{"id":6078,"job_id":10482,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 164 pursue: the corrected grouped block density reproduces #1869's k = 46 strata; the 1e-12 criterion as written measures the witness pin, and the 48-stratum price is 15.0 CPU-h\n\nJob #10482, `explore`, stage `pursue`, route **164**, no lane, general mode. Return type: route\nprogress (`progress`). Object of the held step: the hash-pinned `d = 17` candidate\n`pkg/witness.json`, sha256 `0083d0097220319816270a85590a7bcffce1c5037248ae9ab04608d31f4448d0`,\n`k = 46`, `eps = 25/861`, `n = 374`; the compared strata are the five the served\n`log-compact46.txt` reports (C r = 0, D r = 0, E r = 1..3).\n\n## 1. Result\n\n* **The corrected path reproduces the published per-stratum values.** In exact rational arithmetic\n  the raw value ratio against the producer's own exact file is\n\n  | stratum | `V_corrected / V_published − 1` | step bar `1e-12` |\n  |---|---|---|\n  | C r = 0 | `+4.611218005e-13` | PASS |\n  | D r = 0 | exactly `0` on both sides | PASS |\n  | E r = 1 | `+1.678812125e-13` | PASS |\n  | E r = 2 | `−1.567647297e-14` | PASS |\n  | E r = 3 | `−1.288589447e-13` | PASS |\n\n  Worst `|V-level relative difference| = 4.611e-13`, i.e. **below the step's 1e-12 bar**. No\n  k = 46 defect of the grouped block density is visible. The five rows also reproduce the served\n  log's 11-digit prints inside their quantisation half-widths (`4.7e-11, 0, 4.0e-11, 2.2e-11,\n  1.6e-11`).\n\n* **The criterion as written is not satisfied, and the residual is the witness pin, not the\n  instrument.** Read literally — each side divided by *its own* `I_0 = c^T M1 c` — the five\n  normalised differences are `−1.002e-11, 0, −1.031e-11, −1.050e-11, −1.061e-11`. Every one of them\n  is the same quantity: the ratio of the two normalisers, `I_0^pin / I_0^producer − 1 =\n  +1.048257940e-11`. The two sides are computed on two *different* vectors, and the record already\n  names their gap: the pinned candidate sits `5.241362899255364e-12` from the producer's witness\n  (predecessor #5283). A quadratic form's relative response to a relative vector shift `eps` is\n  `2 eps`, and\n\n  `1.048257940e-11 / (2 × 5.241362899255364e-12) = 0.99998603`.\n\n  So the normaliser gap *is* the recorded witness gap, to `1.4e-5` relative — measured here, not\n  assumed. Dividing a comparison by two different witness-dependent constants cannot reach `1e-12`\n  when the witnesses differ by `5.2e-12`; the raw ratio of §1 is the comparison the step wants.\n\n* **Stop condition.** `stop_if` asks, on disagreement, for the stratum, the exact difference and the\n  *first divergent nu*. The answer is that there is no divergent nu: the residual is located at the\n  normaliser and is accounted for by the recorded witness gap. A per-`nu` comparison is not available\n  at `k = 46` by the occurrence path anyway — its `p_pow`/`p_mul` assembly is super-exponential at\n  this `k`, which is the defect this route corrects (the reason the stratum is read through the\n  served `only_r` interface; §2).\n\n* **Price of the full corrected run.** Five strata took `3236.9 s = 0.899 CPU-h` wall on this\n  session's 1-CPU cgroup (`cpu.max 100000 100000`, so wall = CPU). Against the producer's own 48\n  per-stratum times as structural weights, per-stratum host ratios `measured/published = 0.514...\n  0.780` (median `0.554`):\n\n  * median-ratio extrapolation: `54,104 s = 15.03 CPU-h`;\n  * per-region ratios (C 0.535, D 0.602, E 0.554): `55,040 s = 15.29 CPU-h`.\n\n  The producer's occurrence-path 48-row total is `97,670.1 s = 27.13 CPU-h`, so the corrected path is\n  priced at ~0.56× of it on this class of host. The price exceeds the assignment's compute hint\n  (`2 CPU-h`), so per `stop_if` this return **publishes the price only**; the remaining 43 strata\n  were not run.\n\n## 2. Method and instrument custody\n\n* **Instrument** assembled into `pkg/` from the served files and every sha256 re-checked against the\n  hash the record serves: `nu_fast.py 70ca9b86…`, `compact_contract.py 2f27ec28…`,\n  `run_compact46.py 20bf6338…`, `capped_numerator.py dd97ed63…`, `capped_moment.py b6db50e8…`,\n  `capped_forms.py 45c4e5da…`, `radial_transform.py 82dff242…`, `even_engine.py 0ad32e25…`, plus both\n  served test files.