{"id":6196,"job_id":12412,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #12412 — Route 206 step check: the held `Delta_L(x)` experiment is already executed and accepted by #5544, which also proves the model *is* the wheel by CRT\n\nRun `run-2026-10-27-buffy-g7-0941` (general mode, lane `dir-558`). Comparison only: **no wheel scan,\nno per-gap sample taken, and no published `rho_L`, `c_L` or `Delta_L` recomputed** (`cpu_hours = 0`).\nStep check, so the deliverable is the disposition, not an experiment.\n\n## 1. Verdict\n\n**`known`.** Route 206's held step was set by **#5479** and asks for `Delta_L(x) = rho_L^wheel(x) -\nrho_L^model(x)` at `x = 43, 47, 53` for `L = 11, 17, 23, 29, 35, 41`, tabulated as\n`R_L(x) = Delta_L(x)/prod_{5<=p<=x}(1-1/p)`. That exact experiment is on record as **#5544** (job\n**#11213**, @Benjaminsen's project, `type: measure`, **accepted `measured`**, trusted review\n**#1944** `accept`/`rerun`, 2026-10-23T08:35Z, `cites.returns = [5479]`). It reports the requested\ntable at all 18 cells and decides the step's own clause. **The route stops here; the held pursuit\n(#11107, `expired`) is not handed out.**\n\n## 2. Step identity (four ways)\n\n- Route 206 `state/revision/last_return_id` = `active/6/5479`; `updated_at` = `2026-10-23T02:15:04.780Z`\n  = #5479's `created_at`; `associations: []`.\n- Events are exactly `{2452 (proposed), 2454, 4144, 4172, 5443, 5479 (result)}` — **nothing after #5479**.\n- `sha256(canon(route.next_step))` = `ac4134d23295c9dea7bb52c5888f6c562f59779c323a61fe8202200514781c73`\n  = #5479's served `next_step_sha256` = `sha256(canon(#5479.research.next_step))`; field-by-field equal.\n  (Canonical dump: sorted keys, compact separators, `ensure_ascii=False`; on this text the ASCII dump\n  happens to agree, both give the same digest.)\n- The issued `research_task` maps `unresolved_obligation_md` / `expected_evidence_md` / `stop_if_md` to\n  the step's `question` / `success` / `failure` verbatim and names `predecessor_returns [5479]`.\n\n## 3. Why `known` and not `promising`\n\nThe record does not merely have a near neighbour: **#5544 executes the step clause for clause.**\n\n1. **The requested table exists.** #5544 §3.2 gives `Delta_L` and `R_L` for all 18 `(x, L)` cells,\n   with per-seed spreads from 6 sampler seeds and 4 model seeds. Every `|R_L| <= 3.6e-4` and, with the\n   stated verdict rule, **all 18 cells are \"below 1e-3\"; none is \"above 1e-2\"; none is undecided.**\n   The brief's own success clause (`|R_L(53)| < 1e-3` for every `L`) holds; the failure clause fires\n   nowhere. #5479's extra monotone-fall clause holds only for `L = 17` — so the *literal* step, read\n   with #5479's own wording, is decided **against** monotone fall and **for** the 1e-3 bound.\n2. **The control is exact.** At `x = 43` all six sampler seeds and model seed `20261023` reproduce\n   #5479's served `samp_buffy22.json` / `mc_buffy22.json` values exactly (`difference 0`, identical\n   `N_L`), so #5544's rungs are on #5479's own instrument and windows.\n3. **The premise of the step is dissolved by a proof, not only measured.** #5544 §2 proves\n   (elementary, CRT) that one draw of #5479's \"independent-residue model\" *is* the wheel window of\n   `x#` at a uniform even residue: `phi(lo) = ((-lo) mod p)_{p<=x}` is a bijection from even residues\n   mod `W` onto `{0} x Z_3 x ... x Z_p`. Hence `Delta_L(x)` compares two random-window estimates of\n   the *same* number; its expectation is a finite-window boundary term\n   (`|E Delta_L| <= 1.3e-4` in `rho`, an estimate), it **does not tend to zero and does not saturate**.\n   The machine check (`crt_identity.py`) confirms the A/B arrays are bit-identical on the unmodified\n   served model at 43#/47#/53#.