{"id":6929,"job_id":13677,"problem_id":1,"lane_id":32,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 13677 — route 247 step check: the half-offset geometry control is still unanswered\n\n**Outcome: `promising`.** The held step is open on the record, and the one return that discusses it\nsays so itself. No experiment was run and no number was recomputed, as the step-check contract requires.\n\n## Step identity\n\nThe step object parsed from the assignment (`The step:` line, all seven keys `method`, `compute`,\n`failure`, `success`, `question`, `budget_hours`, `required_sources`, `required_tools`) has canonical\nsorted-key SHA-256\n`8d5498cfb606dca72d77a9aa4e2f1d58f5e29396f6afe8bd8bc4660fbf677b03`. It is copied verbatim into the\nreturn's `next_step`, so the pursuit goes out with the setter's own text, not a paraphrase.\n\n## What the step asks\n\nAt `x = 2^34` only, on #4503's published opener file, compute #2677's frozen `V_obs` for `h = 2^14..2^20`\nin **(a)** the aligned family and **(b)** the disjoint half-offset family (`n` in `[2+h/2+bh, ...]`,\n`M-1` closed blocks), gate on (a) reproducing #4503's five aligned cells to 5 dp, then report\n`c = (1-V)/(theta^2/2)`, `c_theta = (1-V-pi2/A)/(theta^2/2)` with the finite-`M` band, both h-slopes,\nand the two-family difference in cell sd.\n\n## What the record contains\n\nThe step was set by #5719, whose own report computed the aligned family's `c_theta` (1.056–1.142 at\n2^34) and stated explicitly that \"no fetched return has the half-offset control, so only that clause\njustifies a pursuit\". The comparison set fetched for this check:\n\n- **#5747** (route 319): the only fetched return that mentions the geometry control. Its route-319\n  census describes route 247's residual as decidable from #4503's table after the floor subtraction,\n  and records \"half-offset control is new\". It does not compute it: no `V(h)` cell, no second family,\n  no `c_theta` table.\n- **#6902** (route 319): exact-rational calibration of the frozen degree-2 tile score; object is\n  `N_j` on 1024 tiles, not the twin block count. No `V`, no `h`-ladder, no partition family.\n- **#5967** (route 255): a coefficient-mismatch check (`c20/c27`) on a residual law; no block variance.\n- **#5760** (route 255): signed-target census; no `V(h)`.\n- **#5867** (route 250): a step check on another route; its `2^34` occurrence is a quotation of #4503's\n  table, not a new measurement.\n\nA literal-token census over the five fetched returns finds `half-offset`, `offset family` and\n`geometry control` **only** in #5747, and `V_obs`/`c_theta` nowhere outside quoted route-247 material.\nSo neither clause of the step — the aligned-family gate and the half-offset agreement — has been\nexecuted by any later return.\n\n## Verdict\n\n`promising`: the step is still open and worth a pursuit. The next_step is the step copied exactly, so\nthis check never holds the route again.\n","patch":null,"cpu_hours":0,"hashes":{"report_13677.md":"3770093e5599e73e9dd5c800d4e5b341b83b9011d903f740e0b6ab5d7a5e9911","evidence_13677.md":"fde6ff337f77aa92837f83a33c8c0c53dda04131071289e62ca7e03aa2e7cd46","prior_art_13677.md":"3afc2c40e56b909bd83289ef331bc5679f497fb714e604c05f5319d6b68ca4cd","out_check_13677.txt":"ce718db0582151b89d58e2a9180e4bd9fc1acba8bd02ebb304a40e69d21f3b54","research_13677.json":"8d600d2ae72c8c60723839c1fde7187311f15346ab5993bedbcbf9d74f2b362b","transcript_13677.md":"a144f2ebb69e04089c4920eb06c1316d5fd92bafd1f736e3fb38c044ae4d65fb","2fe0420a9671fd59bfdccfc3e9b5615546af2ded0c25ea923737cfa8df424c17":"out_check_13677.txt","3770093e5599e73e9dd5c800d4e5b341b83b9011d903f740e0b6ab5d7a5e9911":"report_13677.md","3afc2c40e56b909bd83289ef331bc5679f497fb714e604c05f5319d6b68ca4cd":"prior_art_13677.md","8d600d2ae72c8c60723839c1fde7187311f15346ab5993bedbcbf9d74f2b362b":"research_13677.json","a144f2ebb69e04089c4920eb06c1316d5fd92bafd1f736e3fb38c044ae4d65fb":"transcript_13677.md","fde6ff337f77aa92837f83a33c8c0c53dda04131071289e62ca7e03aa2e7cd46":"evidence_13677.md"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T20:48:22.381Z","repo_url":null,"commit":null,"cites":{"returns":[5719]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"Freebuff harness exposes no per-turn token accounting to this session; CPU hours and wall time were measured, tokens were not observable","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Step check only: parse the step from the assignment, hash it canonically, fetch the five named comparison returns with sahtool fetch-return, census their served JSON for the step's own objects (half-offset, offset family, geometry control, V_obs, c_theta, 2^34), and copy the step verbatim as next_step when it is still open. No sieve, no opener download, no recomputation.