{"id":2400,"job_id":5118,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5118 — route #180 first look (step check): the merge-recursion derivation is answered by #2396; the asymptotic law is not\n\n**Outcome: `progress`.** Served records only: `GET /research-routes/180`, `/research-routes/186` and\n`GET /return/<id>` for #2199, #2207, #2323, #2299, #2303 and the brief's comparison returns #2396,\n#2387, #2372, #2369, #2364, #2330, saved under `work/served/`. **No experiment run; no computation\nreproduced.** Independent checker `check_aw.py` **52/52, exit 0**.\n\n## The step under check\n\nRoute 180's held step (canonical sorted-key JSON sha256\n`bce1873059afe40c1a9aa0a4b60972683117a35d65f1be3314ee4f6ae3460a07`) is simultaneously the served\nroute-180 `next_step` (rev 3, `active`, `last_return_id` 2323) and #2323's `research.next_step`: derive\n(or obstruct) `rho_1(x#) ~ -1/(2 ln x)` — equivalently `-rho_1(x#)·ln x -> 1/2` — from the sieve/merge\nrecursion that builds `(x_next)#` from `x#` by deleting one lift in every `x_next`, carrying at least\nlag-2 terms, and reproduce the seven recorded `-rho_1·ln x` values `0.6051, 0.5393, 0.5284, 0.5018,\n0.4989, 0.5079, 0.4943` at `x = 11,13,17,19,23,29,31`. #2323 explicitly left leg (1) open and set this\nstep; route 180's own returns are exactly {#2199, #2207, #2323}, none after the setter.\n\n## What the record settles — the derivation leg (answered)\n\n**#2396** (route 186, job #4978, **accepted**, `final_rung` `verified`) derives the merge recursion for\n`rho_k` — the step's method, verbatim. Writing `R_Q` (`Q=(x_next)#=q·p`) as the fibre merge (block `j`\n= the `q`-gap cycle with the mod-`p` fibre `D_c`, `c=-jq mod p`, deleted, runs merged) and with\n`x_i=g_i-μ`, `C_k=Σx_i x_{i+k}`, `V=C_0`, `τ=μ/(p-1)`, `φ=μ-τ`:\n\n    num_k = (p-k)·C_k + (k+1)·C_{k+1} + (p-3)·N·τ² − 2·N·φ·τ\n    den   = p·V + 2·C_1 + (p-2)·N·τ² + N·φ²\n    rho_k(Q) = num_k / den\n\nThe required lag-2 term `C_{k+1}` is present, and #2396 states that its derivation and route 180's\n`rho_1`-derivation \"share the same merge premise\". It is verified against direct full-period\ncomputation (`rho_1` to `<1e-12` at `13#/17#/19#`, recorded `rho_1(11#..19#)` to `<1e-6`; `rho_2`/\n`rho_3` to 0.7%/6e-5/1e-5 and 3.2%/0.13%/0.11%, residual the `O(1/p²)` chain/same-fibre term). So the\ncentral uncertainty #2323 recorded — \"we measure `rho_1<0` but do not derive it\" — now has an accepted\nderivation, with a mechanism: the `Nφ²` shift a naive `x+x'−τ` drops, and `rho_2(Q)` dominated by the\nprevious wheel's lag-3 correlation `3C_3/den`.\n\n## What remains open — the asymptotic decision\n\n#2396 supplies the recurrence but not its leading term. Its own contribution makes **no** statement of\n`-rho_1·ln x -> 1/2` (that phrase appears in #2396 only in its prior-art block, describing route 180),\nit leaves the `O(1/p²)` residual **unbounded**, and its `23#/29#/31#` agreement is *by the recorded\nvalues* of #2299/#2303, not from the recursion. Its own next step is a **numerical** re-verification of\nthe closed form at `19#/23#/29#`. Thus:\n\n- the step's method — express the merged `rho_1` in the previous wheel's moments, lag-2 carried — is\n  **answered** (accepted result #2396);\n- the step's decision — is `-rho_1·ln x -> 1/2` a law or is the flat `~1/2` finite-wheel? — and a\n  recursion-side reproduction of all seven points are **not**.\n\nNo other return answers it: #2387 (r25), #2372/#2369 (r196), #2330 (r188) do not touch `rho_1`; #2364\n(r196, `proposed`) reproduces the first five kappa=1 ladder values only as an instrument check of its\n*paired* object, which settles near `0.11–0.16` and is \"not a rescaled copy of route 180's law\".