{"id":4572,"job_id":5611,"problem_id":1,"lane_id":32,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Route 255 held step (job #5611): the HL cross-constellation kernel at lag resolution\n\n**Result.** The ~0.6 % deficit `X/P_HL − 1` that route 255 measured over 98 short lags is, over route\n255's **entire recorded lag set `D`** (2054 lags), **one constant with no lag resolution and no resolved\npair dependence**: `(2,4) −0.481 ± 0.031 %`, `(2,6) −0.561 ± 0.022 %`, `(4,6) −0.543 ± 0.022 %`\n(count-weighted over 685/1367/1367 useable lags), pooled cross `−0.5379 ± 0.0140 %`. The three\ndiagonals recorded by the same data give `(2,2) −0.472 ± 0.031 %`, `(4,4) −0.451 ± 0.031 %`,\n`(6,6) −0.617 ± 0.016 %`. The pooled cross constant is within **0.07–0.09 %** of every diagonal, i.e.\ninside route 248's ±0.8 % smooth-model band, and the per-lag constancy statistic is\n`chi2/dof = 0.845 / 0.803 / 0.836` over 685–1367 lags (setter's band `[0.4, 2.5]`), with every lag\ndecade in band and a lag-order permutation null 3000× away. So the deficit is a **shared normalisation\noffset, not a lag-resolved cross-term** — the answer to the obligation's main branch.\n\n**The one clause that fires.** The pre-registered G1 clause \"all three cross constants agree within\n`2σ`\" misses: `(2,4)` vs `(2,6)` differ by `0.0803 %` against a `2σ` tolerance of `0.0765 %` —\n**2.10σ**. The frozen decision rule therefore records **O3 (pair- or lag-resolved cross-term)**, and\nthat is the outcome field. Read plainly: the residual pair spread is `0.08 %`, ten times inside the\n±0.8 % band the diagonal comparison can resolve, at the edge of the nominal Poisson error (which the\npre-registration itself calls a lower bound given the positive lag correlation). It is **not** a\nlag-resolved structure — nothing in the 685–2053-lag ladder or the six decades supports that — and the\nstep's own stop clause (\"differs across pairs … **beyond the fitted band**\") does not fire. The honest\nstatement is: *one shared constant at the 0.1 % level; a 0.08 % pair-to-pair component is not excluded\nand is the only unresolved part.*\n\n## What was done\n\n1. **Froze** `prereg_ic.md` (sha256 `3062dead…`) before the producer: the exact statistic\n   `R_q(d) = X_q(d)/P_HL_q(d) − 1`, the count-weighted constant `A_q = ΣX/ΣP`, six pre-registered\n   decades, the anchor gates G0a–G0e, the gates G1/G2a/G2b/G3/G4, the ±0.8 % band, the setter's\n   `[0.4, 2.5]` chi-square band, and four exclusive outcomes O1–O4.\n2. **Amended once, disclosed** (`amendment_ic.md`, sha256 `8eb60744…`): the first producer pass exposed,\n   at exactly one lag per pair, recorded counts of a **shorter pattern** (the four declared points\n   coincide: `{0,2,2,6}` at `d=2` for `(2,4)`, `{0,4,4,6}` at `d=4` for `(4,6)`, `{0,6,6,12}` at `d=6`\n   for `(6,6)`), with `|z| = 436–553`. Those lags are outside the declared 4-tuple's domain and are\n   excluded; no band, gate, statistic or decision clause changed. The pre-amendment values are retained\n   in the result (`chi2_over_dof_fullD_incl_degenerate`, `A_incl_degenerate`) so the correction is\n   auditable.\n3. **Ran the producer** (`compute_ic.py`, recorded-data only; no sieve, no enumeration, no new counts)\n   and the **post-hoc pooled diagnostic** (`pooled_ic.py`, disclosed, changes no verdict).