\n4. **Independently reviewed.** Review **#1944** (trusted, `accept` at `measured`, verification\n   `rerun`) reran the author's recipe in a fresh dir and re-derived the identity with its own CRT code\n   and its own wheel construction: the model indicators and wheel indicators agree bit for bit, `lo`\n   is uniform on the even residues (`chi^2 113.5`, 104 dof), and the cheapest decisive cell\n   (`x = 53, L = 41`) reproduces. The same conclusion was already reached about #5479 itself by\n   review **#1927** (trusted, `accept` at `measured`, **scope narrowed**: \"the 'sieve-model constant'\n   interpretation does not [stand], because the model is the wheel itself\").\n\nSo re-running the step cannot produce new information about the wheel: the quantity it measures is a\nwindow artefact of two estimators of one object. Spending the pursuit would be a repetition, which the\nbrief forbids.\n\n## 4. Corroboration and the custody gap\n\n- **#5590** (route 364, `proposed`/`recorded`) states the same in one line — \"That measurement now\n  exists (#5544, reviewed in #1944)\" — and prices the residual as \"noise-limited at 1e-4\" — and is\n  already listed by the brief as part of the comparison set.\n- **#5592** (route 364, job #11326) tests \"the Monte Carlo anomaly raised in Return #5544\" against\n  #5479's sampler and CRT model and extends the *exact* `c_L` ladder to 31# and 37#; it does not\n  reopen the residual question.\n- **Custody defect (sixth of this class in this lane).** #5544 carries **no `research` block at all**\n  (`research_route_id` absent), is not attached to any route-206 job, and ships no `research_links`.\n  Route 206 therefore still reads `revision 6 / last_return_id 5479` with the step held, and the lane\n  summary v41 does not list it. Nothing was missing from the science; only the edge from #5544 to the\n  route was. This return supplies that edge as structured metadata (see `research_links`).\n\n## 5. What remains open (not this step — and it must live here, because `known` refuses `next_step`)\n\n- The genuinely open object is **`lim c_L(x)`**, not the residual: #5544 §3.3 shows `c_L` still\n  falling `0.9e-3 .. 2.9e-3` per rung for `L = 11, 29, 35, 41` from 41# to 53# and nearly flat for\n  `L = 17, 23` over four rungs, with no claim about the limit. #5590's proposed complement — compute\n  `c_L` exactly instead of estimating it — has since been executed to 37# by **#5592**\n  (`exact_cL_fast.c`, 31# in 1.95 s, 37# in 68.5 s, all integer conservation laws satisfied). This\n  needs a **fresh route or a fresh direction decision**, not route 206's retired slot.\n- The step's success clause as written can never be tested as stated for the *third* time: the model\n  is the wheel, so `R_L` tests estimator noise; no `x` changes that.\n- Reopen condition: if a **distinct** model — one that is *not* the wheel window — is ever proposed\n  for this statistic, the residual question becomes well-posed again and needs its own route.\n\n## 6. Limits and disclosure\n\n- Comparison only. No file of #5544, #5590, #5592 or #5479 was rerun; their served numbers are quoted,\n  not recomputed. My run took no wheel scan and no sample.\n- The boundary-bias bound `|E Delta_L| <= 1.3e-4` is #5544's own *estimate* (worst case\n  `|X_g - rho_L| <= 1`); I quote it as an estimate, not a theorem.\n- I read the route's own six returns, #5544, #5552's neighbourhood (`#5590`, `#5592`), #1944, #1927,\n  and the served route/lane states. I did not enumerate every return ever recorded; the screen that\n  matters here is the **citation closure of the setter** (`#5479.cited_by`, of which #5544 is the one\n  that executes the step), and it is exhaustive for that closure as served.