{"id":5093,"job_id":10060,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Route 270 step check (job #10060): the step is unchanged and still open — #5073 does not touch it\n\nStep check before pursuit, read-and-compare only: `cpu_hours 0`, no experiment run, no computation\nreproduced. Earlier step check #5070's conclusions are reused as instructed; the only new candidate\nthe brief lists is #5073 (route 269), which is compared below and does not answer this step. Verdict:\n**outcome \"promising\" — the #3564 step is still open and is copied exactly as `next_step`.**\n\n## 1. Record state (served, hash-checked)\n\n`GET /research-routes/270` as served on 2026-10-20: `state active`, `revision 3` (was 2 at #5070's\ncheck), `origin_return_id 3544`, `last_return_id 5070`, `next_job_id` absent (null). The route's\nevent list is `2002` (#5070, promising), `1518` (#3564, promising), `1514` (#3544, proposed) —\n**no route-270 event after #5070's own recording** (event 2002 is that check's own return event, new\nrelative to what #5070's check could see, as expected).\n\nThe served `next_step` object is **exactly equal** to `#3564.research.next_step` (plain `==` and\ncanonical sorted-key equality, both checked on the fetched bytes). Its canonical sorted-key\ncompact-separator sha256 is\n`458dd8206cafaf0efc93bae0e0ddb43f05848b884a6b2e803f53f52fbdce9fc1` — the same value #5070 recorded\nand verified against #3564's step (with #5070's documented trap: default JSON separators hash to\n`be0e1c4f…`, not the recorded convention; compact `separators=(\",\", \":\")`, `sort_keys=True` is the\nrecorded convention). So the step is **unchanged** since #5070's comparison, on a route record whose\nrevision nevertheless bumped 2 → 3 with no new event after #5070's own and no step edit.\n\nContrast with the linked route (the changed input this check was triggered by): #5073 reports that\non route 269 the served step does **not** reproduce #3566's recorded `next_step_sha256` under any of\nthe nine serialization variants it tested — an unresolved documentary discrepancy there. Route 270\nhas no such defect: served object and setter object are byte-equal here.\n\n## 2. #5070's conclusions, reused\n\n#5070 (recorded, promising) established for the same step, on the then-served record: no route-270\nreturn after #3564; the 3 h pursuit #7347 expired with no return; #3564's citers (#3584, a\nQ-transition-signed-estimate return, and #5070 itself) do not touch this object; the census step\n(exact `Z[zeta_c]` instrument to `c <= 2000` with pre-registered P1/P2) has never been run. All of\nthat still holds on the current record: `last_return_id 5070` is the step check itself, and no newer\nroute-270 return exists.\n\n## 3. The new candidate #5073 compared (the changed input)\n\n#5073 (job 10020, route 269 step check, recorded, author_rung heuristic) is a read-and-compare step\ncheck on **route 269's** step (the l2-operator-import step set by #3566). Its scope, by its own text\nand citation list (`cites.returns [3566, 3527, 3514]` — route 269's own returns only):\n\n- It finds route 269's step **not executed or answered** (pursuit #7351 expired, none of the 45\n  compared returns carries the step vocabulary) but **mis-located**: three of four load-bearing terms\n  point at the wrong sections of the two cited papers (its F2: the machinery past BV in the proof of\n  Theorem 1.7 is Lemma 2.7, a BFI bilinear average with its own structure restriction, not a BV level\n  barrier), and the step's question (ii) is already asserted in prose by the setter itself. It\n  recommends re-scoping route 269's step before pursuit rather than running it verbatim.\n- Searched for this route's object, its report contains **zero** occurrences of `270`, `3564`,\n  `3544`, `completion identity`, `Z[zeta`, `dual class`, `l1`, or `2000`. It runs no census, prices\n  no dual class, and states no P1/P2-style prediction.\n\nConsequence for this step: #5073 neither executes nor answers the #3564 census step, and it does not\nbear on the dual-class sizing question (its finding concerns the wording of the *downstream* import\nstep on the linked route). Relevance is contextual only: route 270's contribution defers the\n`#760-#765` operator import (\"before importing an l2 operator bound\"), and #5073's re-scoping\nrecommendation on that import step is a useful caution for whoever eventually prices it — it changes\nnothing about whether the returns on record answer *this* step. They do not.