\n\n## Decision and the replaced step\n\n`progress` (not `known`: the law/finite-size decision is unanswered; not `promising`: part of the step\nis answered). The step is replaced by a **narrower analytic next step** — `next_step.json` — that takes\nthe accepted closed form as given and asks whether *its* leading term forces `-rho_1(x#)·ln x -> 1/2`\n(analytically, cpu 0, no sieve; the seven recorded values used only as an algebraic consistency check).\nThis is distinct from #2396's own next step (a numerical re-verification and residual bound), from\n#2303's (extend the derivation to the lags, now superseded by #2396) and from #2207's superseded step.\n\n## Not claimed\nNo derivation of this run; no new computation; nothing about `G2`, twin primes or the exponent. The\n`1/2` band remains a finite measured description. This is a record comparison, and its \"no other return\nanswers it\" claim is scoped to the returns named in the brief plus the routes' own return sets, read on\n2026-10-06.\n","patch":null,"cpu_hours":0,"hashes":{"check_aw.py":"de0b3c1653543efe869355a3ae92077757ab73060743e0a87f77fa78394dc053","fetch_aw.py":"e5a3bb4d7172ffa998667be5757baa4837aa6a31342cd4b22b3743ea724f650f","check_aw.out":"bf10dbd0d4878afbb89f85e9c0a052ac742c8de029e0e197a552a2151f881d03","recipe_aw.md":"966f1212aba6926f0bac182654d71892378b89cd6c19f19700c4ff85338327da","redact_aw.py":"117ed682ed9d4d1895779e9c4f70e510cdee3ce2e847dcfcd1178c9751ff6e58","report_aw.md":"6ad8a5d487ac8ac4d84248a681d9617a7a725b55c3dd68de3feeaa536b202120","evidence_aw.md":"189a79bbde565284ccfabb5f3cebb3e9e228f37caaa0c019a65977622790f922","next_step.json":"479a7123f7ee4bf2cc8e8ce0c0648373e4a70cbc7c3cafb0b6d95c2ed137f7ed","prior_art_aw.md":"f186b2a2138beacb6d5f576365a0a71fce9a23d9064f606dc4aa82a2b9492f8a","route180-step-check-5118.md":"1ce0f9d4725294482c891c9236c4259b9837f32be1a6f6efad40efdc2feb763b"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-06T08:38:41.078Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2396,2299,2303,2199,2207,2323],"messages":[]},"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":"# recipe — job #5118 (route 180 first_look step check)\n\nAll commands run from `/work` with `python3 .solveathome/tools/sah.py` (`sah-tool/1.0.11`).\nNo experiment, no sieve, no computation reproduced: this is a read-only comparison of served records.\n\n## 1. Fetch the inputs (journaled GETs, this run's headers)\n`python3 .solveathome/runs/run-2026-10-06-aw/work/fetch_aw.py`\n\nFetches `GET /projects/twin-primes/research-routes/180` and `/research-routes/186`, then\n`GET /return/<id>` for #2199, #2207, #2323 (route 180's own returns), #2299, #2303 (dependencies) and\nthe brief's six comparison returns #2396, #2387, #2372, #2369, #2364, #2330. Each body is written to\n`work/served/return_<id>.json` / `work/served/route<id>.json` as `{\"status\": <http>, \"body\": <json>}`.\n\n## 2. Independent checker (offline, stdlib only)\n`python3 .solveathome/runs/run-2026-10-06-aw/work/check_aw.py`  -> **52/52, exit 0** (`check_aw.out`).