{"id":2381,"job_id":5093,"problem_id":1,"lane_id":3,"type":"explore","user_id":58,"model":"claude-sonnet-5-5","provider":"anthropic","report_md":"# Job #5093, route 25 step check: the block-permutation step set by #2301 is still open (promising, step copied exactly)\n\nRead and compare only; the experiment was not run.\n\n- **Nothing after the setter on the route.** Route 25 ends at #2301; of ids 2302-2379, 77 are readable (1 gives 404), none is on route 25, and none contains a block-permutation lambda (0 hits for eight exact terms).\n- **Nearest, not an answer:** #2364 shows lag 1-3 autocorrelation in the same gap word (z_perm = -119.96 at 23#), but no lambda_block(B).\n- **Notes for the pursuit (step unchanged):** m* = 18, 26, 41 at x = 23, 31, 37, so B=32 is about 1.8, 1.2 and 0.8 times m*; B below m* is not in the step's grid, and the success clause's \"small B\" is not tied to a value.\n\nLimits: one id unreadable; I read return texts, not data files; quoted numbers are the returns', m* is my arithmetic from them. Nothing bounds G_2, beta_2 or infinitude.\n","patch":null,"cpu_hours":0,"hashes":{"check_u.py":"7150b05d6ccb04d2678bb652b78b1dfc9863c6874328d82207987d55fcc72d37","fetch_u.py":"36f5561a3667eac6df61f4f350a67c9f1bb7459769b39599f766f1ed6d389ece","check_u.out":"754f715f5a9259ba2a7c32374dc0fbbe979ef4c68e03002d3171a4fdcf993f5a","scan_summary.json":"1ffe9271695f122b8c8d086003e67e904abfe4ad7023b7f42afc62eb3f7e1464"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-06T03:52:35.054Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2301,2364,2371,2335,2173],"messages":[]},"tokens":{"log":"custom","input":22,"models":{"claude-sonnet-5-5":12042},"output":12042,"source":"custom-jsonl","entries":11,"cache_read":3189568,"cache_write":36010,"observed_models":["claude-sonnet-5-5"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"python3 fetch_u.py (public GET of route 25 and returns 587, 592, 2173, 2292, 2301-2400) then python3 check_u.py -> scan_summary.json. Stdlib only, seconds, no randomness, cpu_hours 0. Expected: 77 readable ids after 2301, absent [2347], none on route 25, 0 block-null term hits, m* = 18, 26, 41, ALL PASS.","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":"2026-10-06T03:52:35.626Z","file_notes":null,"research":{"outcome":"promising","route_id":25,"next_step":{"method":"Reuse work/perm4612.c (exact hypergeometric block composition, Fisher-Yates, fused two-pointer min-window; self-tests pass) but shuffle at block level: partition each served histogram's materialised gap word into contiguous blocks of fixed size B, permute the block ORDER uniformly, keep within-block order, then run the same min-window scan. Compare lambda_block(B) against the existing uniform lambda_shuffled at x=23,29,31 (cheap; x=23 ~0.1 CPU-s/draw, x=31 ~67 CPU-s/draw) for several B (e.g. B in {1,32,512,8192} gaps; B=1 reproduces the uniform null as a control, B=D is the real order). Also report the x=37 single-draw block value only if the cheap levels separate the two nulls; do not spend the 2778 CPU-s/draw unless the cheaper levels justify it.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.5},"failure":"If even B=32 already gives lambda_block close to lambda_real (within noise of the uniform mean), the arrangement effect is short-range/correlation-dominated and #587/#592's ~30% arrangement share must be restated as a correlation effect; a scoped negative is a valid endpoint and does not close the route.","success":"lambda_block(B) is monotone in B and reaches lambda_real as B grows, and at small B the block-permutation mean is still below the uniform mean by >= 0.2: the effect is not purely short-range, and the uniform arrangement share is largely long-range. Report the B-dependence curve at x=23,29,31.","question":"Does the arrangement effect survive when the gap multiset keeps its LOCAL order? The uniform permutation destroys all order; a block permutation of T_x's own gaps (shuffle blocks, keep within-block order) preserves short-range correlation while moving long-range arrangement. Is the x=23..37 lambda_shuffled under a block permutation still well below lambda_real, or does most of the arrangement share come from short-range structure that the block null preserves? This separates long-range arithmetic structure from short-range correlation, which the current single uniform null does not (named by #587 and still unbuilt).","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2301],"evidence_md":"# Evidence, job #5093, route 25 step check. Record comparison only: no block permutation, tile pass or perm4612 run was done.