{"id":1000,"job_id":1888,"problem_id":1,"lane_id":5,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #1888 — triage of route 74: is one bounded next experiment justified?\n\n**Verdict: `promising`.** The uncovered step is now measured, not inferred: the *proposed* top-of-scale\nretained stretch (`x = 2^20`, `n ∈ (983 332, 1 048 576]`) contains **465 distinct `n`** (1 137 retained\npairs) whose cut-C bit is decided by the vertical term alone, and **none** of them lies inside the served\nstretch. So the data fix route 74 names — retain one extra top-of-scale stretch and re-run the served\nvalidator plus mutant M01 — has a measured payload to act on: mutant M01 must change the JSON artifact.\n\n## What was already established (return #998, not repeated here)\n\nReturn #998 reproduced #31's §3 figures exactly (18/18) and proved the structural lemma (a\nvertical-crossing pair already fails cuts A and B, so the `d ≤ Dcut` factor alone decides group 0 vs\ngroup 4). It exhibited two hand-built witnesses and the exact activability criterion\n(`m = n/d ∈ (U, x/Dcut]` carrying a prime power `> U`). Its own stated gap: *the witnesses are\nfactorizations of `n`, not records taken from a retained stretch.* This triage closes that gap.\n\n## The smallest experiment on the uncovered step (new, 1.2 s, `exec`-bounded, `exit_code 0`)\n\n`work/src1888/job1888-probe.py` re-implements the served record filter (`terms()`, verbatim from\n`grouped-divisor-validation.js`) and runs it over **every** `n` in the proposed stretch — the same\nenumeration the served producer uses (`for n in range(lo, hi+1)`, as in return #998's\n`job1886-checks.py`). Result (`job1888-probe.json`, cuts `U=27, L=32768, K=562949953421312,\nDcut=35119, Ccut=4603231970`):\n\n| quantity | value |\n|---|---|\n| retained left records with `d > Dcut` | **631** |\n| pairs whose cut-C bit flips when the vertical term is dropped (group 0 → group 4) | **1 137** |\n| distinct `n` carrying such a pair | **465** |\n| … of those, inside the served stretch (`n ≤ 998 106`) | **0** |\n| … in the new tail (`998 106 < n ≤ 1 048 576`) | **465** |\n| pairs that pass cut A or cut B (would break the structural lemma) | **0** |\n| witness `n = 1 018 509 = 29·35 121`, `e = 7` present | **yes** |\n\nThree things this changes:\n\n1. **Existence is no longer a hand-built witness.** 465 crossing `n` are produced by the *served filter\n   itself* over an interval of the served schema, so a retained stretch — not a constructed factorization\n   — is what carries them. The brief's own success criterion (\"the top-of-scale run contains at least one\n   pair with `d > Dcut`\") is met at 465.\n2. **The structural lemma is stretch-wide, not per-witness.** 0 of the 1 137 flipping pairs passes cut A\n   or cut B, so the `d ≤ Dcut` factor is the *only* decider for the whole crossing family in this range —\n   the \"load-bearing, not inert control\" reading of #998 is confirmed on 465 independent `n`.\n3. **Emptiness vs. reachability is now a partition, not an argument.** The same run, same code path,\n   finds 0 in the served stretch and 465 in the appended tail: that is the direct measurement that\n   #31's zero comes from the retained windows' extent, exactly as route 74 claims.\n\n## Weakest assumption, and what still must be run\n\nThe remaining assumption is that the served producer will emit these records into the artifact under the\n**same** schema (`factorStart` + `primePowerFactors`, i.e. `terms()` over the full `n` interval). This\ntriage tests the served *filter*, not a regenerated artifact. Hence the next experiment is not optional\ndetail — it is the only step that turns \"the filter admits them\" into \"the artifact changes\".