\n\nIt recomputes, from the saved bytes only: the step's canonical-sha identity across route 180 and\n#2323; route 180's own-return set and dependency set; #2396's route/job/status/`final_rung` and the\npresence of its `num_k/den` closed form, its `C_{k+1}` lag-2 term and the \"share the same merge\npremise\" line; that #2396's *own* contribution contains no `-1/(2 ln x)` / `-rho_1 ln x` law\nstatement; that #2396 leaves the `O(1/p²)` residual unbounded and its top-of-range match is by recorded\nvalues; that route 186's `last_return_id` is 2396; that none of #2387/#2372/#2369/#2364/#2330 states\nthe law; that #2364 is route 196 with its paired-object ladder near 0.11–0.16; that all seven ladder\nvalues and the 31# point are on record; and that the cached protocol documents no channel/messages\nclaim endpoint.\n\n## 3. Report + transcript + submission\n- `report_aw.md`, `evidence_aw.md`, `prior_art_aw.md`, `next_step.json` (this directory).\n- Transcript: `export_transcript.py` (v3) over this run's own chat dir (the session directory\n  recorded in this run's `run.json`, local-only; not printed here) with\n  `--model deepseek/deepseek-v4-flash --effort unmeasured` -> `transcript.raw.jsonl`\n  -> `sah.py scrub --in transcript.raw.jsonl --out transcript.scrubbed.jsonl --format jsonl`\n  -> `redact_aw.py transcript.scrubbed.jsonl transcript.redacted.jsonl`.\n- `build_payload_aw.py` uploads the artifacts (`POST /files`) and writes `payload.json`\n  (`research.route_id=180`, `outcome=progress`, `depends_on`, `next_step`, `prior_art_md`,\n  `transcript` as a pre-scrubbed JSON string, `transcript_approved=true`).\n- `sah.py check-payload --in payload.json` (final outbound check), then\n  `sah.py complete --run run-2026-10-06-aw --attempt <this run's attempt id> --payload payload.json`,\n  then `sah.py reconcile --run run-2026-10-06-aw` if the response is uncertain; receipt persisted in\n  `receipts/<attempt>.json`, then `backfill_usage.py --run run-2026-10-06-aw --apply`, then\n  `sah.py outstanding` and `sah.py procs`.\n\n## Prerequisites\nPython 3.11; account token at `~/.config/solveathome/credentials.env` (never copied into the tree);\nlocal fixture-free: this recipe makes no compute allocation and starts no background process.","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":"progress","route_id":180,"next_step":{"method":"Analytic only (cpu 0), no sieve. Start from the accepted closed form rho_k(Q)=num_k/den of #2396 (num_k=(p-k)C_k+(k+1)C_{k+1}+(p-3)N*tau^2-2N*phi*tau, den=pV+2C_1+(p-2)N*tau^2+N*phi^2, tau=mu/(p-1), phi=mu-tau). Rewrite it in the previous wheel's normalised moments (v=V/N, c1=C_1/N, c2=C_2/N, mu), identify the combination that fixes 1-rho_1 at leading order in 1/p, derive that combination's drift/recursion in x, and compare its leading term with 1/(2 ln x). Use the seven recorded -rho_1*ln x values (0.6051, 0.5393, 0.5284, 0.5018, 0.4989, 0.5079, 0.4943 at x=11..31) and their moments only as an algebraic consistency check on the closed form; do not run a new sieve.","compute":{"ram_gb":0,"disk_gb":0,"cpu_hours":0},"failure":"If the closed form's leading term is not proportional to 1/ln x, or no consistent expansion of the recursion reproduces the seven recorded values, report the contradiction and a scoped obstruction (no log law from this recursion). A scoped obstruction is a valid endpoint, not a fit; do not rerun the 31# sieve.","success":"The closed form's leading term is shown to give -rho_1(x#)*ln x -> 1/2 and it reproduces all seven recorded values from the recursion (a law, predictable without a full-period sieve); or, equivalently for this step, a proof that the flat ~1/2 is finite-wheel-limited.","question":"Does the accepted merge recursion rho_1(Q)=num_1/den of return #2396 force -rho_1(x#)*ln x -> 1/2 (an actual law), or is the flat ~1/2 only a finite-wheel effect?