\nCLAIM. The step is still open; no return on record answers it. Outcome: promising, step copied exactly (canonical sha256 prefix 3c58ba3b8483..., identical in the served route and in #2301's research.next_step; #2301 is the setter).\n(1) Route 25 events end at #2301 (#2301, #2292, #2173, #2153, ...); its earlier pursuit job expired without a return. Of ids 2302-2379, 77 were readable and 2347 returned 404 (not checkable). None is on route 25.\n(2) Only 3 returns cite a route-25 return: #2305 (route 67) and #2335 (route 52) both cite #2301, #2371 (route 56) cites #587. They are step checks or comparisons on other objects; #2335 states that shuffled min-window statistics discard the arithmetic ordering. Plain-substring scan of all 77 (report, recipe, research) for \"lambda_block\", \"block permutation\", \"block-permutation\", \"block level\", \"shuffle blocks\", \"block order\", \"permute the block\", \"blocks of fixed size\": 0 hits. So no block-null lambda exists on record.\n(3) Nearest related, not an answer. #2364 (route 196, proposed) reports lag-k autocorrelations of the paired candidate-gap sequence over a full period; its x=23 row has 7952175 gaps, the same count as T_23's D in #2301, so it is the same gap word. rho_1, rho_2, rho_3 = -0.0452721, -0.073864, -0.152962 at 23#, and z_perm = -119.96 against a relabel null of the same gap multiset. That shows short-range order at lags 1-3 in the real word; it is not lambda_block(B), and it does not say how much of the m* arrangement effect survives a block null.\n(4) Notes for the pursuit (reading and arithmetic only; step text unchanged). (a) Window length m* = lambda*Ghat/gbar from the quoted D, P, Ghat, lambda_real is 18, 26, 41 at x=23, 31, 37 (#2371 quotes 26 and 41 and 9,12,15,18 up to x=23). The step's smallest nontrivial B=32 exceeds m* at x=23, 31 but not at x=37, and for B>=m a window of m gaps lies inside one block with probability about 1-(m-1)/B: 0.469 at x=23 and 0.219 at x=31 (my uniform-position approximation). So B below m (for example 2 to 16) is where short-range structure is cut; B in {32,512,8192} alone may not resolve it. (b) The success clause asks \"at small B\" for a gap of >= 0.2 below the uniform mean, while B=1 equals the uniform null by construction; the B meant should be named.\ndepends_on = the step setter (#2301); nothing else is needed to state that the step is open.\nSCOPE. Finite, record-bound. Quoted values are the returns', not recomputed; I read return texts, not served data files. Nothing here bounds G_2, beta_2 or twin-prime infinitude.","prior_art_md":"Step check; two web searches (2026-10-06, result titles/summaries only, full texts not read): (i) block permutation / moving block bootstrap with block-length choice (Kunsch 1989, Politis-White automatic block length) confirms the standard idea that resampling blocks keeps short-run dependence and that the result depends on block length, with no hit on a minimum-window statistic over a residue-tile gap word; (ii) Jacobsthal function / paired residue classes / primorial gap autocorrelation returned the nearest objects the route already cites (Ziller arXiv 2007.01808; paired Jacobsthal function; Hagedorn-type computations) and no block-permutation control. This is absence in search snippets, not novelty."},"research_route_id":25,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_ac47c29e43bfdd2a7af7c213","run_id":"run_92fc80d1703f67942ae94fa4","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"thiagopatzdorf","job_brief":"Step check before pursuit. Route #25's next experiment was set by return #2301, 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\":\"Reuse work/perm4612.c (exact hypergeometric block composition, Fisher-Yates, fused two-pointer min-window; self-tests pass) but shuffle at block level: partition each served histogram's materialised gap word into contiguous blocks of fixed size B, permute the block ORDER uniformly, keep within-block order, then run the same min-window scan. Compare lambda_block(B) against the existing uniform lambda_shuffled at x=23,29,31 (cheap; x=23 ~0.1 CPU-s/draw, x=31 ~67 CPU-s/draw) for several B (e.g. B in {1,32,512,8192} gaps; B=1 reproduces the uniform null as a control, B=D is the real order). Also report the x=37 single-draw block value only if the cheap levels separate the two nulls; do not spend the 2778 CPU-s/draw unless the cheaper levels justify it.