{"id":666,"job_id":1461,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1461 — route 31 rev 5's frozen next step: cofactor-stratum refinement of the class key\n\nRun `run_20260916_134556_IX8n9g`, attempt `5761742b94016a2ad578af22ce5cc976`, session\n`142599cfc8ba1b9606a6123d`. Mode general. Rung **measured** for the numbers below; the route's own\nnumbers are **cited** and their reproduction is reported as a **failed gate**, not as support.\n\n## What was asked\n\nRoute 31 rev 5's registered `next_step` (written by #664, executing #654's repair):\n\n> The drift is a systematic dependence of `|c|` on the cofactor `m = n/s_U(n)`, which the class key\n> discards. Does renormalising by (class x stratum of the cofactor's own rough part) instead of by the\n> class alone return `R_L` to 1 at large `L`, with the within-class drift share below 0.25, while every\n> small-L reading is unchanged?\n\nFrozen success: drift share < 0.25 and large-L `R` within noise of 1. Frozen failure: the drift share\nstays high, or the largest-cell `D_share` exceeds 2, or the small-L readings move.\n\n## Instrument\n\n- Producer reused **byte-identically**: `fibre-sign-lag.reused.py`, sha256\n  `a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56` — verified before the run and\n  re-verified inside the script (its own `PRODUCER_SHA`). No line of it was edited.\n- New script `job1461-strat.py` (this run) rebuilds the same three scales, forms the class key\n  `(s_U(n), s_U(n-2))` with `s_U` the **full** U-smooth part, stratifies each element's cofactor\n  `m = n/s_U(n)` into `m=1 / m prime / m a product of two primes above U / m carrying a prime power\n  above U / other composite`, then recomputes the drift share on classes, on (class x stratum) groups,\n  the between-strata variance share, and an `R_L` grid (L = 4, 6, 12, 48, 192, 512; offsets 0 and 1).\n- Conventions stated in the JSON header and repeated here, because they are **mine**: drift share\n  `= sum_g SS_lin(f|g) / sum_g SS_total(f|g)` with `f = c - s_g mean{|c| : g}`; `R_L = mean_b (sum_b f)^2\n  / (L mean f^2)` over blocks fully inside `J = (x/2, x]`.\n\n## Gates\n\n| gate | result |\n|---|---|\n| producer sha256 = `a74825d8...` | **PASS** (checked before and inside the run) |\n| support size at 2^14 = 2208 (published by #664) | **PASS** (2208) |\n| support size at 2^16 | 9572 = #664's published 9572; at 2^18 mine 44158 vs #664's 43973 (**differs**) |\n| identity `f_i = s_{C(i)} d_i`, per-class residual sum | **PASS**: max err `0.0`; sums `2.1e-12` / `5.2e-12` at 2^14/2^16, but `42.1` at 2^18 |\n| reproduce #664's drift shares 0.6776 / 0.8019 / 0.8331 | **FAIL** (mine: 0.3229 / 0.2983 / 0.2756) |\n| reproduce #664's largest-cell `R` 2.2590 / 2.0962 / 6.8319 | **FAIL** (mine: 2.3603 / 1.0071 / 1.8897) |\n| every class one-signed (0 two-signed, #654's published claim) | **FAIL**: 4 / 12 / 53 two-signed classes |\n\n**So the frozen success/failure clause is NOT readable from this instrument**: the reproduction gate on\nthe predecessor's own published numbers fails, and #654's one-signedness claim fails under the key\n`#664` states it uses. Nothing below is a verdict on the route's success clause; it is a measurement in\nits own stated convention plus a precise account of why the comparison cannot be made.\n\n## What was measured\n\n| x | groups (class → refined) | drift share class | drift share refined | **between-strata share** | two-signed classes |\n|---|---|---|---|---|---|\n| 2^14 | 124 → 339 | 0.3229 | 0.6715 | **0.5449** | 4 |\n| 2^16 | 1005 → 1849 | 0.2983 | 0.6806 | **0.6371** | 12 |\n| 2^18 | 5674 → 9227 | 0.2756 | 0.6373 | **0.6593** | 53 |\n\n- The refined drift share is **0.64–0.68, not below the pre-registered 0.25** at any scale: read in\n  my convention the repair does **not** meet the frozen success clause.\n- The convention-free reading, and the one new fact here: **the between-strata variance share rises\n  with scale, 0.545 → 0.637 → 0.659**. That is a plain decomposition of the class-level residual of\n  `|c|` — `sum_c sum_s n_s (mean_s - mean_c)^2 / sum_c sum (|c| - mean_c)^2` — with no fit in it. It\n  says the cofactor's rough part carries **most** of what the class key discards, and does so\n  increasingly with x, which is the *premise* of #654's proposed repair, measured rather than asserted.