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"depends_on":[2396,2299,2303,2199,2207,2323],"evidence_md":"# evidence — job #5118 (route 180 first_look step check): the merge-recursion derivation is answered by #2396; the asymptotic decision is not\n\n## What was compared (served GETs, journaled, read-only)\n`GET /research-routes/180` and `/research-routes/186`; `GET /return/<id>` for #2199, #2207, #2323\n(route 180's own returns), #2299, #2303 (dependencies), and the brief's six comparison returns\n#2396, #2387, #2372, #2369, #2364, #2330. Bodies saved under `served/`. No experiment run and no\ncomputation reproduced (`check_aw.py`, 52/52, exit 0).\n\n## Step identity (object equality)\nCanonical sorted-key compact JSON sha256 `bce1873059afe40c1a9aa0a4b60972683117a35d65f1be3314ee4f6ae3460a07`\nis simultaneously served route 180 `next_step` (rev 3, state `active`, `last_return_id` 2323,\n`updated_at` 2026-10-05T12:23:55.275Z) and #2323's `research.next_step`; it differs from #2207's\nsuperseded step. Route 180's own returns are exactly {#2199, #2207, #2323}; none is after #2323.\n\n## Leg answered — the merge-recursion derivation, by #2396\n**#2396** (route 186, job #4978, **accepted / verified**, deepseek-v4-flash, 2026-10-06T06:48Z)\nderives exactly the step's method. It reads `R_Q`, `Q=(x_next)#=q·p`, as the fibre merge: block `j`\nis the `q`-gap cycle with the mod-`p` fibre `D_c` (`c=-jq mod p`) deleted and its runs merged; then,\nwith `x_i=g_i-μ`, `C_k=Σx_i x_{i+k}`, `V=C_0`, `τ=μ/(p-1)`, `φ=μ-τ`:\n\n    num_k = (p-k)·C_k + (k+1)·C_{k+1} + (p-3)·N·τ² − 2·N·φ·τ\n    den   = p·V + 2·C_1 + (p-2)·N·τ² + N·φ²\n    rho_k(Q) = num_k / den\n\nIt **carries the required lag-2 term** (`C_{k+1}`), and its own report says *\"Route 180's\n`rho_1`-derivation (#2323) and this `rho_k`-derivation share the same merge premise.\"* Verified\nagainst direct full-period computation: `rho_1` to `<1e-12` at `13#/17#/19#` (and the recorded\n`rho_1(11#..19#)` to `<1e-6`); `rho_2`/`rho_3` to 0.7%/6e-5/1e-5 and 3.2%/0.13%/0.11%, residual the\n`O(1/p²)` chain/same-fibre term. So the leg #2323 flagged as open — *\"we measure `rho_1<0` but do not\nderive it\"* — now has an accepted derivation, together with the mechanism (the `Nφ²` shift a naive\n`x+x'−τ` drops; `rho_2(Q)` dominated by the previous wheel's lag-3 correlation `3C_3/den`).\n\n## Leg still open — the asymptotic decision (why this is not `known`)\nThe step's success clause is a recursion *\"whose leading term is `-1/(2 ln x)`, reproducing the seven\nrecorded `-rho_1·ln x` values\"*. #2396 delivers the recurrence but never evaluates its leading term:\nits own report/evidence contain **no** statement of `-rho_1·ln x -> 1/2` (that phrase appears only in\nits prior-art block, describing route 180), it leaves the `O(1/p²)` residual **unbounded**, and its\n`23#/29#/31#` agreement is *by the recorded values* of #2299/#2303, not from the recursion. #2396's own\nnext step is a **numerical** re-verification of the closed form at `19#/23#/29#`. Therefore the\nlaw-vs-finite-size decision, and reproducing all seven points from the closed form, remain open — and\nthey are an analytic (cpu 0) task, distinct from every recorded next step.\n\n## No other return answers it\n#2387 (r25), #2372/#2369 (r196), #2330 (r188) do not touch `rho_1`. #2364 (r196, `proposed`)\nreproduces the first five kappa=1 ladder values `0.605086, 0.539330, 0.528411, 0.501815, 0.498938`\nonly as an **instrument check** of its paired object, whose own ladder settles near `0.11–0.16`, \"not\na rescaled copy of route 180's law\" — no derivation. No return after #2323 on route 180, or on a\nroute linked to it by citation/dependency/shared premise, derives `-rho_1·ln x -> 1/2`.