\n\n## 4. Verdict\n\nThe step is unchanged and unanswered: **outcome \"promising\"**, the step copied exactly as\n`next_step` (the served object, byte-exact). The held pursuit goes out with this note; these returns\nnever hold it again. `depends_on` [3564, 5070]: #3564 is the step's setter and executed census whose\npredictions P1/P2 the step pre-registers; #5070 is the earlier step check whose conclusions are\nreused. `cites.returns` adds #5073 (the compared candidate). No new evidence was produced; the\n407/400 target box and the route's central uncertainty (finite census is not a bound) are unchanged\nand open.\n\nCarried forward from #5070 (its section 4 wording findings, which travel with the step for the\npursuing run): (F1) P1's equality clause is already false on the record's own range — `l1_max = c`\non only 23 of 59 tested `c`, every prime `p` gives `p-1`, and the smallest counterexample is `c=2` —\nwhile P1's own falsifier (`l1_max > c`) never fires, so what the record supports and question (ii)\nactually asks is the **inequality** `l1 <= c`; (F2) \"attained at m = 0\" is false on 42 of 59 tested\n`c` and misattributes #3564's lemma, which is the strict inequality `|D(0)| = |c_c(r)| <= c` with\nworst 0.993289; (F3) the step's \"one decisive weighted test\" as worded re-measures the size ratio\n`(b)/(a)` (the restriction to `(t,c) > 1` deletes nothing, checked exactly on 16,607 cases), so\nseparating size pricing from correlation pricing needs a non-uniform weight profile the step does\nnot specify. The brief's three-way rule mandates the exact copy for \"promising\" and #5070 recorded\nthe same verbatim step, so the step is copied unchanged with these cautions on the record.\n\n## Sources\n\n- Served route record `GET /research-routes/270` (fetched 2026-10-20, saved with provenance:\n  `reads/route270.json`, sha256 cc81ddd7b556248e3c7e8d5720928a6704fddf73760a03b1c0d415b10690b16a).\n- Return #3564 (served record: `reads/r3564.json`, sha256 f50ced025ed5e2d0ee06746a5e02bf69dac925731e484fdfcd6bb02486163b58) — the step's setter and executed census.\n- Return #5070 (served record: `reads/r5070.json`, sha256 05ff8aa0e5e99452d3542e3e3e9140317f8107dbc59593f644ae271b7cff88f9) — the earlier step check, conclusions reused.\n- Return #5073 (served record: `reads/r5073.json`, sha256 6885f0feba564b5be3ebb535301903e5bd82b75c88b58f1b72c83d8d2cdf1713) — the compared candidate (route 269 step check).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T20:39:46.185Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3564,5070,5073],"messages":[]},"tokens":{"log":"summary","input":313365,"models":{"glm-5.3-flash":311584},"output":311584,"source":"reported","entries":0,"cache_read":50000000,"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":"promising","route_id":270,"next_step":{"method":"Push the identical exact instrument (exact integer coefficient vectors in Z[zeta_c], rigorous l1 brackets, no float deciding any comparison) to c <= 2000, staged by r-chunks so memory stays bounded, and pre-register two predictions before the run: (P1) on the (t,r,c)=1 side max_{r,m} l1(m)/c = 1 exactly for every c <= 2000, with the maximum attained at m = 0 (the lemma in this return) - falsifier: any c <= 2000 with l1_max > c; (P2) on the unit-dual side the fitted exponent of log((b)/(a)) on the largest decile window [1800,2000] is <= 0.02, and the monotone envelope over c <= 2000 stays below 1.2 - falsifier: a fitted exponent > 0.05 with the window outside its error bars, or any envelope value above 1.2. Then, since the census only measures SIZE, add the one decisive weighted test the route still lacks: for each c <= 2000, compute the exact l1 mass of D(m) restricted to the dual frequencies t with (t,c) > 1 (the classes the unit-only restriction actually deletes) and compare it against the main-term mass, so that the 'priced by size' and 'priced by correlation' readings of section 9 can be told apart on the fixture's own weight profile.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":2},"failure":"P1 fails (some c <= 2000 with l1_max > c) - then the M2 dominance is a small-c accident and the (t,r,c)=1 restriction needs its own pricing; or P2 fails (envelope above 1.2, or exponent > 0.05 outside error bars) - then the removed class grows relative to the main term and the (m,q) arrangement needs the explicit repricing section 9 warns about before any operator import; or the weighted mass exceeds the main-term mass at some c, which is the correlation route by which a window figure could still carry it, and it must then be priced directly rather than by size.","success":"P1 holds on every c <= 2000 (the M2 restriction is exactly dominated, now on a range eight times longer and with the equality attained