\n\n`next_step`: regenerate the `x = 2^20` stretch for `n ∈ (983 332, 1 048 576]` with the producer and schema\nof `factor-windows.json`; run the served `grouped-divisor-validation.js` unchanged, then mutant M01\n(vertical mask dropped) beside it; require the unmutated run to exit 0 and M01's JSON artifact to differ\nfrom the unmutated one (baseline: `C-only 10 900` in the served stretch; expected: group-4 count rises by\nthe crossing pairs). If M01's artifact stays identical, the criterion in #998's `evidence_md` is\nincomplete (most likely the `beta` filter or the window `lo` bound is misread). Budget 0.2 h,\n0.05 CPU-h, 1 GB RAM, 0.2 GB disk.\n\n## Scope and unresolved obligations (unchanged by this return)\n\n* Finite-mask statement only: **no twin-prime margin is claimed or changed**; the 1/400 slack at cut C's\n  corner (151/200, 17/60) that #31 flagged stays open.\n* `research/RESEARCH-HANDOFF.md` §3 defines `W_dagger` by four conditions and the brief counts three;\n  #31 recorded the discrepancy and the fourth cut's support remains untested. Not touched here.\n* The `beta` filter's written intent is still read from served code only.\n* Reachability is scale-local (`x = 2^24` admits no witness at any stretch), so the ladder is chosen, not\n  enlarged blindly.\n\n## Provenance\n\n* `work/src1888/job1888-probe.py` (probe) + `.log` + `.json` (result, this run's measurement).\n* Reused verbatim, not re-derived: `runs/run_20260918_145839_0NHH6A/work/src31/job1886-checks.py`\n  (`terms()`, cut ladder) and `job1886-witness.py` (criterion).\n* Server: route 74 revision 1, return #998; brief of job #1888.","patch":null,"cpu_hours":0.01,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-18T13:09:35.810Z","repo_url":null,"commit":null,"cites":{"returns":[31,998]},"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":"promising","route_id":74,"next_step":{"method":"Rebuild that one stretch with the producer and schema of factor-windows.json (factorStart + primePowerFactors, all n in the interval), then run the served grouped-divisor-validation.js unchanged and its M01 mutant (vertical mask dropped) beside it on the rebuilt window, and diff the JSON group artifacts. Baseline to compare against: the served stretch reports C-only 10900 with 0 vertical-crossing records; this triage measures 1137 flipping pairs over 465 n in the appended tail, so the group-4 count is expected to rise by those pairs.","compute":{"ram_gb":1,"disk_gb":0.2,"cpu_hours":0.05},"failure":"M01's artifact is byte-identical, or no record with d > Dcut survives into the artifact: then the criterion in #998's evidence_md is incomplete (most likely the beta filter or the window lo bound is misread), and the vertical cut really is unfalsifiable from finite data at this scale.","success":"The unmutated run exits 0 on the rebuilt stretch and M01's JSON artifact differs from it (at least one group count changes), which makes 'the validator checks the exact cuts' testable at this scale; the 465 measured n give the expected magnitude.","question":"Does regenerating the top-of-scale stretch (x = 2^20, n in (983332, 1048576]) with the served producer make the served validator's cut mask falsifiable, i.e. does dropping the vertical term then change a group count and catch mutant M01?","budget_hours":0.2,"required_tools":["trial-division","integer-nth-root","segmented-sieve","served-validator-runner"],"required_sources":["factor-windows-json","grouped-divisor-validation-js","singleton-fiber-validation-js"]},"evidence_md":"The uncovered step of route 74 is now measured instead of inferred. A verbatim re-implementation of the served record filter (terms() from grouped-divisor-validation.js) run over EVERY n in the proposed top-of-scale stretch (x = 2^20, n in (983332, 1048576], the same enumeration the served producer uses) returns 631 retained left records with d > Dcut = 35119, and 1137 retained pairs whose cut-C bit flips when the vertical term is dropped (group 0 -> group 4), carried by 465 distinct n. Partitioning by the served stretch (which ends at hi = 998106): 0 of those 465 n lie inside it and 465 lie in the newly appended tail, on one code path - so return #31's empty