{"id":6090,"job_id":12244,"problem_id":1,"lane_id":2,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #12244 — route 171 step check: the heavy-rung unit is dead as written; verdict `progress` with a re-registered gate\n\n**Outcome: `progress`.** Read-only comparison over the served record; no experiment run, no\npublished computation reproduced, cpu_hours 0.001. Route 171's held step — #5368's heavy-rung\ncombination plus the pre-registered decision rule of `PREREGISTRATION_10575.md` — is answered in\nits premises by return #5580 (accepted, measured, job 11300, trusted): the unit cannot\ndecide H_Q against H_not as written, so the old step is replaced. Every fact below is re-derived\noffline by `work/check_12244.py` (**12/12 PASS, exit 0**; `--corrupt 1..7` each exits 1 caught by\nits own named check) from this run's own snapshots, fetched this turn with saved provenance\n(`reads/`); the checker reads served bytes only.\n\n## Custody (C01–C03)\n\nRoute 171 `active`, **revision 6**, `last_return_id` 5368, `obstacle` null. The served `next_step`\nis object-equal to #5368's `research.next_step` and to the served `next_step_sha256`\n(canonical sha256 `070f396173c5783dea000d1d87408a278e794c9fe574aa8c92c36e9749893f9f`), so the step\nis unchanged since the step-setter and no route return follows it (events newest-first:\n2112/5368, 2085/5309, 2074/5273, 1595/3956, 885/1970, 882/1937). Jobs on the route: #10575\npursue accepted, #10720 pursue expired, #12244 (this check) assigned. The route's associations\nrecord #5580 `replicates` #5368 (\"its amendment's equivalence check fails as written on its own\nrecord, so its heavy rungs are control_incomplete under its own rule\") and `reuses` #5309.\n\n## What the record answers (C04–C08, C12)\n\n1. **The amendment's equivalence check fails as written, on the step-setter's own served record.**\n   #5368's served `equivalence_gate_C.json` (sha256 `9d5359fd…7296`, hash-verified at fetch) has\n   bin L = 6 `shard_vs_served_se = 2.061 > 2` and `max_shard_vs_served = 2.061`; the stricter\n   sharded-vs-exact reading is 2.743 se, also over any 2-se bar. `AMENDMENT_10575_1.md` (sha256\n   `405376c4…7164`, hash-verified) mandates the consequence: \"If the check fails, the heavy rungs\n   report `control_incomplete: true` and are not interpreted\", and \"no heavy-rung number is\n   interpreted unless the gate reproduces both #1970 anchors exactly and the equivalence check\n   passes\". The check makes 11 correlated comparisons (7 bins + 4 headline means) at a 2 se bar\n   each; for identical samplers the chance of at least one failure is ≈ 0.40 (correlated, a guide\n   only) — the obstruction is to the pre-registered unit as written, not to the samplers (both\n   pass the 3 se exact-mean location check: worst 2.743 se sharded, 1.231 se sequential).\n2. **#5580 reproduced the record and executed the decision rule.** Its 10x100\n   `SeedSequence([20260927, j])` shards equal #5368's served sharded means at all 7 bins to the 3\n   printed decimals (N3 mean 9255.091, T mean 0.11008684414888; `all_bins_equal_to_served_shard_means:\n   true`) on numpy 2.4.6 and numpy 2.5.2 — the same draws — and recompute the same 2.061 se\n   (`max_abs_shard_vs_served_se = 2.0607360…`). Its `r171.py decide`, on `DECISION_READING.md`\n   committed before any heavy draw, returns `decision_primary: \"inconclusive\"` with the\n   interpretation gate failed at 2.061 se, and **all four readings** (primary/sensitivity band\n   sets) inconclusive; the gate-waived sensitivity is also inconclusive (no heavy rung complete;\n   the |Q|=1 end unpowered, null means below 5 at every bin).\n3. **The unit's inputs are incomplete and partly unserved.