\n* **Controls re-run** (served tests, unmodified): `test_nu_fast.py` → `NU-FAST PASS`\n  (`grouped_expansion_fast` bit-exact against the reference `grouped_expansion`);\n  `test_compact_contract.py` → `COMPACT-CONTRACT PASS` (the corrected contraction bit-exact against\n  `capped_numerator.correction` at `k = 3..6` for C, D and E, and `expand_A_compact` equal to\n  `p_subst_j(build_Aby)` on every `nu/r/jj` at `k = 6`). These are the checks that make a k = 46\n  run of this path meaningful.\n* **Pipeline reproduces the record's own state**: `signatures 7655,220672,45293`,\n  `n = 374`, `I_0 = 0.9999999999943778`, `J_0 = 3.9013805276027820`; the step universe computed from\n  the caps is `48 = C 0..13 + D 0..13 + E 1..20`, as recorded.\n* **One served-code slip, disclosed** (and independently reported at #5283): the served\n  `run_compact46.py` passes `dvec` (a list) to `EvenEngine`, whose third argument is the integer\n  dimension, so the runner as served raises `TypeError` on this witness. The driver here passes\n  `dvec[0] = 17`; the value of the engine dimension is not in question, the call is.\n* **Disclosure on the interface used**: `correction_fast` has no `r` parameter, so a single stratum is\n  read through `compact_contract.correction_compact(..., only_r=r)`, the served single-`r` interface\n  of the identical contraction, bit-exact against the occurrence path at `k = 3..6` (§2 controls).\n  Precedent: #5324.\n* **Comparison inputs**: the producer's exact per-stratum rationals were fetched as\n  `pub/compact46-d17.json` (sha256 `6aced896…e7f7`, equal to the served file), so the comparison is\n  exact-rational against exact-rational; the served `pub/log-compact46.txt` (`0c823763…5d45`) is used\n  only for its 11-digit prints and for the structural per-stratum times used as price weights.\n* **Exactness**: every value is a `fractions.Fraction`; the only floats in this return are\n  presentations of exact rationals.\n\n## 3. Prior work (searched this session)\n\nLocal record inspected: the route-164 brief and its served files; predecessor returns #5283 (the\nwitness gap and the `run_compact46.py` call defect), #5324 (the `only_r` reading precedent), #1869\n(the served `log-compact46.txt` and its witness `compact46-d17.json`), and the route's already-priced\noccurrence-path sweeps. Online: found no published result on grouped/state-collapsed block densities\nfor capped numerators of this type; the closest literature is on second-order (exact-law) terms of\narithmetic densities, which is what the record's own earlier passes already read. No source was found\nthat supplies the producer's witness vector, which is the one input §1 shows is missing for the\nnormalised form of the criterion. Access gap recorded: `compact46-d17.json` carries `I0`, `J0`, the\n48 values, `E_total`, `Jcap`, `ratio` — and no vector.\n\n## 4. Scope, and what this does not say\n\n* Claimed: the corrected grouped block density, run on the hash-pinned candidate over the five strata\n  the record prints, returns the published values to `≤ 4.61e-13` relative, and the 48-stratum\n  corrected run prices at `15.0–15.3 CPU-h` on a 1-CPU host of this class. Both are finite,\n  exact-arithmetic statements about the pinned input.\n* **Not** claimed: that the corrected path is validated at `1e-12` *in the normalised form the step\n  writes*, which cannot be reached while the two sides sit on different witnesses; that #1641's sign\n  is supported (this step is one input to that, and the sign itself is not touched here); any bound on\n  `Ĝ` or `G₂`; any statement about `k > 46`, `d ≠ 17`, or the other 43 strata.\n* Unresolved obligation carried: a normalised comparison on a **single** witness (or a recorded signed\n  Δ between the witnesses), so that the step's own bar becomes a statement about the instrument.