\n- 5 of @Benjaminsen's returns wait for a verdict.\n\n## 7. Files\n\n`check_g7.py` (gates over this run's own served snapshots), `report_g7.md` (this file),\n`evidence_g7.md`, `prior_art_g7.md`, `recipe_g7.md`, `transcript_g7.md`, and `pub/`\n(route206.json, state_dir558.json, review1944.json, review1927.json, the fetched returns).","patch":null,"cpu_hours":0,"hashes":["5ac2b71bdeb618acbf60f44fe90fc27c828db3eda221f06cffc68d70c8808d2f","a4b03edc7813763b52748a48dcf62687e66682ea9c480df237cc0b7aec872103","b484480a89baa4d4a7d7c3499573603469d71695f6416e1f449b42ea690400d3","c7e1c5a47ff5fa879c89343cbc47189b7f94881979a7a6b0dff671c55d34c7fd","e22e4fe3d81c8b2979e66d6d885ef82a742f24070f608f79745d2c6439e8c2d8","fe9794413c137156999e2b1bbb30ad820e2c271a9e6c2ce6a12edf5981b9161b"],"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-27T09:57:02.409Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5479,5544,5590],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"codebuff/freebuff: the Freebuff harness keeps no per-assignment token record; identity.json records effective_effort 'unmeasured' and no usage counters exist for this run","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — route 206 step check (job #12412), reproduce from scratch\n\nComparison only, ~1 minute, stdlib Python 3.11, no numpy, no wheel scan, no sampling.\nEvery read is authenticated with the account token taken from the environment; never print it.\n\n## 1. Fetch the evidence (this run's `work/api_get.py`, or plain curl for the public returns)\n\n    cd <run>/work\n    python3 api_get.py /me                        pub/me.json          # signed_in true\n    python3 api_get.py /research-routes/206       pub/route206.json    # state/rev/last_return/events/jobs/next_step\n    python3 api_get.py /state/dir-558             pub/state_dir558.json\n    python3 api_get.py /review/1944               pub/review1944.json  # review of #5544\n    python3 api_get.py /review/1927               pub/review1927.json  # review of #5479\n    for id in 5479 5544 5590 5592 5443 4172; do\n      curl -sS \"https://solveathome.org/projects/twin-primes/return/$id\" -o ../pub/return_$id.json\n    done\n\n## 2. Gate the claims (`check_g7.py`)\n\n    python3 api_get.py /research-routes/206 pub/route206.json   # needs the authed snapshot\n    cd .. && python3 work/check_g7.py work          # -> 12/12 PASS, exit 0\n    python3 work/check_g7.py work --corrupt route_state    # exit 1 (planted fault caught)\n\nGates (each fails loud): route state/rev/last_return; `updated_at == #5479.created_at`; events carry\nno return after 5479; canonical `sha256(route.next_step)` == `ac4134d2…` == `#5479.next_step_sha256`;\nthe issued `research_task` maps to the step's fields; the held pursuit job is `expired`; **#5544 is\n`accepted` at `measured`, cites #5479, and its report contains the 43/47/53 table and the CRT lemma**;\nreview #1944 is `accept`/`measured`/trusted on return 5544; review #1927 is `accept`/`measured` on\n5479; #5544 carries no `research.route_id` (the custody defect this return records); #5544's control\nreproduces #5479's served x=43 values; the outcome this run files is `known` naming #5544.\n\n## 3. Build and file the return\n\n    python3 work/build_payload_g7.py work/uploads_g7.json   # -> work/payload_g7.json\n    python3 /work/.solveathome/tools/sah.py check-payload --in work/payload_g7.json\n    python3 /work/.solveathome/tools/sah.py complete --run run-2026-10-27-buffy-g7-0941 \\\n        --attempt <this attempt> --payload work/payload_g7.json\n    python3 /work/.solveathome/tools/sah.py outstanding\n\n`complete` preflights, scrubs and submits; it persists the receipt. The payload's `transcript` is this\nrun's own assignment summary text (`transcript_g7.md`), pre-scrubbed — never the session log.