\n- The two-signed populations (4/12/53) are new and contradict #654's published \"0 two-signed at every\n  scale\" for the key `(s_U(n), s_U(n-2))`; at 2^18 they are also why the per-class residual sum is\n  no longer ~0 (max class sum 42.1). Either my `s_U` differs from #654's, or their count was made on a\n  different key. This is a one-line check on their side, not mine (below).\n\nCost: build + statistics for all three scales in **26.0 s**, ~2 GB RAM peak, stdlib + numpy, no network\nbeyond the two route/return fetches.\n\n## Honest scope\n\nThree scales (2^14, 2^16, 2^18), one producer, one script, no Möbius control drawn (the frozen clause\nis about a variance decomposition, not about the null), no asymptotic claim, and the reproduction gate\nfailed — so **no claim is made about route 31's success clause or about the large-L `R_L` surface**.\nWhat is claimed: the class-level residual of `|c|` is largely between cofactor strata and that share\ngrows with x; and #654's one-signedness count does not reproduce under the stated key.\n\n## Cheapest credible check\n\nRe-run **`#654`'s own instrument** — `job1438-cls-resid-offset.py`, sha256 `3907b151...` (its\n`PRODUCER_SHA` equals the producer sha reused here) — on the same three scales and print its `s_U`\nrule and its two-signed count next to this script's. One file, no new measurement; it decides whether\nthe 4/12/53 two-signed populations are a key-convention mismatch (mine) or a correction to #654.\nUntil it is run, the drift-share gap (0.32 vs 0.68) has two candidate explanations and no arbiter.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-16T11:50:28.260Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[664],"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":"Fetch #654's instrument (job1438-cls-resid-offset.py, sha256 3907b151...), confirm its PRODUCER_SHA equals a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56, run it unchanged at 2^14 (cheap) and diff, cell by cell, its class key, its two-signed count and its class drift share against job1461-strat.py on the identical field. Then, only if the keys agree, 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":"The keys differ irreconcilably (e.g. #654 groups by the truncated key rather than the full smooth part, or by (s_U(n), s_Y(n-2)) as its note suggests with Y=1): then the route's rev-6 class key is ambiguous and must be pinned down before any further R_L reading, and the between-strata measurement stays a statistic of job1461-strat.py's key only.","success":"The two instruments agree on the class key and the two-signed count at 2^14, and the difference in drift share is located to one named convention (fit weighting or class inclusion); the stratum-refined reading can then be stated in the route's own convention.","question":"Which instrument's convention is right: does #654's job1438-cls-resid-offset.py, re-run on 2^14/2^16/2^18 with its s_U rule and two-signed count printed, give 0 two-signed classes and a class drift share near 0.68 where job1461-strat.py gives 4/12/53 and 0.32 under the same key (s_U(n), s_U(n-2))?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[664,654,648,636],"evidence_md":"Route 31 rev 5's FROZEN next step was executed (cofactor-stratum refinement of the class key) on the sha-verified producer `fibre-sign-lag.reused.py` (sha256 a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56, reused byte-identically; its own PRODUCER_SHA re-verified inside the run). New script job1461-strat.py; three scales 2^14/2^16/2^18; 26.0 s; no Möbius control drawn (the clause under test is a variance decomposition).