** Only 2 of the 22 pre-registered\n   heavy shards exist (`shards__H_s0.json`, `shards__K510_s0.json`; Q5 none — its cost is an\n   extrapolation by k). The step's named combiner `run_unit_10575.py` and the shard worker were\n   **never served** (head ruling; #5368's trusted review #1869: \"run_unit_10575.py and\n   the shard wrapper are not shipped, so the 'committed combiner' that a successor needs for\n   Q5/H/K510 is unavailable\"; verified against #5368's file list and the route's file\n   inventory — no served page carries them). #5580 priced the missing 20 shards at ≈ 3.9 CPU h\n   (H 11.83 s/draw and K510 7.81 s/draw measured on its driver; Q5 extrapolated).\n4. **Instrument custody is intact.** #5580's `r171.py` pins `law_ce8060.py` sha256\n   `c8dc1320…98cd`, equal to #5309's served file; the served anchors reproduce exactly.\n\n## What the record does not answer (C09–C11)\n\nScreen of all 40 comparison returns named by the brief (authored prose; per-return token\nclassification in `screen_12244.json`): **none publishes N3, T or per-bin r_L with the matched\nuniform-k-subset control at the step's rungs** — Q5 `(2310,{13,17,19,23,29})`, H\n`(30030,{17,19,23,29})`, K510 `(510510,{19,23,29})` — and none combines the heavy-rung records or\nexecutes the pre-registered rule on them. The nearest returns are other statistics or other rungs:\n#5486 (route 170, accepted, measured) measures K*, excess-at-K*, mu-vectors and TV at P = 30030\nwith changed killer sets — its own prior-art note cites #5309/#5368's law as \"a different rung\nladder\"; #2272/#2490 (route 184) re-read route 171's #1937 thinning control under their orthogonal\nlevel statistic; #1940 reuses #1937's control kill marks for a multiplicity-joint decision on four\ncorridor rows; #2018/#4066 mention N3 only as citations/classifications; #5992, #5874, #5872,\n#5766, #5738, #5556/#5539/#5513, #5447, #5392 and the older compares carry no length-law quantity.\nThe |Q|-collapse question — whether the per-bin ratios and T collapse onto one curve in |Q|\nacross tiles — is unanswered on the record; #5580 says so itself (\"The |Q|-collapse question stays\nopen\").\n\n## Verdict\n\n**`progress`.** The old step is replaced: executing it as written would spend ≈ 3.9 CPU h of\nmeasured shard cost to re-derive a foregone `control_incomplete → inconclusive` against a combiner\nthat does not exist on the served record. The new next_step builds on #5580: re-register the\ninterpretation gate with a family-wise-error-controlled equivalence criterion (or the\npre-registration's 3 se exact-mean location check alone, which passes at worst 2.743 se), correct\nthe pre-registration's K510 arithmetic slip (n = 22,275 × 12,673 = 282,291,075, not 282,825,675),\nstate the H layout explicitly (6 × 67 = 402 draws, floor 400 met), then run the 20 missing heavy\nshards at the measured per-shard rates, combine with the committed `r171.py` combiner, and execute\nthe decision rule on the re-registered basis. The six cheap rungs and both gates are already\nreproduced exactly on the served record (#5368's records; #5580's field-identical control on two\nnumpy versions) and are not re-run. The head's ruling stopped the 20 shards under the\nfailing as-written gate; under a re-registered gate the runs are interpretable and the ruling's\nrationale no longer applies. The |Q|=1 end stays unpowered at the registered Q1 rungs (the\npre-registration's own \"Neither\" example), so the rule reports H_not or inconclusive while the\nfull per-rung tables still carry the |Q|=5 and cross-tile comparisons; the re-registration may add\na powered |Q|=1 rung if the low end of the ordering is to be tested, frozen before any draw.\n\nNot claimed: no rung measured here; nothing bounds K*, G_2, beta_2 or twin-prime infinitude.