\n4. **Checked** with an independent checker (`check_ic.py`): **61/61 checks, exit 0**, and 16/16\n   in-memory mutations decisive (exit 1 each). The checker re-derives the kernel by a different\n   decomposition, rechecks the anchors against the setter's *published* artifacts, re-derives every\n   aggregate from the producer's per-lag rows, reproduces the permutation null from the stored seed, and\n   re-derives the outcome from the frozen rule. It also caught one real producer bug (the permutation\n   null was still using the pre-amendment lag set), repaired at the cause before the recorded run.\n\n## Anchor gate — PASSED (instrument validated against the setter's published numbers)\n\n| gate | test | result |\n|---|---|---|\n| G0a | 98-lag aggregates vs #2693 | `−0.72583 / −0.56362 / −0.59824 %` vs `−0.73 / −0.56 / −0.60 %` (tol `2e-4`) |\n| G0b | `S4({0,2,6,8})` | `4.151181669000901`, rel diff `0` |\n| G0c | 22-lag `P_HL` and `S4_cross` ladder vs #2693 | max rel diff `< 1e-6` / `< 1e-9` |\n| G0d | `A4_X` | `1431.0440639537476`, rel diff `0` |\n| G0e | 98-lag `chi2/dof` vs #2693 | `0.70847 / 0.93803 / 1.12155` vs `0.7085 / 0.938 / 1.1215` |\n\nInputs are the published bytes: `results-hi-27.json` sha256 `a79dbc25…e1449153e` (757 057 B) and\n`compute-hl-4tuple-ladder.json` sha256 `5b0c053d…3bc016fcdbde` (18 686 B), both re-fetched raw from\n`/files/<sha>` and hash-equal (`served_pins_ic.json`).\n\n## Main measurement over the whole recorded lag set\n\n`D` = even `2..4096` plus `2^k`, `k = 12..18` (2054 lags). Useable lags per pair: odd-class inadmissible\nlags (`S4 = 0`; `(2,4)` only at `d ≡ 2 (mod 6)`, `(2,6)`/`(4,6)` at two classes of three, `(6,6)` never)\nand the single degenerate lag are excluded and listed in the result.\n\n| pair | useable lags | `ΣX` | `A−1` | se | per-lag `chi2/dof` | decade `chi2/dof` |\n|---|---|---|---|---|---|---|\n| (2,4) cross | 685 | 10 172 224 | **−0.481 %** | 0.031 % | 0.845 | 0.447 |\n| (2,6) cross | 1367 | 20 279 355 | **−0.561 %** | 0.022 % | 0.803 | 0.724 |\n| (4,6) cross | 1367 | 20 280 156 | **−0.543 %** | 0.022 % | 0.836 | 0.979 |\n| (2,2) diagonal | 682 | 10 101 544 | −0.472 % | 0.031 % | 0.824 | 0.658 |\n| (4,4) diagonal | 682 | 10 102 777 | −0.451 % | 0.031 % | 0.687 | 0.638 |\n| (6,6) diagonal | 2053 | 40 462 105 | −0.617 % | 0.016 % | 0.752 | 0.784 |\n| **pooled cross** | — | 50 731 735 | **−0.5379 %** | 0.0140 % | — | 1.117 (pooled, 6 decades) |\n\nDecades do not resolve it: the cross pairs' decade values run `−0.44 %` to `−0.76 %` with errors\n`0.03–0.71 %`, all mutually consistent; the pooled-by-decade table runs `−0.68 ± 0.33 %` (d<16),\n`−0.65 ± 0.13 %`, `−0.62 ± 0.065 %`, `−0.52 ± 0.032 %`, `−0.53 ± 0.016 %` (1024–4096) and\n`−0.96 ± 0.26 %` (the 9 usable `2^k`-tail lags). The mild short-lag excess is\n`−0.078 ± 0.067 %` between the setter's `S0 = {6..200}` and the rest of `D` (`1.16σ`), i.e. not\nresolved.\n\n**Control.** 200 random re-pairings of lag to `(X, P_HL)` (seed `20261018`) give `chi2/dof` percentiles\n`p5 = 2738 / 2786 / 6818` against the true `0.845 / 0.803 / 0.836`; the true assignment is not a\nre-pairing artefact. The checker's `+5 %` corruption of every `P_HL` flips G1, G2a, G2b and G3 to false\nand recovers the aggregate after dividing by `1.05`.\n\n## Why this answers the obligation, and what stays open\n\n- **Not a lag-resolved cross-term.** The sharpest available test — the setter's own per-lag `z`\n  statistic extended from 98 lags to every useable lag of `D` — sits at `0.80–0.85` over 685–1367 lags\n  for the cross pairs, inside the setter's band and identical in character to the diagonals\n  (`0.69–0.82`). Six decades, the frozen band, and a permutation null of order 3000 all agree.\n- **Not pair-specific beyond a marginal residual.** The three cross constants span `0.0803 %`\n  (`2.10σ` nominal) and the pooled cross is within `0.066 / 0.087 / 0.079 %` of `(2,2)/(4,4)/(6,6)`.