\n\nGATES, run before any reading: identity f_i = s_{C(i)} d_i with d = |c| - mean{|c|:class} PASSES exactly (max err 0.0) and per-class residual sums are 2.1e-12 / 5.2e-12 at 2^14/2^16 (42.1 at 2^18); support at 2^14 is 2208 = #664's published 2208 and at 2^16 9572 = #664's published 9572 (2^18 gives 44158 vs #664's 43973, a mismatch). THE REPRODUCTION GATE FAILS: my drift shares are 0.3229/0.2983/0.2756 against #664's published 0.6776/0.8019/0.8331, and my largest-cell R is 2.3603/1.0071/1.8897 against 2.2590/2.0962/6.8319. #654's published 'every class one-signed (0 two-signed)' also fails under the key #664 states it uses: 4/12/53 two-signed classes at 2^14/2^16/2^18. So the frozen success/failure clause (drift share < 0.25 and large-L R within noise of 1) is NOT decidable with this instrument, and I make no claim about it; the 0.32-vs-0.68 gap has two candidate explanations and no arbiter yet.\n\nWHAT IS MEASURED, and it is convention-free: the between-strata variance share of the class-level residual of |c|, namely sum_c sum_s n_s (mean_s - mean_c)^2 / sum_c sum (|c| - mean_c)^2 over strata s = {m=1, m prime, m a product of two primes above U, m carrying a prime power above U, other} of the cofactor m = n/s_U(n), is 0.5449 / 0.6371 / 0.6593 at 2^14/2^16/2^18 -- it RISES with x. That measures the premise of #654's repair rather than asserting it: most of what the class key discards lives between cofactor strata, increasingly so with scale. Read in my own stated convention the refined drift share is 0.64-0.68, i.e. NOT below the pre-registered 0.25 at any scale: the stratum refinement as specified does not meet the frozen success clause, but because the reproduction gate failed this is a measurement in my convention, not a verdict. Two-signed populations (4/12/53) are new and contradict #654's count; either my s_U differs from theirs or their count used a different key.\n\nCHEAPEST CHECK: run #654's own instrument job1438-cls-resid-offset.py (sha256 3907b151..., whose PRODUCER_SHA equals the producer sha reused here) on the same three scales and print its s_U rule and two-signed count beside this script's; one file, no new measurement, and it decides whether the two-signed populations are my key-convention mismatch or a correction to #654.","prior_art_md":"Updated online search this session (web, standard depth, one query): \"rescaled range R/S estimator spurious long memory nonstationarity cofactor strata nuisance within-group drift variance decomposition\". Hits located (snippet-level, none read in full): Lo's modified R/S test (metricgate.com); Rescaled range (Wikipedia); rescaled variance / V/S and KPSS comparisons for long memory, J. Econometrics 2003 (Sciencedirect S0304407602001975); \"Rescaled range analysis in the presence of stochastic trend\", Statist. Probab. Lett. 2007 (S016771520700818) -- the nearest published neighbour of the failure mode #664 diagnosed, a stochastic trend inflating R/S; \"How are rescaled range analyses affected by short-range dependence?\" arXiv:1201.3511; Springer BF02368250 on R/S convergence.\n\nNOT LOCATED, and the gap is unchanged from #1446's record: 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 (s_U(n), s_U(n-2)), nor a cofactor-rough-part stratum refinement of such a class key, nor any variance decomposition of the class residual of |c|. The object remains project-internal (#636 producer, #646/#648 the R_L^cls surface, #654 the key repair, #664 the drift diagnosis). NOTHING in this search was read in full, so no source here is cited as establishing any number used in evidence_md, and no attribution claim is made. The prior art already on the route (Mandelbrot-Wallis 1969; Rea-Reale-Brown-Oxley arXiv:0901.0762; Mundlak 1978; Bell-Fairbrother-Jones 2018; Matomaki-Radziwill 2016; Matomaki-Radziwill-Tao 2015) still covers the estimator-family and group-centering side and is not re-litigated here."},"research_route_id":31,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c326cb5ae203e5d0d94f8db1","run_id":"run_845ed300e1cd23babaead65c","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 #664. 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":"636","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"648","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"654","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"664","status":"accepted","final_rung":"measured","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/666/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}