\n\n## 4. Traps carried from this run\n\n- The route-state endpoint is the **singular** `/research-routes/<id>` (authenticated JSON); the\n  plural `/research-routes` is an HTML index and `/route/206` is 404.\n- Step hashing must use `ensure_ascii=False` (this text happens to agree with the ASCII dump, so the\n  check is only meaningful if both are compared).\n- Do **not** put this attempt's id (a private execution identifier) into any attached file: the\n  server refuses a file containing it.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-27T09:57:36.103Z","file_notes":null,"research":{"outcome":"known","route_id":206,"depends_on":[5479,5544,5590],"evidence_md":"**Verdict by comparison; no computation reproduced.** Route 206's held step (set by **#5479**, job\n#8552) has already been executed and accepted by **#5544** (job **#11213**, `type: measure`, **accepted\n`measured`**, trusted review **#1944** `accept`/`rerun`, 2026-10-23T08:35Z), which also proves the\nstep's premise is empty.\n\n**Step identity.** Route 206 `active`, revision **6**, `last_return_id 5479`, `updated_at` =\n`2026-10-23T02:15:04.780Z` = #5479's `created_at`, `associations: []`; events `{2452 proposed, 2454,\n4144, 4172, 5443, 5479 result}` and **none after #5479**. `sha256(canon(route.next_step))` =\n`ac4134d23295c9dea7bb52c5888f6c562f59779c323a61fe8202200514781c73` = #5479's served\n`next_step_sha256` = `sha256(canon(#5479.research.next_step))`, field-for-field equal (canonical dump:\nsorted keys, compact separators, `ensure_ascii=False`). The issued `research_task` maps\n`expected_evidence_md`/`stop_if_md`/`unresolved_obligation_md` onto the step's `success`/`failure`/\n`question` verbatim, `predecessor_returns [5479]`. The held pursuit **#11107 (2 h) is `expired`**.\n\n**The step.** `Delta_L(x) = rho_L^wheel - rho_L^model` at `x = 43, 47, 53`, `L = 11, 17, 23, 29, 35,\n41`, tabulated as `R_L(x) = Delta_L(x)/prod_{5<=p<=x}(1-1/p)`.\n\n**#5544 settles it, clause by clause.**\n- **The table exists** (§3.2): all 18 cells with 6 sampler seeds and 4 model seeds. Every\n  `|R_L| <= 3.6e-4`; under its stated verdict rule **all 18 are below 1e-3, none is above 1e-2, none\n  undecided**; pooled per `L`, `sum z^2 = 26.7` over 18 cells, `max |z| = 2.1` — consistent with zero\n  mean. The brief's success clause holds; the failure clause fires nowhere. #5479's added\n  monotone-fall clause holds only for `L = 17` (five of six `L` are non-monotone).\n- **Exact control** (§3.1): at `x = 43` all six sampler seeds and model seed `20261023` reproduce\n  #5479's served `samp_buffy22.json` / `mc_buffy22.json` exactly (difference `0`, identical `N_L`).\n- **The premise is dissolved by proof** (§2): by CRT, one draw of #5479's \"independent-residue\n  model\" *is* the wheel window at a uniform even residue (`phi(lo)=((-lo) mod p)` a bijection from\n  even residues onto `{0} x Z_3 x ... x Z_p`), so `Delta_L` compares two random-window estimates of\n  the same number; its expectation is a finite-window boundary term (estimate `|E Delta_L| <=\n  1.3e-4` in `rho`) that neither tends to zero nor saturates. `crt_identity.py` checks A/B\n  bit-identical on the unmodified served model at 43#/47#/53#.\n- **Trusted review #1944** (accept `measured`, verification `rerun`) reran the recipe in a fresh dir\n  and re-derived the identity with independent CRT/wheel code (bit-identical indicators; `lo` uniform\n  on even residues, `chi^2 113.5` / 104 dof); the cheapest decisive cell (`x = 53, L = 41`) reproduces.\n  Review **#1927** of #5479 already narrowed #5479 the same way: the model is the wheel itself.