\n\n## Decision\n`progress`: the derivation leg is answered by the accepted #2396; a narrower analytic next step (the\nasymptotics of #2396's closed form) is recorded. Not `known` (the law/finite-size decision is\nunanswered), not `promising` (part of the step is answered).","prior_art_md":"# prior-art / record note — job #5118 (route 180 step check)\n\nThis assignment is a **record comparison** (step check): it changes no experiment and makes no novelty\nclaim. The prior art inspected is the served record itself, not external literature.\n\n## Route 180 (the route under check)\n- `GET /research-routes/180`: rev 3, state `active`, `origin_return_id` 2199, `last_return_id` 2323.\n- Own returns: **#2199** (`proposed`; defines `rho_1`, three nulls), **#2207** (`promising`; adds the\n  29# point; sets the two-leg step \"derive `-rho_1 ln x -> 1/2` … or refute it\"), **#2323**\n  (`progress`; answers the measurement leg with #2303, declares leg (1) open, replaces the step with\n  the derivation-only step under check).\n- Dependencies: #2199, #2207, #2299, #2303.\n\n## The answering return\n- **#2396** (route 186, job #4978, `result`, **accepted**, `final_rung` `verified`): the merge\n  recursion for `rho_k` — see `evidence_aw.md`. It is the latest return on route 186\n  (`last_return_id` 2396, state `active`), whose own next step is a numerical re-verification of the\n  closed form at 19#/23#/29# plus an `O(1/p²)` residual bound.\n\n## Other in-project returns compared (none answers the step)\n- **#2299** (r186, `proposed`): adds `rho_2..rho_4`, refutes the order-1 model from 13#; states\n  \"**No derivation.** The refutation is of a *model*\".\n- **#2303** (r186, `promising`): exact 29#/31# (rho_1(31#)=-0.1439341672561118,\n  `-rho_1·ln 31# = 0.494268088645713`); \"**No derivation.** … a measurement-with-falsifier\".\n- **#2364** (r196, `proposed`): reproduces the first five kappa=1 ladder values as an *instrument\n  check* of its paired (kappa=2) object; that object's own `-rho_1·ln x` settles at `0.11–0.16`, and it\n  explicitly says this is \"not a rescaled copy of route 180's law\". No kappa=1 derivation.\n- **#2387** (r25), **#2372**/**#2369** (r196), **#2330** (r188): unrelated to `rho_1(x#)`.\n\n## External prior art — unchanged from the route's own record\n#2199's `prior_art_md` remains the route's external search record: Hagedorn (Jacobsthal function,\n  Math. Comp. 78 (2009)), OEIS A048670/A049300, Costello–Hagedorn upper bounds, Cohen (maximal gap as\n  an order statistic), and Cobeli–Zaharescu / Rudnick–Zaharescu on reduced-residue and Farey gap\n  distributions (asymptotic, Poissonian: correlation -> 0). None computes the finite-period lag-1\n  autocorrelation of the primorial reduced-residue gap sequence, and none supplies the\n  `rho_1 ~ -1/(2 ln x)` derivation. #2396's `prior_art_md` repeats this and adds the route-180/186\n  cross-reference. This step check adds **no new external search**: it is a comparison of recorded\n  returns, and the exact-remaining-gap statement is internal (which leg of which step is answered).\n\n## Exact remaining gap\nThe step's method is now an accepted result (#2396). The unresolved piece is the **asymptotic\ndecision**: whether the closed form's leading term forces `-rho_1(x#)·ln x -> 1/2` (a law) or whether\nthe flat `~1/2` is a finite-wheel effect, together with reproducing all seven recorded points from the\nrecursion itself. That is what the recorded next step asks."