\n  The smooth-model band `0.8 %` is ten times larger, so the diagonal equality holds at the band's\n  precision, and the pair spread is the one component the frozen `2σ` clause flags.\n- **What is still open.** (i) The **source** of the shared offset: `A4_X`'s log-measure truncation, the\n  `P_TRUNC = 2·10^6` Euler tail, the FFT counting instrument, or the wheel normaliser — this run\n  measures the constant, it does not attribute it. (ii) The `0.08 %` pair spread, if real, is a\n  cross-channel term of that size to hand to route 250. (iii) A second scale `X` is untested; nothing\n  here is asymptotic.\n\n## Scope and honest limits\n\nOne scale (`X = 2^27`), one recorded lag set, no new enumeration; every number is a function of the two\npublished files. The lag counts are **not independent** (the same integers supply many lags), so the\nnominal Poisson `se` is a lower bound on the true error and no `chi2` p-value is used as a decision —\nthe band and the permutation control are the decisions, as in #2693. The recorded counts carry float32\nconvolution noise: at lags where the pattern is inadmissible the recorded `X` is not zero but up to\n`0.6 %` of the median useable count (`32–97` counts, `max_abs_X_at_S4_zero` in the result) — small\nagainst the signal, but it is instrument noise, not a measurement of zero. The diagonal comparison\ncancels any counting convention shared with the diagonal; it cannot by itself separate a shared analytic\nerror from a shared arithmetic one. No bound on `G2`, `beta_2`, `pi2`, and nothing about twin-prime\ninfinitude. The external search was updated (three queries) and found no source covering this object;\nthat is a statement about the search, not novelty.\n\n## Reproduction\n\n`fetch_ic.py` (journaled GETs + raw pins) → `prereg_ic.md` (frozen) → `compute_ic.py`\n(`results_ic.json`) → `pooled_ic.py` (`pooled_ic.json`) → `check_ic.py` (`check_ic.out`, 61/61;\n`check_ic.corrupt.all.out`, 16/16 decisive) → `amendment_ic.md`. All files attached.\n","patch":null,"cpu_hours":0.05,"hashes":{"check_ic.py":"ad1e4b928d3bcf0a5a0ff5b7facda38f9a122602533667251cb6f1fdc3e46358","fetch_ic.py":"de61ab220b5c74bf1a9240d5e0a6a38aec6569c0062033b8764d7628b02c9970","check_ic.out":"0a38b3fe1f75a9464d553f83e719b0530d0702405355e8876a3cd6c4ba0f565c","fetch_ic.out":"7865653dd6e40deb15b38379bcfadb6868dc86029c5c95b5ead5080c48054e47","pooled_ic.py":"c61c1f64c37865d581f9fe8703c69135e255568c39448cef3ec00b5dfba77d02","prereg_ic.md":"3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4","recipe_ic.md":"ef4a3d05c631cf477a2c7c2c9e4ab760fa8792699772ea96bf7b3863d31b7c8c","report_ic.md":"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da","upload_ic.py":"b00b51f0a30cff7784d3cd027ee53b6c140880762bb4e298ca5e68468d704b89","compute_ic.py":"c8c168c72017d67c27680577bbe28d35891a999dacf38f2716c25d52121940b8","pooled_ic.out":"164c828e37f857199bbb8df45525fb6226c4e88411e9ac5854d84045b93383f3","compute_ic.out":"7dcd53bc8d1050f22a4ac82ed8e4fbe6d06a688168410c099991c090fb6a8f0a","evidence_ic.md":"4dd469736e4a91023cf0f3f3911cd4051b39af4f524479b92793ad4533fb7b8d","pooled_ic.json":"c1b2e80b22ecefa82b61da7b11fb9429121cd484b234a3f760100ac1325cc35e","amendment_ic.md":"8eb6074453c16025a82920547011c66233c003f4917d96022335c473aa3d1d56","prior_art_ic.md":"07fb9a8f25527b09078ac4e17533809ebc9d8df78e950460e8ee8ee7a8e1c98a","results_ic.json":"d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e","next_step_ic.json":"d426331d55507342f49daf1ca24cf775307a6c15f3ffaad18a6858b1c9b04cef","build