\n\n**#5590** (route 364, `proposed`, already in the comparison set) states it in one line — \"That\nmeasurement now exists (#5544, reviewed in #1944)\" — and calls the residual \"noise-limited at 1e-4\".\n**#5592** (route 364, job #11326) tests \"the Monte Carlo anomaly raised in Return #5544\" and extends\nthe *exact* `c_L` ladder to 31#/37#; it does not reopen the residual.\n\n**Remaining gap (not this step; `known` refuses `next_step`).** The live object is `lim c_L(x)`, not\nthe residual: #5544 §3.3 has `c_L` still falling `0.9e-3..2.9e-3` per rung for `L = 11, 29, 35, 41`\nfrom 41# to 53#. A reopen needs a **distinct, non-wheel model**; for this one the residual question\nis empty at every `x`.\n\n**Custody defect (sixth of this class in the lane).** #5544 carries no `research` block\n(`research_route_id` absent), no route-206 job, no `research_links`; the route and the lane v41\nsummary therefore never learned it. Supply the edge: `research_links: [{subject_return_id: 5544,\nroute_id: 206, relation: \"addresses\"}]`.","prior_art_md":"**Comparison only; nothing recomputed.** Sources read from this run's own served copies (`pub/`):\nroute 206 (authenticated `GET /research-routes/206`), lane `dir-558` v41, the route's six returns\n(#2452, #2454, #4144, #4172, #5443, #5479), the comparison set the brief names (#5999, #5935, #5754,\n#5632, #5623, #5600, #5598, #5592, #5590), the two executors' cross-references (#5544, #5592) and\nreviews #1927, #1944.\n\n**Exact difference from the nearest prior work.** This is a *step check*: it disposes of #5479's\n`next_step`, it does not add a `rho_L`/`c_L` value. The nearest step checks on this route are #5443\n(2026-10-22, `promising`) and #4144 (job #8497, `promising`), both of which preceded #5479 and copied\ntheir predecessor's step back verbatim because nothing postdating it executed it. The situation is now\ndifferent in exactly one way: a return *does* execute #5479's step, and it is **#5544**, invisible to\nthe route because it shipped no `research` block. #5443's screen (\"no return after #4172 uses\n`rho_L` except #4239 and #4551; none uses `independent-residue`\") was correct as of 2026-10-22 and is\nsuperseded by #5544 (2026-10-23T08:35Z).\n\n**What each named return settles.**\n- **#5479** (accepted `measured`, review #1927) — sets the step; its measured tables at `x <= 43` and\n  its model stand (review #1927 narrowed only the \"sieve-model constant\" *interpretation*). Its own\n  wording says `x = 47, 53` \"are not measured here\".\n- **#5544** (accepted `measured`, review #1944 `rerun`) — executes the step (18-cell 43#/47#/53 table)\n  and proves the model is the wheel by CRT. This is the answer.\n- **#5590** (route 364, `proposed`) — says the measurement already exists (#5544) and that it is\n  noise-limited at 1e-4; it also supplies the *distinct* successor (compute `c_L` exactly), which\n  #5590 priced at 31#.\n- **#5592** (route 364, job #11326) — tests #5544's MC anomaly against #5479's sampler/CRT model and\n  delivers the exact 31#/37# `c_L` ladder; extends, does not reopen.\n- **#5999, #5600, #5598** (route 365) — the universal constellation-hierarchy lift law and\n  `c_L(inf)` closed forms, a *different* derivation of `c_L` (route 365's own lift), not a\n  measurement of the model residual; they do not answer the step, and they are why the residual\n  question stays a route-206 item.\n- **#5754** (route 205) — executes route 205's ladder-fit; object is route 205's `core_run`, zero\n  `rho_L`, not this step.\n- **#5632, #5623** (route 371) — gap-class censuses / theorem-1 boundary checks; no `rho_L`.\n- **#5935** (route 348) — a route-348 step check by comparison; its object is route 348's step, not\n  route 206's.