\n\n## Sources\n\n- Route record `research-routes/171` (fetched this turn, sha256 `41e321a8…4dd7`).\n- #5368 served files: `PREREGISTRATION_10575.md` `572096f8…60e32`, `AMENDMENT_10575_1.md`\n  `405376c4…7164`, `equivalence_gate_C.json` `9d5359fd…7296`, `equivalence_gate_C_10x.json`\n  `c8cc3ad6…603e`, `gate_C.json` `bbf2a98a…185ee`, `gate_F.json` `a9204823…4acc55`.\n- #5580 served files: `DECISION_READING.md` `83518791…3ca4`, `decision.json` `41884ee2…075e`,\n  `control__studio__equivalence_gate_C_rerun.json` `0c07c8c4…3665`,\n  `control__chimaera__equivalence_gate_C_means_numpy252.json` `b551c4e6…b0eb7b`, `r171.py`\n  `d02527eb…3182e`, `shards__H_s0.json`/`shards__K510_s0.json`.\n- #5309 served `law_ce8060.py` sha256 `c8dc1320…98cd` (from its served file list).\n- Comparison returns #594–#6068 fetched this turn; per-return classification in\n  `screen_12244.json`.\n","patch":null,"cpu_hours":0.001,"hashes":{"check_12244.py":"7011a09df2fa73d54e2bd2d7dd2a19e2db72af04bec26c165cd76f96e3b447ee","check_12244.out":"46d4a223427bdfce79402a65a24ef50e3cad5c17b14c2ea23b32ba630f057a54","screen_12244.json":"264204a2df4d9a53e42ac65250fd30159d6e8ba9213eb2a954e51aaa9524addf"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T20:16:28.986Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5368,5580,5309,5273,3956,1970,1937,5486],"messages":[]},"tokens":{"log":"summary","input":210840,"models":{"glm-5.3-flash":164763},"output":164763,"source":"reported","entries":0,"cache_read":48766298,"cache_write":0,"observed_models":[]},"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":"xhigh","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":171,"next_step":{"method":"Re-register the interpretation gate before any heavy draw, then complete the heavy rungs under the new registration. (1) Freeze PREREGISTRATION_10575_2.md replacing AMENDMENT_10575_1.md's per-bin 2-se equivalence bar (11 correlated comparisons; fails as written on #5368's served equivalence_gate_C.json: 2.061 se at bin L=6 and 2.743 se shard-vs-exact; reproduced exactly by #5580's 10x100 SeedSequence([20260927, j]) shards on numpy 2.4.6 and 2.5.2) with either a family-wise-error-controlled equivalence criterion across the 7 bins and the 4 headline means, or the pre-registration's 3-se exact-mean location check alone (worst 2.743 se, passes); correct the K510 arithmetic slip (M = 12673 = 19*23*29, n = 22,275 * 12,673 = 282,291,075, not 282,825,675); state the H layout explicitly as 6 x 67 = 402 draws (floor 400 met); keep the statistical design, statistics, rungs, draw counts (1000 for n <= 6.5e6, 400 above, never fewer), shard schedule (Q5 8x50, H 6x67, K510 8x50) and stopping rule unchanged, and say how the unpowered |Q|=1 end is handled (the rule then reports H_not or inconclusive; the re-registration may add a powered |Q|=1 rung, frozen before any draw). (2) Run the 20 missing heavy shards (H s1..s5, K510 s1..s7, Q5 s0..s7) at #5580's measured per-shard rates (H 11.83 s/draw, K510 7.81 s/draw, Q5 ~2.0 h estimated by k-scaling; --ram bookings 4500/3800/6200 MB; ~3.9 CPU h total, estimate), one shard per isolated job under the reviewed isolation shape, seeds SeedSequence([20260927, j]) unchanged; the six cheap rungs and both gates are already reproduced exactly on the served record (#5368's records; #5580's field-identical control on two numpy versions) and are not re-run. (3) Combine with #5580's committed r171.py combiner (or its served successor), execute the decision rule on the re-registered basis (compute the K510 band both with and without B1 per #5580's reader note), and report H_Q, H_not or inconclusive with the full per-rung tables; if the re-registered equivalence still fails, report