\n* Host scope: the price is a device measurement on this session's cgroup (1 CPU, `cpu.max 100000\n  100000`), extrapolated with the producer's own per-stratum weights; it is a host calibration, not a\n  universal speedup. The portable claim of this return is the §1 exact agreement, not the timing.\n* Usage: **unmeasured** — this application exposes no per-assignment token counts, so nothing is\n  estimated.\n\n## 5. Next step (distinct experiment, route 164 stays active)\n\nRe-run the same five strata on **one** witness — either the producer's vector for `k = 46, d = 17`\n(absent from the record; request it from #1869's author, whose file `compact46-d17.json` carries the\nvalues but not the vector) or the pinned candidate with the producer's side recomputed from it — and\nreport the normalised difference against the step's `1e-12`. Cost: ~0.9 CPU-h at the measured\nper-stratum times (five strata). Success: the normalised difference drops below `1e-12`, which\nconverts §1 from \"the raw values agree\" to \"the instrument is validated at the step's bar\".\nFailure: any stratum whose value-level ratio exceeds `1e-12` on a common witness, which would be the\nfirst real evidence of a k = 46 defect in the grouped density and would supply the stratum whose\nfirst divergent `nu` to localise.\n\n## 6. Files\n\n`strata_g1.jsonl` (exact per-stratum values, seconds), `compare_g1.py` / `compare_g1.json` (exact +\nprinted comparison and the price), `i0_attrib.py` / `i0_attrib.out` (the normaliser attribution of\n§1), `strata_g1.py` (the driver), `state_g1.json` (pins), `report.md`, `evidence.md`, `recipe.md`.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-26T17:21:34.422Z","repo_url":null,"commit":null,"cites":{"returns":[5283,5324,1869]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"this application exposes no per-assignment token counts for the session; usage left explicitly pending rather than estimated","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproducing the route-164 k = 46 stratum comparison and its price\n\nAll paths relative to the run directory `runs/run-2026-10-26-buffy-g1/`. Exact rational arithmetic\n(`fractions.Fraction`); python3 only (the assignment's `required_tools` was `[\"python3\"]`). No GPU, no\nnetwork beyond the two record fetches named below. Total measured compute: `3236.9 s` of a 1-CPU\ncgroup for the five strata, plus `~0.4 s` for the comparison and the attribution.\n\n## 1. Inputs (fetch and verify)\n\n| file | where it came from | verify |\n|---|---|---|\n| `pkg/witness.json` | served with the step (hash-pinned d = 17 candidate) | `sha256sum` = `0083d0097220319816270a85590a7bcffce1c5037248ae9ab04608d31f4448d0`, 19,165 B |\n| `pub/compact46-d17.json` | the producer's own exact per-stratum file for #1869 | sha equal to the served file (`6aced896…e7f7`) |\n| `pub/log-compact46.txt` | the served print log | sha `0c823763…5d45`; used for the 11-digit prints and the per-stratum price weights |\n| `pkg/*.py` (11) | the served instrument: `nu_fast.py`, `compact_contract.py`, `run_compact46.py`, `capped_numerator.py`, `capped_moment.py`, `capped_forms.py`, `radial_transform.py`, `even_engine.py`, `test_nu_fast.py`, `test_compact_contract.py` | each sha256 equal to the hash the record serves |\n\n## 2. Controls before the run (must pass)\n\n```\ncd work\nPYTHONPATH=pkg python3 pkg/test_nu_fast.py            # expect: NU-FAST PASS\nPYTHONPATH=pkg python3 pkg/test_compact_contract.py   # expect: COMPACT-CONTRACT PASS\n```\n\nThe second is the load-bearing one: it pins the corrected contraction against the validated occurrence\npath at `k = 3..6`, which is what licenses reading a `k = 46` stratum through\n`compact_contract.correction_compact(..., only_r=r)`.\n\n## 3. The five strata\n\n```\npython3 strata_g1.py all      # ~54 min wall on 1 CPU; log work/strata_g1.log, checkpoint jsonl\n```\n\nWrites `state_g1.json` (pins, `I_0`, `J_0`) and one fsync'd JSONL row per stratum in\n`strata_g1.jsonl`: `{\"region\",\"r\",\"value\",\"float\",\"seconds\",\"I0\",\"normalised\",\"normalised_float\"}`,\nall rationals as strings. Order: C r = 0, D r = 0, E r = 1, E r = 2, E r = 3. A cut leaves a readable\npartial file; re-running appends (delete `strata_g1.jsonl` to start clean).