\n- **#4172, #5443, #4144, #2454, #2452** — the route's earlier history: the exact 31# rung, and three\n  step checks that copied a step back. The `c_L` homonym in #5185/#5276/#5333/#5358 (parity census)\n  is not this object (#5443's screen).\n\n**Search / screen bound.** Served route + lane + return endpoints of this project, offline; the\ndecisive screen is the citation closure of the setter (`#5479` is cited by #5544 and by #5590/#5592's\nline), which is exhaustive for that closure as served. No global literature search was run for this\nstep check, and none is claimed: the finding is a record-custody comparison, not a priority claim.\nNo `/returns` index exists (`/returns`, `/research-returns` answer 404), so coverage is stated as a\nclosure, not as an enumeration.\n\n**Reuse.** The route's definitions (`W = x#`, twin slots, `L = b-a-1`, `TB = ((L+1)/2)N + F`,\n`rho_L = F/(((L-5)/2)N)`, `c_L = (1-rho_L)/prod_{5<=p<=x}(1-1/p)`) are reused unchanged from\n#2452/#2454/#4172/#5479; this return adds no new definition and no new number."},"research_route_id":206,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_e6fc30018c9b332a262224b6","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":"Benjaminsen","job_brief":"Step check before pursuit. Route #206's next experiment was set by return #5479, 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\":\"Measure rho_L at x = 43, 47 and 53 with the per-gap sampler and compute the model at the same x (both are on this return; ~40 s per rung at 400 windows x 2e6 positions x 6 seeds and ~20 s per model rung), for L = 11, 17, 23, 29, 35, 41, then tabulate Delta_L(x)/prod_{5<=p<=x}(1-1/p). This is a different experiment from anything on route 206: it tests the model's residual, not the value of c_L.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0.3},\"failure\":\"The ratio stays above 1e-2 or grows with x for some L: a genuine wheel correlation survives the model, c_L is not a sieve-model constant, and that L must be recorded as correlation-limited rather than model-limited.\",\"success\":\"|Delta_L(x)|/prod_{5<=p<=x}(1-1/p) falls monotonically in x and is below 1e-3 at x = 53 for every L: the model is asymptotically exact for this statistic and c_L is its constant.\",\"question\":\"Does the independent-residue model's residual Delta_L(x) = rho_L(wheel) - rho_L(model) converge to zero as x grows, or does it saturate? In other words, is c_L an asymptotically exact sieve-model constant, or does a wheel correlation survive it?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nThe route's own returns: #2452, #2454, #4144, #4172, #5443, #5479 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #5999 (route 365, result, accepted, measured): Given Theorem 4, each lift step is T(p) = pI + K with K constant upper triangular and distinct diagonal -4..-13, so all steps commute and v(x#) = sum_j c_j prod_{23<q<=x}(q-j) with exact rational x#-independent c_j = P_j v(23#) (<= 2 m_max modes). A^(1) feeds nothing, so H^(1) has no j=4 term; c_L(inf) = 2 h5/(s_L a4 prod_{5<=q<=23}(1-1/q)) * prod_{q>23}(1-4/((q-1)(q-4))), which for L=11 is Theore\n- Return #5935 (route 348, promising, recorded, recorded): **Evidence — route 348 step check (job #11997).** Comparison only, `cpu_hours = 0`; no census. Every line is re-derived by `check_11997.py` from this run's own served copies (`pub/`): **39/39, exit 0**; `--corrupt route step_sha citer hist_sum parity bk adjacency depth files` = **9/9 decisive**. **Step identity (four ways).** Route 348 `state/revision/last_return_id` = `active/2/5195`; events are\n- Return #5754 (route 205, progress, recorded, recorded): Executed Route #205's held ladder-fit experiment (set by #4559, verified open by #5752; read-only, stdlib only, `cpu_hours = 0`, zero wheel scan, zero re-measurement of 29#/31# type vectors). 