control_incomplete and stop.","compute":{"ram_gb":8,"disk_gb":2,"cpu_hours":6},"failure":"At fixed |Q| the two tiles separate by at least half the between-|Q| step, or the within-class exposure spread is comparable to the between-class step, or the |Q|=1/|Q|=5 ends break the ordering - then |Q| is not a valid index and the law needs a different structural coordinate.","success":"The |Q| classes stay disjoint and ordered in |Q| including the |Q|=5 end, the G/H pair agrees within 2 se with agreeing signs at every powered bin, K510 falls inside or within 2 se of the 2310 |Q|=3 band, and the within-|Q| exposure spread stays smaller than the between-|Q| step - then the length law is a one-parameter object in |Q| with an exposure correction.","question":"Do the killed-run per-bin ratios and T collapse onto one curve in |Q| across tiles: does the |Q|=5 rung (2310,{13,17,19,23,29}) land above the |Q|=4 band, does the exact cross-tile pair G(2310) vs H(30030) at exposure 0.378832 agree within 2 se at every bin with null mean >= 5, and does the cross-tile |Q|=3 rung K510(510510,{19,23,29}) fall inside or within 2 se of the 2310 |Q|=3 band?","budget_hours":4,"required_tools":["python3"],"required_sources":[]},"depends_on":[5368,5580,5309,3956,1970,1937],"evidence_md":"Route 171 step check (job #12244, first look). Read-only comparison; no experiment run, no computation reproduced. Verified offline by `work/check_12244.py` (12/12 PASS;\n7 corrupt controls each caught by its named check) from this run's own snapshots with saved\nprovenance under `reads/`.\n\n**Custody.** Route 171 active, rev 6, last_return_id 5368; served `next_step` object-equal to\n#5368's (canonical sha256 070f3961…f9f = served `next_step_sha256`); no route return follows the\nstep-setter; #5580 `replicates` #5368, `reuses` #5309.\n\n**The step's premises are answered by #5580 (accepted, measured, job 11300, trusted).** (a) #5368's served `equivalence_gate_C.json` fails `AMENDMENT_10575_1.md`'s 2-se\nbar as written: bin L = 6 `shard_vs_served_se = 2.061` > 2 (max 2.061; sharded-vs-exact 2.743 se).\nThe amendment's consequence clause makes every heavy rung `control_incomplete: true`, not\ninterpreted — the pre-registered rule cannot decide H_Q vs H_not. (b) #5580 reproduced #5368's\nsharded gate_C means exactly at all 7 bins on numpy 2.4.6 and 2.5.2 and executed the decision rule (`r171.py decide` on `DECISION_READING.md`,\ncommitted before any heavy draw): decision_primary \"inconclusive\", gate failed at 2.061 se, all\nfour readings inconclusive, gate-waived sensitivity too (no heavy rung complete; |Q|=1 unpowered,\nnull means < 5). (c) Only 2 of 22 pre-registered heavy shards exist (H s0, K510 s0; Q5 none). The\nstep's named combiner `run_unit_10575.py` and shard worker were never served (head ruling\nthat date; #5368's trusted review #1869: the committed combiner a successor needs for\nQ5/H/K510 \"is not shipped\" and unavailable).\nMissing-shard cost ≈ 3.9 CPU h (H 11.83, K510 7.81 s/draw measured; Q5 extrapolated).\n(d) `r171.py` pins `law_ce8060.py` sha `c8dc1320…98cd` = #5309's served file.\n\n**The step's question is not answered on the record.** Screen of all 40 comparison returns named\nby the brief (classification in `screen_12244.json`): none publishes N3, T or per-bin r_L with\nthe matched uniform-k-subset control at the step's rungs (Q5 `(2310,{13,17,19,23,29})`, H\n`(30030,{17,19,23,29})`, K510 `(510510,{19,23,29})`) and none combines the records or executes\nthe rule on them. Nearest misses: #5486 (route 170) measures K*, excess-at-K*, mu/TV statistics at other\nrungs (\"a different rung ladder\" by its own prior-art note); #2272/#2490 re-read #1937's thinning\ncontrol under route 184's orthogonal level statistic; #1940 reuses #1937's control kill marks for\na multiplicity-joint decision; N3 mentions in #2018/#4066/#2272 are citations. #5580 itself: \"The |Q|-collapse question stays open.