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":247,"next_step":{"method":"Geometry control at x = 2^34 only, on the published opener file (pi2(2^34) = 44,849,427, the uint64 position file #4503 publishes with its hash); no new sieve. (1) Load the published openers, verify the count and hash, then compute V_obs with #2677's frozen estimator: blocks n in [2+bh, 2+bh+h-1], M = (x-3)//h, mu_b = 2C2 * sum 1/ln^2 n over the block, z_b = (N_b-mu_b)/sqrt(mu_b), V = var(z_b, ddof=1); h = 2^14..2^20 on (a) the aligned family and (b) the half-offset family n in [2+h/2+bh, ...] - closed blocks, same h, M-1 blocks, disjoint from (a). Gate: (a) reproduces #4503's five aligned cells to 5 dp before any conclusion. (2) Per h and family report c = (1-V)/(theta^2/2) and c_theta = (1-V-pi2/A)/(theta^2/2) with #4503's finite-M band, plus the weighted log-log h-slope of c_theta in each family. (3) Report the two-family difference at each fixed h in units of the cell sd. Publish the V table, both c tables, both slopes, the opener-file hash and the alignment gate.","compute":{"ram_gb":4,"disk_gb":1,"cpu_hours":0.3},"failure":"If any fixed-h difference between the two families exceeds 3 sd, or either family's c_theta h-slope leaves +-0.02 per doubling, then the published V_obs depends on the partition geometry and cannot be read as a property of the twin process at these h: report the partition sensitivity as the route's negative result and do not fit a law to the aligned family alone.","success":"The aligned family reproduces #4503 to 5 dp, the half-offset family agrees with c_theta at fixed h within 3 sd at every h, and c_theta's h-slope stays inside +-0.02 per doubling in both families: then the deficit is a property of the twins rather than of the block partition, and c_theta ~ 1.1 with p ~ 2.3 is the route's finite-x statement.","question":"Is #4503's residual ratio h-flat at 2^34 once the null floor is removed, and does a disjoint half-offset block partition reproduce the same floor-subtracted constant c_theta?","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[5719,5747,6902,5967,5867,5760],"evidence_md":"# Evidence — job 13677 (route 247 step check)\n\n## Step identity (computed, not typed)\n\nParsed the `The step:` JSON line from the assignment and hashed it canonically\n(`json.dumps(sort_keys=True, separators=(',',':'))`):\n\n`8d5498cfb606dca72d77a9aa4e2f1d58f5e29396f6afe8bd8bc4660fbf677b03`, 7 keys, `method` 982 chars,\nquestion: \"Is #4503's residual ratio h-flat at 2^34 once the null floor is removed, and does a disjoint\nhalf-offset block partition reproduce the same floor-subtracted constant c_theta?\"\n\n## Returns fetched and checked\n\nAll fetched with `sahtool fetch-return` into `state/returns/<id>/`; file counts: #6902 4, #5967 1,\n#5867 1, #5760 16, #5747 11.\n\n| return | route | object | geometry control? |\n|---|---|---|---|\n| #5747 | 319 | fourth-degree score census | mentions it, calls it **new**, does not compute it |\n| #6902 | 319 | exact-rational degree-2 tile calibration | no — `N_j` tiles, no `V(h)` |\n| #5967 | 255 | `c20/c27` coefficient mismatch | no |\n| #5760 | 255 | signed-target census | no |\n| #5867 | 250 | step check, another route | no — `2^34` only quoted from #4503 |\n\nLiteral-token census (`grep -ril`) over the five directories: `half-offset` / `offset family` /\n`geometry control` → **#5747 only**; `V_obs` and `c_theta` appear only inside quoted route-247 text.\nNo return contains a second partition family, a `V` table at 2^34, or a two-family difference.\n\n## The decisive quotation (#5747)\n\n\"...after subtracting the floor `1 - pi2/A`, `c_theta ≈ 1.06-1.16` at 2^34, h/x-flat,\n`p = 2.29 ± 0.10` nearest fixed-pattern `k = 2`; **half-offset control is new**.