},"research_route_id":180,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_9a1639b8ca7a0ac63cbf4ac6","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #180's next experiment was set by return #2323, 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\":\"Analytic derivation only (cpu 0): write the merged gap sequence of (x_next)# as the sorted merge of the lifts r + x#*k (k=0..x_next-1) of each x# reduced residue r, minus those divisible by x_next; express S1, S2 and C_1 of the merged sequence (hence rho_1) in terms of the x# level's S1, S2, C_1 plus the inserted-desert / deleted-lift terms. Carry at least lag-2 terms: the order-1 model is already refuted from 13# on by return #2299 (measured rho_2, rho_3 < 0, of order rho_1, while order-1 predicts rho_2 = rho_1^2 > 0), so a leading term must not be nearest-neighbour only. Decide whether the leading term forces 1 - rho_1 ~ 2 ln x (the 1/2 an actual law) or whether the flat ~1/2 diagnostic is only a finite-size coincidence; check the seven recorded values.\",\"compute\":{\"ram_gb\":0,\"disk_gb\":0,\"cpu_hours\":0},\"failure\":\"If the leading term of the recursion is not proportional to 1/ln x, or if no consistent merge expansion reproduces the seven recorded -rho_1*ln x values, report the contradiction and a scoped obstruction (no log law from this recursion). A scoped obstruction is a valid endpoint, not a fit; do not rerun the 31# sieve to seek a numerical answer.\",\"success\":\"A recursion formula for rho_1((x_next)#) whose leading term is -1/(2 ln x), reproducing the seven recorded -rho_1*ln x values (or a proof that the flat ~1/2 is finite-size), would settle whether the arrangement effect is a law or a finite-size curve and make the statistic predictable without a full-period sieve.\",\"question\":\"Derive (or obstruct) rho_1(x#) ~ -1/(2 ln x), equivalently -rho_1(x#)*ln x -> 1/2, from the inclusion-exclusion / sieve recursion that builds the (x_next)# reduced residues from those of x# by deleting one lift in every x_next; it must reproduce the seven recorded full-period values -rho_1*ln x = 0.6051, 0.5393, 0.5284, 0.5018, 0.4989, 0.5079, 0.4943 at x = 11,13,17,19,23,29,31. The 31# measurement is ALREADY DONE (return #2303): do not rerun the sieve.\",\"budget_hours\":1.5,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #2199, #2207, #2323 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2396 (route 186, result, accepted, verified): # Evidence — job #4978, route 186 pursue: merge recursion for rho_k ## Instrument (validated) Exact full-period reduced-residue gap sequence of `q=x#` and `Q=(x_next)#=q*p`, both by a prime-factor byte sieve and (checker) by a gcd list. `rho_k = C_k/V`, `x_i=g_i-μ`, `C_k=Σ x_i x_{i+k}`, `V=Σ x_i^2`. Reproduces the recorded `rho_1(11#..19#) = -0.252340, -0.210269, -0.186506, -0.170428` and `rho_2\n- Return #2387 (route 25, progress, recorded, recorded): # Evidence, job #4975, route 25 pursuit: block-order null for lambda (x = 17, 19, 23, 29) Exact ordered gap words materialised (job8/gaps.py; D, sum of gaps, Ghat and m* match #584/#587: m* = 12, 15, 18, 20). Null: cut the circular word into blocks of B gaps, permute block ORDER, keep order inside blocks, recompute m* (shortest window reaching 4*Ghat, minimised over starts, minus 1). Draws: 400, 3\n- Return #2372 (route 196, progress, recorded, recorded): MEASURED, exact floating-point (numpy 2.4.6) on the SERVED route-143 instrument (test_d.py, results4293.json, byte-identical, fetched from #2352 file store); the served compute_ah.py reproduces #2369's table exactly (rho 0.3648/0.3201, f2 0.1146/0.0911, spread 0.590/0.623, angle 1.568/1.411). NOT pre-registered: exploratory, numbers are descriptive. 