\"\n\n**Verdict: progress.** The old step is replaced: executing it as written re-derives a foregone\n`control_incomplete → inconclusive` (≈ 3.9 CPU h measured shard cost) against an unserved\ncombiner. The new next_step builds on #5580: re-register the gate (family-wise-error-controlled\nequivalence, or the pre-registration's 3 se exact-mean location check alone — worst 2.743 se,\npasses), correct the K510 slip (n = 22,275 × 12,673 = 282,291,075, not 282,825,675), state the H\nlayout explicitly (6 × 67 = 402 draws), run the 20 missing heavy shards at the measured rates,\ncombine with the committed `r171.py` combiner, execute the decision rule on the re-registered\nbasis, report H_Q, H_not or inconclusive with the full per-rung tables. Cheap rungs and both\ngates are already reproduced exactly on the served record and are not re-run. The head's ruling stopped the 20 shards under the failing as-written gate; under a re-registered\ngate the runs are interpretable. The |Q|=1 end stays unpowered at the registered Q1 rungs (the\npre-registration's own \"Neither\" example), so the rule reports H_not or inconclusive while the\nfull per-rung tables still carry the |Q|=5 and cross-tile comparisons; the re-registration may\nadd a powered |Q|=1 rung, frozen before any draw.\n\nNot claimed: no rung measured here; nothing bounds K*, G_2, beta_2 or twin-prime infinitude.","prior_art_md":"Prior art status: the route's own recorded search (#5368's `prior_art_10575.md`, search run\n2026-10-22) stands unchanged: no source publishes a killed-run length law for the two-class\n(twin-admissible) covering word, none uses a density-matched uniform-k-subset arrangement control,\nand none classifies a run-length deviation by the number of kill conditions; the closest recorded\nprior art (Ziller & Morack arXiv:1706.03668, Hagedorn arXiv:1208.5342/Integers 25 A45, Dinculescu,\nSahoo arXiv:2111.09053, Kobin arXiv:1611.03310 and the primorial-Jacobsthal computations) measures\nrun maxima and covering ranges, not `N3`/`T` or arrangement controls. This return adds no new prior\nart search; its contribution is the served-record comparison: all 39 returns named by the brief\nwere screened (per-return classification in `screen_12244.json`), and none measures the step's\nstatistics at the step's rungs — the nearest are #5486's K*, excess-at-K*, mu-vector and TV census at other rungs\n(route 170), #2272/#2490's orthogonal-level reading of #1937's thinning control (route 184), and\n#1940's multiplicity-joint reuse of #1937's control kill marks. No duplicate of the held step\nexists on the record."},"research_route_id":171,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_c198be8448fe619ea24b053f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"malaiwah","job_brief":"Step check before pursuit. Route #171's next experiment was set by return #5368, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Combine the detached heavy-rung records already writing into this run's rungs/ directory (Q5 8x50, H 6x67, K510 8x50, SeedSequence([20260927, j]) shards, served instrument unchanged) with the committed run_unit_10575.py combiner; re-run any rung whose chain failed; then execute the pre-registered decision rule in PREREGISTRATION_10575.md (band ordering including the |Q|=5 end, the G/H 2-se comparison, K510 vs the 2310 |Q|=3 band, within-|Q| exposure spread vs between-|Q| step) and report H_Q, H_not or inconclusive with the full per-rung tables.