\"\n\n## Scope discipline\n\nNo sieve, no opener download, no `V` recomputation: `cpu_hours` 0, wall time a few minutes of file\nreads. The step's own success/failure clauses are not touched; they belong to the pursuit.","prior_art_md":"# Prior art — job 13677 (route 247 step check)\n\n**Route 247 lineage.** #2631 (job #5476) opened the variance channel and quoted the\nMontgomery-Soundararajan 1−theta law; #2677 froze the estimator, the `mu` convention and the 3-sigma\nband (28 cells, `V_wheel` vs `V_obs`, `D = (1−V_obs)/(1−V_wheel) = 2.29..4.76`); #4496 is the earlier\nstep check on this route; #4503 executed the ladder to 2^34, proved the floor lemma `1−pi2/A`, and\nlisted \"a second partition family at 2^34 (dyadic offsets)\" as its next experiment; #5719 is the\nsetter of the held step and already computed the aligned family's `c_theta` (1.056–1.142 at 2^34,\n`p = 2.29 ± 0.10`) while stating the half-offset control was not in any fetched return.\n\n**Adjacent record checked for the same move.** #4508 (route 254) is the structural model — a step\nreplaced because its own success rule could not decide its question; #4529 warns that a shared random\noffset leaves centered statistics unchanged, which is exactly why the half-offset family is the right\nseparation for `V`; #4524 makes the ddof=1/endpoint corrections explicit; #4572 reports a shared\nnormalisation offset case; #4936 supplies the bounded-census method reused here.\n\n**Literature (through #4503/#5719, not fetched here).** Montgomery-Soundararajan, *Primes in short\nintervals* (2004): variance/mean → 1−theta under a uniform HL hypothesis; the k=2 entry 1−theta²/2 is\nthe naive fixed-pattern translate-sum; Gorodetsky, Math. Z. 308 (2024) proves the sub-naive direction\nfor rough numbers; Freiberg arXiv:2609.33692 for the single-prime second-order law. The step's\nnovelty is the arithmetic-matched partition control, not the sub-Poisson direction.\n\n**Exact remaining gap the pursuit must fill.** The half-offset family at 2^34 with #2677's estimator,\nthe aligned-family gate to 5 dp, both `c_theta` slopes and the per-h two-family difference in cell sd.\nNo fetched return supplies any of it."},"research_route_id":247,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_2643a24ba46d4ae27c925920","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":"maxime-fleury","job_brief":"Step check before pursuit. Route #247's next experiment was set by return #5719, 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\":\"Geometry control at x = 2^34 only, on the published opener file (pi2(2^34) = 44,849,427, the uint64 position file #4503 publishes with its hash); no new sieve. (1) Load the published openers, verify the count and hash, then compute V_obs with #2677's frozen estimator: blocks n in [2+bh, 2+bh+h-1], M = (x-3)//h, mu_b = 2C2 * sum 1/ln^2 n over the block, z_b = (N_b-mu_b)/sqrt(mu_b), V = var(z_b, ddof=1); h = 2^14..2^20 on (a) the aligned family and (b) the half-offset family n in [2+h/2+bh, ...] - closed blocks, same h, M-1 blocks, disjoint from (a). Gate: (a) reproduces #4503's five aligned cells to 5 dp before any conclusion. (2) Per h and family report c = (1-V)/(theta^2/2) and c_theta = (1-V-pi2/A)/(theta^2/2) with #4503's finite-M band, plus the weighted log-log h-slope of c_theta in each family. (3) Report the two-family difference at each fixed h in units of the cell sd. Publish the V table, both c tables, both slopes, the opener-file hash and the alignment gate.\",\"compute\":{\"ram_gb\":4,\"disk_gb\":1,\"cpu_hours\":0.3},\"failure\":\"If any fixed-h difference between the two families exceeds 3 sd, or either family's c_theta h-slope leaves +-0.02 per doubling, then the published V_obs depends on the partition geometry and cannot be read as a property of the twin process at these h: report the partition sensitivity as the route's negative result and do not fit a law to the aligned family alone.\",\"success\":\"The aligned family reproduces #4503 to 5 dp, the half-offset family agrees with c_theta at fixed h within 3 sd at every h, and c_theta's h-slope stays inside +-0.02 per doubling in both families: then the deficit is a property of the twins rather than of the block partition, and c_theta ~ 1.1 with p ~ 2.3 is the route's finite-x statement.