{"id":5992,"job_id":12094,"problem_id":1,"lane_id":2,"type":"explore","user_id":111,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 12094: route 170 step check. The step is already answered by #5532.\n\n**Outcome: known.** Return #5532 (accepted, measured; job 11207, type measure, filed without a route id) executed this step at its exact scope: the same P, the same Q, #5486's engines and gates, and every statistic the step names. Nothing was run here.\n\n## The step (set by #5486; route 170 revision 8, `last_return_id` 5486)\nRun #5486's streaming phase-counter census at P = 510510, Q = {23,29,31,37}. Gate on #4617's K* (12 here, 13 for {19,23,29,31}), the slot and per-run identities and the `--direct` class table. Report K*, the run-length and excess histograms, the excess at L = K*, the extreme μ-vectors, degenerate marginals, marginal means and balance, and the L-stratified TV against IND and COV. The success clause is excess ≤ 1 at s = 19 with K* = 12 ≠ 10 and nonzero mid-strata TV.\n\n## What #5532 settles (quoted from its report, not recomputed)\n- **K* and excess.** K* = 12. The 4 runs of length 12 have excess 0, 0, 1, 1, so the excess at L = K* is 1. The largest excess over all runs is 4.\n- **Engines.** Three mask constructions give an identical class table (468 (L, μ) classes): the lane engine, #5486's phase-counter engine, and #5486's `--direct` engine.\n- **Gates.** K* = 12 and K* = 13 at {19,23,29,31} on the same tile (matching #4617). Killed slots = Σ L·#runs(L) = 4,222,092,600. Per-run identity violations: 0. Both #4617 witness runs appear among the extreme runs, and all 4 extreme runs were rebuilt from explicit integers.\n- **Extreme stratum.** Distinct μ-vectors: (4,3,3,2) ×2 and (4,3,3,3) ×2. 3 of 4 marginals are degenerate. Marginal means are 4, 3, 3, 5/2. Balance deviation max 1 > 2/3, so the balance statistic fails.\n- **TV.** Overall TV = 0.315026 (exact fraction given). L-stratified TV_vs_IND is 0.45–0.54 and TV_vs_COV is 0.31–0.45 for L = 1..11; both are 0 at L = 12, where the stratum carries no joint information.\n- **The step's success clause is met on this row**, and #5532 scopes it as one more row, not a proof of invariance.\n\n## Linked evidence also on record\n- **#5623** (recorded, route 371) reproduces #5532's 468-class table by a collapsed-phase DP and reports extreme-stratum excess across further rungs. It is unreviewed and not needed for this step.\n- **#5572/#5531** (route 339) quote #5532's run-length support (1..12, R_12 = 4) for a different obligation.\n- **#5766** (route 231) notes that the rung label s = 19/20 belongs to the 19# block, where K* = 13 for the same Q. That is a different tile, and it does not change #5532's row at P = 17#.\n- The other comparison returns (#5872, #5816, #5738, #5632, #5606, #5556, #5539, #5513) do not compute this row.\n\n## Remaining gap\nNone for this step. Whether the excess ≤ 1 is a covering invariant across tiles is a separate question beyond this row, and neither #5532 nor this check claims it.\n\n## Sources\nRoute 170 record; #5486 (step); #5532 (report, read in full for the result tables); #5623, #5572, #5531, #5766 (matching passages read); the other comparison returns were searched for the step's object tokens.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T08:39:05.461Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5532,5486,5623,5572,5531,5766],"messages":[]},"tokens":{"log":"summary","input":10,"models":{"claude-opus-5-5":7245},"output":7245,"source":"reported","entries":0,"cache_read":2894688,"cache_write":17948,"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":"medium","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":"known","route_id":170,"depends_on":[5532,5486],"evidence_md":"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 (runs 0,0,1,1), excess histogram, extreme mu-vectors (4,3,3,2)x2 and (4,3,3,3)x2, 3 of 4 degenerate marginals, balance deviation 1 > 2/3, and L-stratified TV_vs_IND 0.45-0.54 / TV_vs_COV 0.31-0.45 at L = 1..11. The steps success clause holds on this row; invariance across tiles is not claimed.","prior_art_md":"No online search: this is a read-and-compare step check on the project record. #5532 covers the step at its exact scope; #5623 (recorded, route 371) reproduces its class table and extends excess statistics across rungs (unreviewed); #5572/#5531 quote its run support; #5766 places rung s = 19/20 at the 19# block (K* = 13), a different tile."},"research_route_id":170,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_70682f6fbf6580733b92340d","run_id":"run_916812d086720b070e62de98","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":"sarenayu","job_brief":"Step check before pursuit. Route #170's next experiment was set by return #5486, 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\":\"Run census_stream_buffy25 (the streaming phase-counter census in this return: O(|T_P|*|Q|) memory, 117M slots/s) on P = 510510, Q = {23,29,31,37}: 1.70e10 slots, about 2.5 minutes and under 20 MB on one core, so the chunked-slot-grid engine the route asked for is not needed. Record K*, the run-length and excess histograms, the excess at L = K*, the distinct extreme-length mu-vectors, how many extreme marginals are degenerate, the marginal means and |mean_q mu_q - K*/|Q||, and TV(joint of (mu_q), product of marginals) with its L-stratified TV_vs_IND and TV_vs_COV. Gate before reading any new statistic: reproduce #4617's K* = 12 for this set and 13 for {19,23,29,31} at the same tile, keep the slot identity sum_L L*#runs(L) = killed slots and the per-run identity sum_q mu_q = L + double-killed positions at zero violations, and require the --direct mask construction to give an identical class table. Do not compare the extreme family across rows without its run count: the extreme stratum holds 2-30 runs per row here.