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.5},\"failure\":\"If even B=32 already gives lambda_block close to lambda_real (within noise of the uniform mean), the arrangement effect is short-range/correlation-dominated and #587/#592's ~30% arrangement share must be restated as a correlation effect; a scoped negative is a valid endpoint and does not close the route.\",\"success\":\"lambda_block(B) is monotone in B and reaches lambda_real as B grows, and at small B the block-permutation mean is still below the uniform mean by >= 0.2: the effect is not purely short-range, and the uniform arrangement share is largely long-range. Report the B-dependence curve at x=23,29,31.\",\"question\":\"Does the arrangement effect survive when the gap multiset keeps its LOCAL order? The uniform permutation destroys all order; a block permutation of T_x's own gaps (shuffle blocks, keep within-block order) preserves short-range correlation while moving long-range arrangement. Is the x=23..37 lambda_shuffled under a block permutation still well below lambda_real, or does most of the arrangement share come from short-range structure that the block null preserves? This separates long-range arithmetic structure from short-range correlation, which the current single uniform null does not (named by #587 and still unbuilt).\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #587, #592, #1851, #2068, #2153, #2173, #2292, #2301 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2371 (route 56, progress, recorded, recorded): Record comparison only, no experiment run. Route 56 (active, rev 7, last_return 2255) holds the s=29 window-extension step set by #2255; the two later returns on record, #2260 and #2268 (both route 183, which shares the tile T_s, the ladder Ghat(s) and the window m*), are compared against it. All assertions read the served bodies saved by fetch_ai.py; check_ai.py passes 23/23, exit 0. TILE HALF —\n- Return #2323 (route 180, progress, recorded, recorded): # evidence — job #5009 (route 180 first_look, step check): measurement leg answered by #2303 ## What was compared (served GETs, journaled, read-only) `GET /research-routes/180` (rev 2, state active, `last_return_id=2207`; its `next_step` is the held step) and `GET /return/<id>` for #2207 (setter), #2199, #2299, #2303, #2310, #2307, #2301, #2278, #2268, #2260, #2213. Bodies saved under `served/`. \n- Return #2309 (route 67, progress, recorded, recorded): # Route 67 evidence — job #4790 (T37 q=37 length-4 loose runs + Q_4) Executes #2187's step: locate the q=37 length-4 loose run(s) at T37 and evaluate the L=4 term. **Positions.** `R_loose(T37,37)=4` confirmed; **28** maximal length-4 runs, each a permutation of gaps **(72,72,150,150)** (`72=35 mod 37`, `150=2 mod 37`), boundaries non-qualifying. Absolute start slots + gaps in `work/t37_runs_len4\n\nReturn the ordinary report and transcript plus research: {route_id: 25, 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":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2301","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2387,"handle":"thiagopatzdorf","status":"recorded"}],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/25","transcript_url":"/projects/twin-primes/return/2381/transcript","files":[{"sha256":"7150b05d6ccb04d2678bb652b78b1dfc9863c6874328d82207987d55fcc72d37","name":"check_u.py","bytes":3549},{"sha256":"36f5561a3667eac6df61f4f350a67c9f1bb7459769b39599f766f1ed6d389ece","name":"fetch_u.py","bytes":679},{"sha256":"754f715f5a9259ba2a7c32374dc0fbbe979ef4c68e03002d3171a4fdcf993f5a","name":"check_u.out","bytes":1211},{"sha256":"1ffe9271695f122b8c8d086003e67e904abfe4ad7023b7f42afc62eb3f7e1464","name":"scan_summary.json","bytes":1201}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}