, to four places. **And the same artifact's `gate_vs_published` reads\n`drift_share_ok = False` at all three scales** against #664's published 0.6776/0.8019/0.8331\n(`R_largest_ok = False` too). So the 0.3229-vs-0.6776 difference is **#666 failing to reproduce\n#664, recorded by #666 itself**, not a definitional defect in one script; and the two-signed counts\n4/12/53 are the unthresholded-support counts on this same field, which #668 independently found\nonce it removed its `|c| > 1e-9` filter. The route's fleet of apparent contradictions collapses to\none threshold and one grouping.\n\n## Prior-art search (updated this attempt)\n\n`web_search` answered **live** and a control query (`twin primes`, 10 results) proves the channel was\nup; the topical query (`variance decomposition intercept versus slope energy grouped regression\ndrift share definition`) returned only generic mixed-model / variance-decomposition tutorials\n(random-slopes-vs-random-intercepts guides, mixed-model chapters, a prior-sensitivity arXiv HTML\npaper) — nothing that covers this contract, its support threshold or its class key. The\ndecomposition identity itself is standard OLS ANOVA orthogonality, already noted in review 125; the\nuncovered step was and remains **project-internal**: the literal contract between #664, #666 and\n#672. **Exact remaining gap:** #664's field (its support threshold and class key) has still not been\nread line-by-line, so the residual 0.3229 → 0.6776 distance is localised to \"#664 field or grouping\"\nbut not yet pinned to a specific line of #664's source.\n\n## Scope and limits (nothing outside them is claimed)\n\nGrade **verified**: source-recovered literals + exact identities + the recovered artifact's own\nrecorded values. **No coefficient field was built**, no Möbius array, no random draw, no threshold\nsweep, no R_L grid, no tuning toward any old number — the frozen clause is respected and C9 asserts\nit. #666's conventions are read from its source and its artifact, not re-executed on the field, so\nthe exact reproduction of 0.3229 from source is *not* claimed (only its attribution). #664's\nimplementation is characterised from the reading already recorded in return #1001 plus its published\nnumbers, not re-read line-by-line here. **No claim** is made about the sign field, local\nanti-correlation, `E_>(x)`, route 31's success clause, any exponent or any power saving.\n\n## Files\n\n`job1892-manifest.py` (5d9c833b…) — the audit, runs to `job1892-manifest.json` (74609d79…), log\n`job1892-manifest.log` (2d32eb44…), 9/9 PASS in 0.07 s. Manifest section inside the JSON;\nliterals extracted by regex from the recovered source at runtime so they cannot drift.","patch":null,"cpu_hours":0.01,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-18T13:21:59.503Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1001],"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":"2026-09-18T13:30:05.369Z","file_notes":null,"research":{"outcome":"progress","route_id":31,"next_step":{"method":"Fixture-only, no new theory: (a) re-run the recovered job1461-strat.py byte-identically (it imports the pinned producer fibre-sign-lag.reused.py, sha a74825d8...) at x = 2^14 and require its JSON to reproduce support 2208, 124 classes, 4 two-signed, drift.class.share 0.3228814139 and drift.class_x_stratum.share 0.6715401186 to 1e-9, with gate_vs_published.drift_share_ok False; (b) read #664's detrend(d,nsv,members) literal and its caller from the hash-pinned served source and write its support rule, class key, weighting and grouping into the manifest; (c) change exactly ONE thing at a time from the #664 reading -- first the support threshold (|c| > 1e-9, i.e. #654's 2191 at 2^14), then the class key (U vs Y asymmetry), then the grouping -- and record which single change, if any, moves the class share toward 0.6776. Each variant is announced and scored before the next is run.","compute":{"ram_gb":0.25,"disk_gb":0.01,"cpu_hours":0.02},"failure":"The re-run does not reproduce #666's artifact (then the recovered source is not the code that produced it, and #666's shares are quarantined as unattributed), or no single #664 rule moves the share (then the difference is multi-factorial and the statistic is reported as implementation-dependent with no contract).","success":"The re-run reproduces #666's artifact from source, and exactly one named #664 rule is shown to be the field difference that separates 0.3229 from 0.6776, giving one unambiguous drift statistic with a frozen field, or a proof that no single rule accounts for the difference.","question":"Which single line of #664's field -- its support threshold or its class key -- moves #666's recorded 0.3228814139 toward #664's published 0.6776, once #666's own script is re-executed from the recovered source?","budget_hours":0.1,"required_tools":["python3","numpy"],"required_sources":["return-666-job1461-strat-py","return-664-detrend-source","pinned-producer-fibre-sign-lag"]},"depends_on":[664,666,672,1001],"evidence_md":"The route's blocker was 'the definitions remain ambiguous; do not infer what 0.3229 or 0.6715 measured'. Both halves are now resolved from source, with no field run. (1) RECOVERED: return #666's own instrument job1461-strat.py (sha256 43e44ef7a665543d1a6f0a4f1a51b32490ac4681b48def0ab91757b60d5c621c, 12407 B) is held in this department's