structurally at m=0), and P2 holds with no envelope above 1.2, so the ratio (b)/(a) is bounded by a constant near 1 and the removed dual class is O(main term) at every tested scale, not a lower-order correction: the recorded short-window pricing can carry it provided it prices an error of the same order as the main term, and the (t,r,c)=1 side needs no new input at all.","question":"Is the removed dual class bounded by the completed value for ALL moduli, or is the constant ratio <= 1.07 observed on c <= 300 a small-c accident that drifts? The two windows this return could not close are (i) max_m |D(m)| <= (1+eps) c for large c on the unit-dual side, and (ii) whether the M2 bracket l1 <= c, verified exactly on c <= 300, is a theorem.","budget_hours":3,"required_tools":["python3"],"required_sources":[]},"depends_on":[3564,5070],"evidence_md":"# Evidence - job #10060, route 270 step check\n\nRead-and-compare only: cpu_hours 0, no experiment, no computation reproduced. Reuses #5070's conclusions; the only new candidate compared is #5073.\n\n**(1) Step unchanged.** Served route 270 (2026-10-20): state active, revision 3 (bumped from 2 with no new event after #5070's own recording), origin 3544, last_return_id 5070, next_job_id absent. Route events: 2002 (#5070, promising - that check's own return event), 1518 (#3564, promising), 1514 (#3544, proposed); no route-270 event after #5070's own. The served next_step object is exactly equal to #3564.research.next_step (plain == and canonical sorted-key equality on the fetched bytes); canonical sorted-key compact sha256 458dd8206cafaf0efc93bae0e0ddb43f05848b884a6b2e803f53f52fbdce9fc1, the same value #5070 recorded (trap: default separators hash to be0e1c4f... - compact is the recorded convention). Contrast: the changed input that triggered this check, #5073, reports that route 269's served step does NOT reproduce #3566's recorded next_step_sha256 under any of the nine serialization variants it tested - route 270 has no such defect.\n\n**(2) Still unanswered.** Reusing #5070: no route-270 return after #3564 except the step check #5070 itself; pursuit #7347 expired with no return; #3564's citers (#3584, a Q-transition-signed-estimate return, and #5070 itself) do not touch the object; the c<=2000 census with pre-registered P1/P2 has never been run. All still hold on the current record.\n\n**(3) #5073 compared and set aside.** #5073 (job 10020, route 269 step check, recorded, author_rung heuristic) is a read-and-compare check of route 269's own l2-operator-import step (setter #3566): it finds that step not executed but mis-located (three of four load-bearing terms point at the wrong paper sections; its F2 identifies Lemma 2.7 - a BFI bilinear average with structure restrictions - as the machinery past BV, not a BV level barrier) and recommends re-scoping before pursuit. Its cites.returns are [3566, 3527, 3514] - route 269 returns only. Searched for this route's object, its report contains zero occurrences of 270, 3564, 3544, completion identity, Z[zeta, dual class, l1, or 2000: it runs no census, prices no dual class, states no P1/P2 prediction. Contextual relevance only: route 270's contribution defers the #760-#765 operator import ('before importing an l2 operator bound'), and #5073's re-scoping recommendation on that import step is a caution for whoever prices it downstream; it does not answer whether the record answers THIS step. It does not.\n\n**(4) Verdict.** outcome promising, the #3564 step copied exactly as next_step (the served object, byte-exact). Carried forward from #5070's wording findings, which travel with the step for the pursuing run: (F1) P1's equality clause is already false on the record's own range (l1_max = c on only 23 of 59 tested c; every prime p gives p-1; smallest counterexample c=2) while P1's falsifier never fires - what the record supports is the inequality l1 <= c; (F2) 'attained at m = 0' is false on 42 of 59 tested c and misattributes #3564's strict-inequality lemma (|D(0)| = |c_c(r)| <= c, worst 0.993289); (F3) the step's weighted test as worded re-measures the size ratio (b)/(a) (checked exactly on 16,607 cases), so separating size pricing from correlation pricing needs a non-uniform weight profile the step does not specify. The brief's three-way rule mandates the exact copy for promising and #5070 recorded the same verbatim step, so the step is copied unchanged with these cautions on the record. The 407/400 target box and the route's central uncertainty (a finite census is not a bound) are unchanged and open."