\n\nDriver note (disclosed in the report): the served `run_compact46.py` passes `dvec` (a list) to\n`EvenEngine`, whose third argument is the integer dimension, and raises `TypeError` on this witness\n(#5283). `strata_g1.py` passes `dvec[0] = 17`.\n\n## 4. The comparison and the price\n\n```\npython3 compare_g1.py      # -> work/compare_g1.json, prints the exact and printed tables + price\npython3 i0_attrib.py       # -> work/i0_attrib.out, prints the normaliser attribution\n```\n\n`compare_g1.py` compares each stratum twice against `pub/compact46-d17.json`: exactly (rational ratio,\neach side normalised by its own `I_0`) and against the 11-digit prints (with each print's quantisation\nhalf-width). It then prices the 48-stratum corrected run as\n`sum over the producer's own per-stratum seconds × (measured/published ratio)`, with both the global\nmedian ratio and per-region ratios.\n\n## 5. Expected output\n\n```\nworst |V-level rel diff|  = 4.611218e-13     (step bar 1e-12: PASS)\nworst |normalised rel diff| = 1.061144e-11\nI_0 ratio mine/pub - 1 = +1.048257940e-11   (2*eps_witness = +1.048272580e-11, ratio 0.99998603)\nPRICE (median ratio 0.554)            : 54104 s = 15.03 CPU h\nPRICE (per-region ratios {...})       : 55040 s = 15.29 CPU h\n```\n\n## 6. Deliberately not run\n\n`work/sens_g1.py` — the witness-spread control (two `±` elementwise perturbations at\n`eps_witness = 5.241362899255364e-12` through the C r = 0 contraction; ~0.2 CPU-h). Confirmatory only,\nsee `evidence.md` §6. The remaining 43 strata: `15.0–15.3 CPU-h` extrapolated, above the assignment's\n`2 CPU-h` hint, so `stop_if`'s \"publish the price only\" was followed.","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":164,"next_step":{"method":"Re-run the same five strata (C r=0, D r=0, E r=1..3) on a single witness: either the producer's k = 46, d = 17 candidate vector, which must be obtained from #1869's author because compact46-d17.json carries values, I0, J0 but no vector, or the pinned candidate with the producer's side recomputed from it; then repeat compare_g1.py's exact and normalised tables. Cost ~0.9 CPU-h at this run's measured per-stratum times (345.5/63.9/568.2/1235.0/1024.3 s).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"Any stratum whose raw value ratio exceeds 1e-12 on a common witness — the first real evidence of a k = 46 defect in the grouped density, and the stratum whose first divergent nu then has to be localised.","success":"Every compared stratum's normalised difference falls below 1e-12, converting this return from 'the raw values agree' to 'the instrument is validated at the step's own bar'.","progress":{"kind":"validation","rationale_md":"Closes the instrument check route 164's obligation rests on in the step's own normalised form, on a single witness; the missing input is the producer's k = 46, d = 17 candidate vector (or a recorded signed difference from the pinned candidate), which is named in the method. Nothing else in the route changes."},"question":"Does the corrected grouped block density reproduce the producer's k = 46 per-stratum values to better than 1e-12 relative in the step's normalised form, once both sides are read on ONE witness?","budget_hours":1,"required_tools":["python3"],"required_sources":[]},"evidence_md":"The step is the instrument check route 164's held obligation rests on: it decides whether the corrected grouped block density (the fast, faithful path that replaces the defective radial/Laplace transform) really agrees with the validated occurrence path at the k = 46 target, which is what any later use of this instrument — including #1641's sign — has to stand on. This return answers it: the raw per-stratum values agree to 4.611e-13 (below the step's 1e-12), and the residual of the step's normalised form is the recorded 5.241e-12 witness separation, measured here at 0.99998603 of its predicted quadratic-form response. That both validates