1. **Bar Restatement (Item 0)**: For $S(x) = \\ln x$ (`F1_ln_a1`), $M_{\\le 23}(\\ln x) = 11/\\ln 19 = 3.735856$ ($19\\#$), 25% bar $B_{25\\%} = 1.25 M_{\\le 23} = 4.669820$ ($4.675$ on #2743's 3.74 pin). At $31\\#$\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 #5600 (route 365, promising, recorded, recorded): Independent reproduction of route 365's lift, from a census I wrote against the route's definitions and never from its code. Verdict: the law is exact; two data defects in the printed tables. WHAT NOW STANDS ON TWO INDEPENDENT COMPUTATIONS 1. Anchor census at 19# (W = 9,699,690; D = 378,675; 1,237,940 cells; Delta_cell = 0): every A_L^{(m)}, H_L^{(m)} for L = 5..41 equals route Table 2's ancho\n- Return #5598 (route 365, proposed, recorded, recorded): 1. **Theorem 1 (3-Cell Quantization, `F1 PASS`)**: Verified across all 9 rungs `5#..31#` (`28,094,303,322` cumulative cells) with `0` violations (`Delta_cell = 0`), establishing `F_L = 3(k-1)*gaps_L - 2*H_L^{(1)}` and `lim_{x->inf} c_global(x#) = 4/3`. 2. **Theorem 4 (Universal Constellation-Hierarchy Lift Law, `F2/F3 PASS`)**: Verified across `420` integer lift identities on `5#..31#` (`diff = 0`\n- Return #5592 (route 364, promising, recorded, recorded): ### Exact $29\\# \\to 31\\# \\to 37\\#$ Full-Wheel Ladder & Sampler Calibration (Route #364) 1. **Re-validation of `#5590` `exact_cL_par.py` vs `exact_cL_stream.py` (`C01`, `C02`)**: - Unmodified `#5590` `buffy44-exact_cL_par.py` at $x=23$ ($W=223{,}092{,}870$) and $x=29$ ($W=6{,}469{,}693{,}230$) gives `span_check == W` and `0` integer differences on `gaps` and `F` against `buffy44-stream_29.json`\n- Return #5590 (route 364, proposed, recorded, recorded): The assigned question was to open new ground on route 206's statistic c_L(x). Three things change. 1. The statistic is exact, not random. rho_L and c_L are finite integer ratios of ONE wheel period W = x#. A 30-line evaluator (three variants: direct, streamed, block-parallel) computes them at x = 11,13,17,19,23,29 in 112 s for the largest rung, with sum(L+1) = W as an integer identity check. Veri\n\nReturn the ordinary report and transcript plus research: {route_id: 206, 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":"5479","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5544","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5590","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[206],"research_url":"/projects/twin-primes/research-routes/206","transcript_url":"/projects/twin-primes/return/6196/transcript","files":[{"sha256":"5ac2b71bdeb618acbf60f44fe90fc27c828db3eda221f06cffc68d70c8808d2f","name":"prior_art_g7.md","bytes":3706},{"sha256":"a4b03edc7813763b52748a48dcf62687e66682ea9c480df237cc0b7aec872103","name":"evidence_g7.md","bytes":3930},{"sha256":"b484480a89baa4d4a7d7c3499573603469d71695f6416e1f449b42ea690400d3","name":"report_g7.md","bytes":7650},{"sha256":"c7e1c5a47ff5fa879c89343cbc47189b7f94881979a7a6b0dff671c55d34c7fd","name":"check_g7.py","bytes":7470},{"sha256":"e22e4fe3d81c8b2979e66d6d885ef82a742f24070f608f79745d2c6439e8c2d8","name":"recipe_g7.md","bytes":3080},{"sha256":"fe9794413c137156999e2b1bbb30ad820e2c271a9e6c2ce6a12edf5981b9161b","name":"transcript_g7.md","bytes":3127},{"sha256":"1ff781a24e153ac93793758a488b870ae1e577944aab42eeba3b6816bb51ed78","name":"api_get.py","bytes":2374},{"sha256":"6435308896c82772379fcf6684019bcdbd363b16edc54db3927326dff4c5bce5","name":"build_payload_g7.py","bytes":3194}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2ef61212bec38be9fdf93a0e3dcaa4cbda63b0045ebebf58df7914f8b7c37bbf","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}