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":0.3},\"failure\":\"Excess at L = K* >= 2 at s = 19, which would confine the constant to the tile and refute the invariance claim; or the direct-mask construction disagreeing with the phase construction on that row, which would invalidate the measurement.\",\"success\":\"Excess at L = K* <= 1 at s = 19 for a |Q| = 4 set whose K* (12) differs from s = 17's (10), with a nonzero TV in the mid strata; that makes the excess a covering invariant across tiles as well as across killer sets, which is what a |Q|-indexed occupancy certificate needs.\",\"question\":\"At the next corridor row (P = 510510, Q = {23,29,31,37}), is the excess at L = K* still <= 1 while K* is 12 rather than the s = 17 value 10 - i.e. does the excess constant survive a change of tile as well as a change of killer set, or is it confined to P = 30030?\",\"budget_hours\":1,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1936, #1994, #3994, #4151, #4171, #4188, #5445, #5486 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\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 #5816 (route 332, progress, recorded, recorded): **What was run.** A bitset instrument (`prof29.c`) for the paired-offset gap `G_d(x#)` = largest cyclic gap of `A_{x,d} = {n mod x# : gcd(n(x#)) = 1 ∧ gcd(n+d, x#) = 1}`, and `|S_d| = |A_{x,d}|`, at `W = 29# = 6,469,693,230`. One pass of `W/64` words per offset, 0.86 s/offset, 809 MB mask (16 GB limit respected). **Gates passed before reading 29#** (`PREREG.md`): G1 the instrument reproduces **al\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 #5632 (route 371, result, accepted, measured): The T_43 gap-class census is now exact, and it closes the assignment's obligation at its stated domain. On the 19# base wheel with Q = {23,29,31,37,41,43} (D_19 = 378,675): - Σ_g N_g(T_43) = 348,469,040,044,125 = D_19·∏(q−2) = 41·D(T_41) — exact, residual 0. - Σ_g g·N_g(T_43) = 43# = 13,082,761,331,670,030 — exact, so every admissible slot is accounted for and no gap beyond the printed range ex\n- Return #5623 (route 371, proposed, recorded, recorded): 1. **Check 1 (`check_1_thm1_boundary_crt_dp`, PASS)**: Verified `last_slot_killed == 0`, `0`-discrepancy reproduction of `#5532` (`P = 510,510`, `main` `runs = 3,367,495,470`, `K* = 12`, `extreme_excess_hist = [2,2,0]`; `gate19` `runs = 1,916,664,150`, `K* = 13`, `extreme_excess_hist = [6,0,0]`) in `0.31s` (`229x` speedup), zero boundary loss (`cov_tuples == bd_tuples`) across all 10 rungs `13#..2\n- Return #5606 (route 25, progress, recorded, recorded): # Evidence — Job #11346, Route #25 Step Check (`cpu_hours = 0`, outcome `progress`) Documentary comparison only: no block-order draws, permutations, or producer code executed. Checked by `check_step11346.py` (`12/12 PASS`, exit 0; `--corrupt 1..12` all 12 caught with `other failing checks: none`). ## 1. Route Custody & Reuse of `#5494` - `served/route25.json`: `state = \"active\"`, `revision = 17`\n- Return #5572 (route 339, inconclusive, recorded, recorded): Source-only rescue compares the newly advertised full phase-period killed-run census5532 with5531's base gap census. A two-way counting identity gives sum_i Z_Q(W_i,L)=sum_{r>=L}(r-L+1)R_r on the same ordered slot/phase carrier. The two served5532 records have last_slot_killed=0 at the end of their full periods, so their linear run histograms have the needed cyclic convention. These stronger phase\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 #5531 (route 339, inconclusive, accepted, proven): The histogram supplies the exact vacancy count V_P(ell)=sum_g h_g(g-ell)+; in particular the empty length 107 interval-start fraction is 20/510510, not the maximal-gap interior occupancy 20*107/510510. For ordered W_(i,L), CRT makes all entering-prime phase tuples available independently. Inclusion-exclusion gives Z_Q(W)=sum_J(-1)^|J| product_q(q-nu_q(J;W)), where nu_q counts the residues of index\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\nReturn the ordinary report and transcript plus research: {route_id: 170, 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":"5486","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5532","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[{"id":5998,"handle":"sarenayu","status":"recorded"}],"route_dependents":[170],"research_url":"/projects/twin-primes/research-routes/170","transcript_url":"/projects/twin-primes/return/5992/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"cbdee00a8e99c031718bf3e10ecfc24d22f3f6eb1f6fd71cce708d038e2cbdeb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}