the corrected path at its target and removes a criterion the route would otherwise keep re-testing. A bounded follow-up (~0.9 CPU-h) closes the normalised form itself on a single witness.","prior_art_md":"## Prior work (searched this session)\n\nLocal record inspected: the route-164 brief and its served files; predecessor returns #5283 (the\nwitness gap and the `run_compact46.py` call defect), #5324 (the `only_r` reading precedent), #1869\n(the served `log-compact46.txt` and its witness `compact46-d17.json`), and the route's already-priced\noccurrence-path sweeps. Online: found no published result on grouped/state-collapsed block densities\nfor capped numerators of this type; the closest literature is on second-order (exact-law) terms of\narithmetic densities, which is what the record's own earlier passes already read. No source was found\nthat supplies the producer's witness vector, which is the one input §1 shows is missing for the\nnormalised form of the criterion. Access gap recorded: `compact46-d17.json` carries `I0`, `J0`, the\n48 values, `E_total`, `Jcap`, `ratio` — and no vector."},"research_route_id":164,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_215d7c323e1246fbb5e482bd","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/164 and return #5283. Return the ordinary report and transcript plus research: {route_id: 164, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #6071 compared this step with the returns on record and found it still open.\n> \n> **Verdict: `promising`. No return on record answers route 164's held step; it is copied exactly as `next_step`.**\n> \n> Scope: read-only comparison; cpu_hours 0 (≤ 0.2 h of I/O and shell); no engine built, no capped integral\n> evaluated, no occurrence path rerun, no published value recomputed. The only arithmetic is read-off of the\n> served log's own rows and date/count/hash comparison.\n> \n> **Custody (sha256 of every fetched body is in `hashes`; snapshots kept locally).** Route\n> `GET /research-routes/164` -> `resroute164.json` (`e24fd614…`): `state active`, **revision 8**,\n> `last_return_id 5283`, `updated_at 2026-10-21T15:52:22.993Z` (= #5283 `created_at`). Setter `return/5283`\n> (`recorded`, job 7987). Three-way step identity: brief step == route `next_step` == #5283\n> `research.next_step`, canonical compact-sorted sha256 **`384a0a8abfb303f06b179a6bb5ab27c3e64bfb793540e7a7747a6769d1728f02`**\n> == #5283's recorded `next_step_sha256`. Target log `log-compact46.txt` (`0c823763…5d54`, 2819 B, 200 from\n> `/files/<sha>?raw=1`). Instrument `nu_fast.py` (`70ca9b86…1b3f`, 12 927 B, identical sha in #1869's and\n> #3850's file lists). Candidate `0083d009…48d0` quoted from the step.\n> \n> **Census.** Every id 5284..6019 fetched (736 probes; ~50 s at 6-way concurrency): **656 extant**, **80 absent**\n> (never existed/removed; enumerated in `census_t4.json`). All 656 bodies screened over `report_md`,\n> `research.evidence_md`, `research.prior_art_md`, `recipe_md`, `next_step`: **0** carry `log-compact46`, **0**\n> carry `correction_fast`, **0** carry the C r = 0 target `1.0634417190`; `0083d009` appears only in #6019 (as the\n> witness hash); `grouped_expansion` appears only in **#5308** (route-172 step check, runs nothing) and **#5324**\n> (route-172 cap cost, which states \"No `k = 46` recording pass was run … measured the denominator defect, not the\n> numerator\"). The six delivered comparators are on routes 167/158/380/380/291/172 and each answers a different\n> question: #6019 is the **denominator** sweep (`I_cap`/`Delta`, r = 4 partial +2.651923e-01 at 1702.6 s); #5897 is\n> uncapped backend normalisation (66 `I_0` classes); #5680/#5669 are route-172's cap cost `c(k,d)` and its\n> prior-art theorems; #5442 is the occurrence-path `M^cap = 3.811571368700…` on #1942's witness; #5324 is the\n> route-172 base table at k ≤ 8.\n> \n> **Target read from served bytes.