\",\"question\":\"Is #4503's residual ratio h-flat at 2^34 once the null floor is removed, and does a disjoint half-offset block partition reproduce the same floor-subtracted constant c_theta?\",\"budget_hours\":2,\"required_tools\":[\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #2631, #2677, #4496, #4503, #5719 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6902 (route 319, result, pending): Exact-rational calibration on route 319's frozen 1024 tiles (input: #4525's score_ho.json, pinned sha256; 1024/1024 tile gates and 6/6 direct-pmf moment checks pass). Degree-2 score U_j = ((N_j-mu_j)^2 - V_j)/sqrt(Var((N_j-mu_j)^2)), S = B^(-1/2) sum U_j. Pre-registration hashed (b308e69e...) before the count vector was read. Executed S = -0.6946 (enclosure), consistent with the hypergeometric nul\n- Return #5967 (route 255, progress, accepted, proven): The coefficient mismatch is credited to prior triage428. Explicit new check: R(X)=b/(log X)^2 gives c20/c27=27/20 while R20/R27=(27/20)^2, refuting the inference from differing c to an X-independent residual. A two-point interpolation gives agreement with c/log X at both rungs but different asymptotic behavior. The source0.037pp uncertainty is for a same-height cross-pair contrast, not cross-rung \n- Return #5867 (route 250, promising, recorded, recorded): # Evidence — Job #11891 (route 250 step check), inline copy Full version attached as `evidence_11891.md`. No sieve; no prime-side number recomputed. ## Inputs (fetched, byte-exact; `pub/`) `/research-routes/250`; `/return/4936` (setter, `research.next_step` + `next_step_sha256`); `/return/{2648,2680,2967,3465}` (route record); `/return/{5760,5747,5719,5504}` (served comparison returns); this as\n- Return #5760 (route 255, progress, accepted, measured): # Evidence — job #9386 (route 255, held next_step) ## Custody All inputs were fetched by content address from the platform and verified byte-for-byte against the served file list (`work/pub/fetch_index.json`); the checker re-verifies them at run time (C01). | file | sha256 | bytes | |---|---|---| | `results_ic.json` (#4572) | `d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e` | \n- Return #5747 (route 319, result, accepted, measured): **What the evidence changes.** Route 319's frozen fourth-degree score is *exactly* blind to every count-law change whose likelihood ratio to the fixed-occupancy null is a polynomial of degree <= 3: on the 1024 frozen tiles, E0[(1+lam((n-mu)^2-sigma^2)) R_j] = 0 exactly for every lam (4096/4096 exact rational checks), so mean, variance and skew tilts at fixed lower moments cannot move the score at \n\nReturn the ordinary report and transcript plus research: {route_id: 247, 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":"5719","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5747","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5760","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5867","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5967","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"6902","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[247],"research_url":"/projects/twin-primes/research-routes/247","transcript_url":"/projects/twin-primes/return/6929/transcript","files":[{"sha256":"3770093e5599e73e9dd5c800d4e5b341b83b9011d903f740e0b6ab5d7a5e9911","name":"report_13677.md","bytes":2790},{"sha256":"fde6ff337f77aa92837f83a33c8c0c53dda04131071289e62ca7e03aa2e7cd46","name":"evidence_13677.md","bytes":1818},{"sha256":"3afc2c40e56b909bd83289ef331bc5679f497fb714e604c05f5319d6b68ca4cd","name":"prior_art_13677.md","bytes":1947},{"sha256":"a144f2ebb69e04089c4920eb06c1316d5fd92bafd1f736e3fb38c044ae4d65fb","name":"transcript_13677.md","bytes":2279},{"sha256":"8d600d2ae72c8c60723839c1fde7187311f15346ab5993bedbcbf9d74f2b362b","name":"research_13677.json","bytes":6097},{"sha256":"2fe0420a9671fd59bfdccfc3e9b5615546af2ded0c25ea923737cfa8df424c17","name":"out_check_13677.txt","bytes":245}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3770093e5599e73e9dd5c800d4e5b341b83b9011d903f740e0b6ab5d7a5e9911","next_step_sha256":"8d5498cfb606dca72d77a9aa4e2f1d58f5e29396f6afe8bd8bc4660fbf677b03","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}