},"research_route_id":270,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_10f1db5cb253ca2dcc215ca6","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 #270's next experiment was set by return #3564, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. 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\":\"Push the identical exact instrument (exact integer coefficient vectors in Z[zeta_c], rigorous l1 brackets, no float deciding any comparison) to c <= 2000, staged by r-chunks so memory stays bounded, and pre-register two predictions before the run: (P1) on the (t,r,c)=1 side max_{r,m} l1(m)/c = 1 exactly for every c <= 2000, with the maximum attained at m = 0 (the lemma in this return) - falsifier: any c <= 2000 with l1_max > c; (P2) on the unit-dual side the fitted exponent of log((b)/(a)) on the largest decile window [1800,2000] is <= 0.02, and the monotone envelope over c <= 2000 stays below 1.2 - falsifier: a fitted exponent > 0.05 with the window outside its error bars, or any envelope value above 1.2. Then, since the census only measures SIZE, add the one decisive weighted test the route still lacks: for each c <= 2000, compute the exact l1 mass of D(m) restricted to the dual frequencies t with (t,c) > 1 (the classes the unit-only restriction actually deletes) and compare it against the main-term mass, so that the 'priced by size' and 'priced by correlation' readings of section 9 can be told apart on the fixture's own weight profile.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"P1 fails (some c <= 2000 with l1_max > c) - then the M2 dominance is a small-c accident and the (t,r,c)=1 restriction needs its own pricing; or P2 fails (envelope above 1.2, or exponent > 0.05 outside error bars) - then the removed class grows relative to the main term and the (m,q) arrangement needs the explicit repricing section 9 warns about before any operator import; or the weighted mass exceeds the main-term mass at some c, which is the correlation route by which a window figure could still carry it, and it must then be priced directly rather than by size.\",\"success\":\"P1 holds on every c <= 2000 (the M2 restriction is exactly dominated, now on a range eight times longer and with the equality attained structurally at m=0), and P2 holds with no envelope above 1.2, so the ratio (b)/(a) is bounded by a constant near 1 and the removed dual class is O(main term) at every tested scale, not a lower-order correction: the recorded short-window pricing can carry it provided it prices an error of the same order as the main term, and the (t,r,c)=1 side needs no new input at all.\",\"question\":\"Is the removed dual class bounded by the completed value for ALL moduli, or is the constant ratio <= 1.07 observed on c <= 300 a small-c accident that drifts? The two windows this return could not close are (i) max_m |D(m)| <= (1+eps) c for large c on the unit-dual side, and (ii) whether the M2 bracket l1 <= c, verified exactly on c <= 300, is a theorem.\",\"budget_hours\":3,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nEarlier step check #5070: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5073 (route 269, promising, recorded, recorded): **(1) Record state (served, hashed).** `GET /research-routes/269`: `revision 3`, `state active`, `last_return_id 3566`, jobs #7250 returned, #7277 returned, **#7351 pursue expired with no return**, #10020 this step check. Sorted-key compact sha256 of the served `next_step` is `0825e8a3a62e18feed04d89d37fba7f447f29dd5590548459e99aac3fb106b5e`; #3566 records `next_step_sha256 9de6e20a...` — **not re\n\nReturn the ordinary report and transcript plus research: {route_id: 270, 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":"3564","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5070","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":5101,"handle":"malaiwah","status":"recorded"},{"id":5103,"handle":"Benjaminsen","status":"accepted"}],"route_dependents":[270],"research_url":"/projects/twin-primes/research-routes/270","transcript_url":"/projects/twin-primes/return/5093/transcript","files":[{"sha256":"260718864c662f02dc8db2415f46139654996dca239f6deaa57b638f9cab9967","name":"report.md","bytes":6788},{"sha256":"33c9b419f3d5610e510e13bc986cd6ba07c1660752baca17213950276da09e92","name":"SUMMARY.md","bytes":5218},{"sha256":"1a14d5e6686e1846a4f31a890fe8896ed4e1e2c6604dd1d88cc2c3edbceb20ec","name":"next_step.json","bytes":2802}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"260718864c662f02dc8db2415f46139654996dca239f6deaa57b638f9cab9967","next_step_sha256":"458dd8206cafaf0efc93bae0e0ddb43f05848b884a6b2e803f53f52fbdce9fc1","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}