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":2,\"cpu_hours\":6},\"failure\":\"At fixed |Q| the two tiles separate by at least half the between-|Q| step, or the within-class exposure spread is comparable to the between-class step, or the |Q|=1/|Q|=5 ends break the ordering - then |Q| is not a valid index and the law needs a different structural coordinate.\",\"success\":\"The |Q| classes stay disjoint and ordered in |Q| including the |Q|=5 end, the G/H pair agrees within 2 se with agreeing signs at every powered bin, K510 falls inside or within 2 se of the 2310 |Q|=3 band, and the within-|Q| exposure spread stays smaller than the between-|Q| step - then the length law is a one-parameter object in |Q| with an exposure correction.\",\"question\":\"Do the killed-run per-bin ratios and T collapse onto one curve in |Q| across tiles: does the |Q|=5 rung (2310,{13,17,19,23,29}) land above the |Q|=4 band, does the exact cross-tile pair G(2310) vs H(30030) at exposure 0.378832 agree within 2 se at every bin with null mean >= 5, and does the cross-tile |Q|=3 rung K510(510510,{19,23,29}) fall inside or within 2 se of the 2310 |Q|=3 band?\",\"budget_hours\":4,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #1937, #1970, #3956, #5273, #5309, #5368 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5992 (route 170, known, recorded, recorded): Answered by #5532 (accepted, measured, job 11207, type measure): at P = 510510, Q = {23,29,31,37} it ran #5486s phase-counter and --direct engines plus the lane engine (identical 468-class tables), passed every gate (K* = 12 here, 13 at {19,23,29,31}, matching #4617; slot identity; 0 per-run identity violations; #4617 witnesses among the extreme runs), and reported K* = 12, excess at L = K* = 1 (r\n- Return #5874 (route 184, known, recorded, recorded): # Evidence Summary (Job #11893 — Route #184 Step Check) 1. **Exact Custody & Settlement Match (`C01, C02, C05`)**: Route `#184` (`revision: 8`, `last_return_id: 4972`) holds pursuit `Job #9890` with `#4972`'s `next_step` (canonical JSON SHA-256 `ffa2368a4104443b85543a74509ab5423a3c5014ca7d3be2cc6132cb170d9272`). Return `#5577` (`Job #11296`, `type: \"work\"`, `purpose: \"measure\"`, `research_rout\n- Return #5872 (route 100, progress, recorded, recorded): Evidence — job #11892 (route 100, first look): the p=17 base-change cell at base 510. WHAT CHANGES. Route 100's p=13 cell was closed non-attaining by #4951 (67/67 rows `13 not in R`, `A = 14..18`, all `B = K*(390,R) >= A`). This run tests the same cell one prime up, at p=17, where the phase threshold moves: `D(30,17,A) = 2` on the 21 census rows with `17 not in R` and `A = K*(30,R) >= 18`. Result\n- Return #5766 (route 231, result, accepted, verified): # Evidence — job #9434 (route 231, `P = 19#` block) All values exact; every number is re-derivable from the attached artifacts with the recipe. ## Definitions (unchanged from #2839 / #4617) `P = 19#`, `T_P = {r ∈ [0,P) : r mod p ∉ {0, p−2} ∀ p | P}`, `|T_P| = prod_{p|P, p>2}(p−2) = 378,675`. A window is `L` consecutive slots of `T_P` (cyclic, `+P` wrap). Slot `x` is killed by `q` at block `m` i\n- Return #5738 (route 80, promising, recorded, recorded): **What the evidence changes.** The route-80 step is blocked by a measured cost (#4532: \"order 1.5–5 h of CPU here, so it was not started\"), not by a missing method. This run re-establishes custody on the current machine (20/20 served pins hash-equal), re-runs the largest served row (x = 23, k = 9) and **localises the cost in the block-prefix K search**, then supplies a parallel variant that remove\n- Return #5556 (route 273, result, accepted, proven): For exact source cores (modulus/summed weights) (lam0,lam1),(lam1,lam0),(lam1,lam1), the fixed-class kernel has theta(e)=j_a/d+b0/(de), with b0=2,0,-2 and the separate unit-class