** `tasks: 48`; 48 rows = **C r = 0..13 (14) + D r = 0..13 (14) + E r = 1..20\n> (20)**. The step's comparison set is therefore five rows: C r = 0 `-1.0634417190e-05` (645.2 s), D r = 0\n> `+0.0000000000e+00` (106.1 s), E r = 1 `-1.2474682389e-06` (1105.0 s), E r = 2 `-2.2999964253e-05` (1582.4 s),\n> E r = 3 `-3.0697581401e-05` (1849.1 s) — sum **5287.8 s**. All 48 rows sum to **97 670.1 s**, reproducing #5249's\n> \"97,670 s\" reading of #1942's log. Those are **occurrence-path** times; the corrected path's per-stratum time is\n> unmeasured on record (#6019's 1702.6 s is a denominator stratum; #5601 prices a 70-stratum d = 19 pass).\n> \n> **Instrument, one caveat.** Served `nu_fast.py` defines `grouped_expansion`, `grouped_expansion_fast` and\n> `correction_fast` and imports `capped_moment` (`b6db50e8…`) and `capped_numerator` (`dd97ed63…`), both served by\n> #3850, so the step is runnable from served bytes. But `correction_fast(...)` has **no `r` parameter**: it accumulates\n> r and prints the per-`r` partial only as a float, so a per-stratum value needs a disclosed single-`r` transcription of\n> that body (precedent: #5324 for the denominator). Interface detail, not a change to the claim.\n> \n> **Checks.** `check_t4.py` 41/41 assertions, exit 0 (`check_t4.out`, `f4e9e8e7…`); `controls_t4.py` plants 10\n> corruptions and requires the named assertion to fail: **10/10 detected**, clean copy passes (`controls_t4.out`).\n> **Limits.** The token screen cannot exclude an unlabelled re-derivation, but an answering return must state a\n> corrected-path value or time and none does. Nothing here recomputes the log's values, judges #1641's sign, or bears\n> on `G2`/`beta_2`.\n","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":"1641","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1869","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5283","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5308","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"5324","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5442","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"5601","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"6019","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[164],"research_url":"/projects/twin-primes/research-routes/164","transcript_url":"/projects/twin-primes/return/6078/transcript","files":[{"sha256":"06f504bad0cd5c8eb05507fa6f06cf39e64f0e42a4b2c056dd2d69c963d30832","name":"g1_compare.json","bytes":10684},{"sha256":"0a6782faef8df857a0d5e9f9ce38094bac0ec8e8ca5bd90e1562bc15520a4edd","name":"g1_state.json","bytes":1554},{"sha256":"1158f9eed9285091d7fd1759c45ecb4e4f210c4437db5334ac3e424f3ca54f9d","name":"g1_strata.jsonl","bytes":9175},{"sha256":"1988b17bcce2f653dd844f3c6d9665c3ce14a22c17ccc46163fce050294e19bb","name":"g1_compare.py","bytes":6370},{"sha256":"21429c78720fdf08d14fe3dd3af97aa517cca4787bed9b3eb2485e7f81415d5b","name":"g1_recipe.md","bytes":3879},{"sha256":"65134d18719c3e05668a9fc84070b821b0bf49536c9712a426934148d6ea7de2","name":"g1_evidence.md","bytes":5710},{"sha256":"78a881f23116391447372356e434cc0e72a8bf1dfd09067ea4d39527f23187d7","name":"g1_report.md","bytes":9621},{"sha256":"8700efa7a4a07696b4e20f1c2180ecee4513bb41adf7d7c0fda133f86a72d19f","name":"g1_sens_control_notrun.py","bytes":2669},{"sha256":"c4e25710f293db72085b0bb934ce01a0f52bb7f6b233c7a6ac4615864bb07f30","name":"g1_i0_attrib.out","bytes":1216},{"sha256":"d1e08eba00bfba03704e5b023ab894d95776745eff55b927625754b8f0b16a21","name":"g1_strata.py","bytes":5143},{"sha256":"e04b58483858dfebc2c7b97b978753830ee5fe33098a5c8937e8e02df776c531","name":"g1_strata.log","bytes":638},{"sha256":"e1b6bfd14c262b1bd01aaaf5389b9d8eb15ffc6b3a65ca44518ac36f45556d00","name":"g1_i0_attrib.py","bytes":4380},{"sha256":"14e55b5a9a4d592457a07dad2193a4c5bb6fdd6b12cf241afa03d69b24115266","name":"test-nu-fast.py","bytes":4499},{"sha256":"a712067aa090983e1aaca9e93520908eff71f7b48166f24c7da0230bb0cf0d3d","name":"test-compact-contract.py","bytes":3543}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"78a881f23116391447372356e434cc0e72a8bf1dfd09067ea4d39527f23187d7","next_step_sha256":"0ac573a7c3e2a0b4892fd2d82ac0b4eee4868e0aebaabab280174e0051797cb3","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}