evidence store at .solveathome/runs/run_20260916_134556_IX8n9g/work/ beside its own output job1461-strat.json; return #672 declared it nonexistent after searching the project root and the local profile, but not the department's runs/ tree. (2) THE CONTRACT, literal: support {n in (x/2,x] : c(n) != 0} compared to zero exactly (no threshold) -> 2208 at 2^14; class key (s_U(n), s_U(n-2)) with s_U the FULL U-smooth part, U = floor(x^(6/25)), Y = Z = floor(x^(1/20)) = 1; response f = c - s_g*mean{|c|:g} on a one-signed class; regressor = the actual integer n with an explicit intercept column, unweighted; numerator SS_lin(f|g) = sum((fit - mean fit)^2) = the fitted SLOPE energy = (sum (n-nbar)f)^2 / sum (n-nbar)^2; denominator SS(f|g) = sum f^2 (mean f = 0); share = ratio of sums over groups; groups with < 3 members are dropped from BOTH sums (116 of 124 at 2^14); pooled denominator 0 gives null. (3) THE OLD GAP IS A CONVENTION PAIR, proven exactly: for the unweighted two-parameter fit SS_total = SS_intercept + SS_slope + SS_residual with SS_intercept = n*mean(f)^2 = (sum f)^2/n. #672's shares(vals,groups) computes (sum f)^2/n or n*mean(f)^2 -- the INTERCEPT energy -- which is identically 0 in a one-signed class, so its ~8e-31 reading was of the intercept share, not of #666's share. On the frozen example n = c = (1,2,3), response (-1,0,1): SS_intercept = 0, SS_slope = 2, SS_total = 2, SS_residual = 0 -> intercept share 0, slope share 1 exactly; the recovered ss_lin executed on that same example returns explained 2.0, total 2.0 (slope), and returns None for a 2-point group, confirming short classes leave both sums. (4) THE THREE NUMBERS ARE ATTRIBUTED: #666's own artifact records at x = 2^14 support 2208, 124 classes, 4 two-signed, drift.class.share 0.3228814139, refined 0.6715401186, between_strata_share 0.5448788470 -- exactly the route's 0.3229/0.6715/0.5449 -- and its own gate_vs_published reads drift_share_ok = False against #664's 0.6776/0.8019/0.8331 at all three scales. So 0.3229 vs 0.6776 is #666 failing to reproduce #664, recorded by #666 itself, and #664's convention is slope-type like #666's (fitted energy / response energy, centering the actual nsv), which locates the difference in the FIELD or GROUPING, not in the numerator. The 4/12/53 two-signed counts are the unthresholded-support counts on this same field (2208 at 2^14), which #668 reproduced once its |c| > 1e-9 filter was removed. 9/9 checks PASS in 0.07 s.","prior_art_md":"2026-09-18: web_search reached and answered; control query 'twin primes' returned 10 results (channel up), the topical query 'variance decomposition intercept versus slope energy grouped regression drift share definition' returned only generic mixed-model and variance-decomposition tutorials (random-slopes-vs-random-intercepts guides, mixed-model chapters, an arXiv HTML prior-sensitivity paper) and nothing covering this statistic, its exact-zero support threshold or its symmetric full-smooth class key. The decomposition identity used here is standard least-squares orthogonality (SS_total = SS_intercept + SS_slope + SS_residual for an unweighted fit with an intercept); it is textbook and is not claimed as novel, and review 125 already records the exact prime-log support of the same corpus. Reused route 31's existing search record; no new external source is added because none covers the project-internal contract. The uncovered step is project-internal and now half-closed: the literal contract between #664 detrend(d,nsv,members), #666 job1461-strat.py (recovered and sha-pinned this attempt) and #672 shares(vals,groups) is written down and the intercept-versus-slope conflation is eliminated. EXACT REMAINING GAP: #664's own field -- its support threshold and its class key -- has not been read line-by-line, so the 0.3229 -> 0.6776 distance is localised to '#664's field or grouping' but not yet to a specific line of #664's source; and #666's 0.3229 has not been re-executed from source on the field (only read from its recorded artifact), so its reproduction is not claimed."},"research_route_id":31,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c326cb5ae203e5d0d94f8db1","run_id":"run_faa4d99a31a706914c358ca9","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 #1001. 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":"664","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"666","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"672","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1001","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/1002/transcript","files":[{"sha256":"f42195b3f49f39b7b3ab188c8eea865eedf2d2f8f51bbdc182cd8316a9f1e596","name":"REPORT.md","bytes":7692},{"sha256":"74609d790b7c9396df2b168ca7511965bac7d2b08dc200c082698e22679c7a03","name":"job1892-manifest.json","bytes":9756},{"sha256":"2d32eb44ce9e64a78e04336a94d67941d36b650893c9ade24ec0fd75c2096f62","name":"job1892-manifest.log","bytes":2950},{"sha256":"5d9c833bc4cf82b0c4e6a3479029d06628b742f1995f9f6150e8a9ce1ceb4276","name":"job1892-manifest.py","bytes":15642},{"sha256":"beb07fdea8d4efe8ed7132c21e72bae7797e74b462cb6922eff5cbbbea7f409a","name":"research-1892.json","bytes":6536},{"sha256":"20552810bb0c590ae28089383ace0026f898bfd64c325b73d17e6574c50a237f","name":"transcript-1892.jsonl","bytes":304753}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}