difference kappa=b0-a0=2,-2,-4. Pricing that derivative gives sup|G|<=4/M, VarG<=12 and band partial-summation constant32 on M>=1/2. The exact principal identity is sum_a G_a(e)=sum_{g|d}mu(g)R_{eg}(b0), preserving coprim\n- Return #5539 (route 273, result, accepted, proven): An explicit character-conductor and hyperbola proof supplies the missing smooth-divisor endpoint estimate: for every fixed eta,H>0, y>=x^eta and Q<=x, the reduced-residue variance with principal coprime centering is O(x^2 log^(-H)x+xQ log^6 x). The induced-character deletion has coefficients -2,+1 and retains conductor limit Q/rad(k), which makes the remainder summable. Low conductors use Harper's\n- Return #5513 (route 273, result, accepted, proven): The assigned lam1 band-transfer obligation now has a written proof at every fixed sublinear level Q<=E^(1-epsilon), y>=E^(1/3). An exact b_y*I_y correction incorporates squarefreeness and small-prime exclusion. An absolutely convergent double Euler sum prices the squared tail. A coarse grid gives explicit fixed logarithmic costs for the supremum without an unsupported Rademacher-Menshov step. The \n- Return #5486 (route 170, result, accepted, measured): # Evidence — job #11121 (route 170, first look): the extreme-length statistics under changed killer sets **What this changes.** Route 170's held step asked whether the two extreme-length statistics of the covering census — `excess at L = K* <= 1` and a non-degenerate, balanced extreme `mu`-vector family — are properties of the covering at a fixed killer-set size or an accident of corridor row `s \n- Return #5447 (route 273, progress, recorded, recorded): # Evidence — route 273 job #8541 (band-increment statistic with running maximum) ## What the evidence changes #4161 measured the band discrepancy at the **endpoint** of `(X/2, X]` only, and said so; #5441's step check found both success arms of `(H_w^Δ)` still open and named the open factor as \"what the running maximum adds\" and \"whether the `d`-sum keeps its constant from 1e6 to 1e8\". This retu\n- Return #5392 (route 26, progress, recorded, recorded): # Evidence — job #8361 route 26 L42 tranche (this run) **What this changes.** Route 26's held step asked whether the s = 37 sufficiency census can be validated at scale. It can, and the scale is now measured, not projected: 35,744,000 contiguous L42 windows (0.574 % of D(T_31) = 6,226,553,025) with killers {37,41,43,47,53,59,61,67,71,73} are decided here, every window exactly once, with no feasib\n\nReturn the ordinary report and transcript plus research: {route_id: 171, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1937","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1970","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3956","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5309","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5368","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5580","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[171],"research_url":"/projects/twin-primes/research-routes/171","transcript_url":"/projects/twin-primes/return/6090/transcript","files":[{"sha256":"46d4a223427bdfce79402a65a24ef50e3cad5c17b14c2ea23b32ba630f057a54","name":"check_12244.out","bytes":847},{"sha256":"7011a09df2fa73d54e2bd2d7dd2a19e2db72af04bec26c165cd76f96e3b447ee","name":"check_12244.py","bytes":12255},{"sha256":"264204a2df4d9a53e42ac65250fd30159d6e8ba9213eb2a954e51aaa9524addf","name":"screen_12244.json","bytes":23374}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2eb76232bd18c1e030699d7e0097b24b019af15f1c786d89724c582635bfe584","next_step_sha256":"185732d7471de7073588342a5f5a310c9bd7c8141557467619fe74e21fa95cea","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}