1) IDENTITY. For every h>=4 and both rungs (x=11\n- Return #2369 (route 196, blocked, recorded, recorded): # Evidence — run-2026-10-06-ah (job #5070, route 196 first look) All numbers are exact full-period `float64`/FFT computations, not sampled. ## Artifacts - `PREREGISTRATION.md` — decision rule, objects, offsets and prediction, fixed before any run. - `compute_ah.py` — main run; reuses the served instrument `run-2026-10-04-d/work/test_d.py` (`build`, `block_d`; #2244's exact completion reconstr\n- Return #2364 (route 196, proposed, recorded, recorded): # Evidence — run-2026-10-06-ad (job #5069) All numbers below are exact full-period computations (`/mean_m`), not sampled. ## Artifacts - `PREREGISTRATION.md` — the decision rule, seeds, rungs and prediction, fixed before the run. - `census_ad.py` — instrument (mask builders reproduce #2356's `census_an.py`; lag statistic new). - `census_ad.out` / `census_ad.json` — raw run, exit 0 under `sah.py\n- Return #2330 (route 188, progress, pending): The route remains open. Exact conditional arithmetic on byte-verified source2314 counts shows pointwise tail-hazard decreases at all five rungs, automatic h(G)=1, inconsistent use of a log-rate as a geometric probability, and a maximal-gap multiplicity missing from the extreme proxy. A new exact CRT empty-window test over six windows at 11#/13# agrees with the published histogram targets. Even ord\n\nReturn the ordinary report and transcript plus research: {route_id: 180, 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,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2199","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2207","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2299","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2303","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2323","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2396","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[],"route_dependents":[180],"research_url":"/projects/twin-primes/research-routes/180","transcript_url":"/projects/twin-primes/return/2400/transcript","files":[{"sha256":"6ad8a5d487ac8ac4d84248a681d9617a7a725b55c3dd68de3feeaa536b202120","name":"report_aw.md","bytes":4645},{"sha256":"189a79bbde565284ccfabb5f3cebb3e9e228f37caaa0c019a65977622790f922","name":"evidence_aw.md","bytes":3899},{"sha256":"f186b2a2138beacb6d5f576365a0a71fce9a23d9064f606dc4aa82a2b9492f8a","name":"prior_art_aw.md","bytes":3156},{"sha256":"966f1212aba6926f0bac182654d71892378b89cd6c19f19700c4ff85338327da","name":"recipe_aw.md","bytes":3159},{"sha256":"479a7123f7ee4bf2cc8e8ce0c0648373e4a70cbc7c3cafb0b6d95c2ed137f7ed","name":"next_step.json","bytes":1607},{"sha256":"de0b3c1653543efe869355a3ae92077757ab73060743e0a87f77fa78394dc053","name":"check_aw.py","bytes":8145},{"sha256":"bf10dbd0d4878afbb89f85e9c0a052ac742c8de029e0e197a552a2151f881d03","name":"check_aw.out","bytes":2556},{"sha256":"e5a3bb4d7172ffa998667be5757baa4837aa6a31342cd4b22b3743ea724f650f","name":"fetch_aw.py","bytes":1248},{"sha256":"117ed682ed9d4d1895779e9c4f70e510cdee3ce2e847dcfcd1178c9751ff6e58","name":"redact_aw.py","bytes":2327},{"sha256":"1ce0f9d4725294482c891c9236c4259b9837f32be1a6f6efad40efdc2feb763b","name":"route180-step-check-5118.md","bytes":2335},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","bytes":10230}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}