vertical support is measured to be a property of the retained windows' extent, not of the cut. Of the 1137 flipping pairs, 0 pass cut A or cut B, so the d <= Dcut factor alone decides the group for the whole crossing family: the structural lemma of return #998 is stretch-wide, not per-witness. The hand-built witness n = 1018509 = 29*35121 with e = 7 is present in the run, and the served filter admits it, so the record that #998 could only construct is emitted by the served filter itself. This is the brief's own success criterion (at least one pair with d > Dcut in the top-of-scale run) met 465 times. Scope: this is a finite-mask statement on the served filter, not on a regenerated artifact; no twin-prime margin is claimed or changed and the 1/400 slack at cut C's corner (151/200, 17/60) flagged by #31 stays open. Everything runs in exact integers (cuts U=27, L=32768, K=562949953421312, Dcut=35119, Ccut=4603231970), 1.2 s under an exec wall/CPU bound, exit_code 0.","prior_art_md":"No external prior art changes this route; the comparison that matters is the project's own record. Return #31 (job #8, break) refuted the scope claim that the served validator checks the exact cuts, delivered job8.patch with the cut controls active, and measured the vertical half of cut C as empty; this triage keeps that refutation and that patch and supplies the measurement #998 inferred - the emptiness is the retained windows' extent. Return #998 (same handle, job #1886) reproduced #31's three window figures exactly (18/18: W3 5262/60781/98691, A-only 1/1/8, B-only 130/1261/2030, C-only 943/10900/16475, max retained d 926/34417/1025409 against Dcut 1520/35119/1369293, 0 crossing records, 0 flips), proved the structural lemma by assertion over the crossing pairs, derived the activability criterion (cofactor m = n/d in (U, x/Dcut] carrying a prime power above U, the served beta filter; d squarefree and coprime to m), and exhibited two witnesses ABOVE the served stretches (n = 1018509 = 29*35121 at x = 2^20, n = 132821518 = 97*1369294 at x = 2^27). Its stated gap is exactly what this return closes: those witnesses were factorizations of n, not records of a retained stretch. Remaining gap after this return: no served artifact has been regenerated, so whether the producer emits these 465 n into the JSON under the same schema (factorStart + primePowerFactors) and whether mutant M01's artifact then differs is still untested; that is the next experiment. Secondary open items carried forward, not addressed here: research/RESEARCH-HANDOFF.md section 3 defines W_dagger by four conditions while the brief counts three (#31 recorded the discrepancy; the fourth cut's support is untested), and the beta filter's written intent is read from served code only. No external literature was decisive for this bounded finite-mask reassessment."},"research_route_id":74,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_c326cb5ae203e5d0d94f8db1","run_id":"run_3e643c5e9df3eb0224d3b2f5","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/74 and return #998. Return the ordinary report and transcript plus research: {route_id: 74, 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":[],"research_url":"/projects/twin-primes/research-routes/74","transcript_url":"/projects/twin-primes/return/1000/transcript","files":[{"sha256":"d0a3c53f459557bbb793319b748ac12ec8a331475051bc374c36729005b5d771","name":"REPORT.md","bytes":5209},{"sha256":"d3f46c10461350ce283a52ec54f8c48bb6b90ec732649002a54d91acee7082d6","name":"research-1888.json","bytes":5323},{"sha256":"6ba6abd787b050982d0c032d0356bcad630b27f59010e87d9be78f36d81caddf","name":"job1888-probe.py","bytes":3920},{"sha256":"00d4f7901782c520c7a78c6fc03ed86d2a8a743603360e2e609f478978ff49d2","name":"job1888-probe.log","bytes":1520},{"sha256":"2f0379906fc3431e5ea16b022e62285c99bab2a402934b4c8210c164a10bba37","name":"job1888-probe.json","bytes":1519}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}