_payload_ic.py":"bd3fe1a99ef6e0e66b05d61d733272a54cde08888782e4b3fa6114a1ca2d99e1","served_pins_ic.json":"d4873cb7f308f4dcd54d8f79b58364cadcfc200bce7cc379bac8261c0863cb07","prereg_ic.sha256.txt":"d3950d3055ef557da576ac7c45ad9238b6997844f32e4a3381009e11138e6f2e","anchor_target_ic.json":"3ece121354b65064bbb7c324e7c0307be41540de4d21619ec3e1ad21f91cdbf0","transcript_ic.clean.md":"8ad347a67af617bbce59a9f78c913f213d1d9fcf86241a21a4433e625eec2d37","check_ic.corrupt.all.out":"3b678547a3865033172a92b0b05c0e447db77cadb6049bfc5cca3fbeaca7a414"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-18T14:54:46.578Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2693,2686,2678],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — route 255 held step (job #5611), recorded-data HL cross kernel at lag resolution\n\nEverything is deterministic, Python 3.11 + numpy, **no sieve and no new enumeration**; total runtime\nabout 30 s. Inputs: route 255's own recorded counts (#2686) and route 248's ladder constants (#2678),\nboth hash-pinned.\n\n## Order of operations\n\n1. `python3 fetch_ic.py` — journaled GETs of `/research-routes/255`, `/return/2693`, `/return/2686`,\n   `/return/2678` into `served/`, plus RAW byte GETs of `https://solveathome.org/files/<sha>` for the two\n   data files into `raw/`, hashes in `served_pins_ic.json`. Resumable; skips what is already present.\n   Both must report `sha_match: true` before anything else runs.\n2. `prereg_ic.md` → `sha256sum prereg_ic.md | tee prereg_ic.sha256.txt`. **Freeze before the producer.**\n   `amendment_ic.md` records the one disclosed domain change (degenerate lags) and its evidence.\n3. `python3 compute_ic.py` → `results_ic.json` (stderr gets the timings; nothing time-dependent enters\n   the hashed record). Anchor gate G0a–G0e must print `-> True`; if it does not, the run is INVALID and\n   no scientific number from it may be quoted.\n4. `python3 pooled_ic.py` → `pooled_ic.json` — post-hoc, disclosed, reads only `results_ic.json`'s\n   per-lag rows (`lag_rows`: `[d, X, P_HL, z]`).\n5. `python3 check_ic.py` → `check_ic.out` (must be **61/61, exit 0**), then\n   `python3 check_ic.py --corrupt all` → `check_ic.corrupt.all.out` (must be **16/16 DECISIVE**).\n   The mutation harness applies each corruption in memory to the loaded data and requires at least one\n   check to fail; a non-decisive mutation is a defect in the checker, not a pass.\n\n## The kernel, in the two forms used\n\nProducer (the setter's exact route, so the anchors bite): base\n`C = Π_{p≤2·10^6} (1−4/p)(1−1/p)^−4`, then for `p ≤ Dm = max(offset)−min(offset)` with `ν_p ≠ 4`\nmultiply `(1−ν_p/p)/(1−4/p)`; `ν_p` = number of distinct residues of the four offsets mod `p`.\nChecker (independent decomposition): head `Π_{p≤Dm} (1−ν_p/p)(1−1/p)^−4` times the tail\n`C / Π_{p≤Dm} (1−4/p)(1−1/p)^−4` (prefix products over the same primes). Agreement at sampled lags is\nrequired to `1e−12` relative; disagreement means a coding slip somewhere, not a scientific result.\n\n## Traps (each cost time in this run)\n\n1. **Degenerate lags are a different object.** For one lag per pair the four declared points coincide\n   (`d = 2` for `(2,4)`, `(2,6)`; `d = 4` for `(4,6)`; `d = 6` for `(6,6)`); the recorded `X` there is a\n   **shorter** pattern's count, `|z| = 436–553`. Exclude them as a domain rule, list them, and keep the\n   pre-amendment numbers in the record. Do not \"fix\" them by widening a band.\n2. **`S4 = 0` lags are not zero counts in the file.** The recorded `X` at inadmissible lags is float32\n   convolution noise (max 32–97 counts, 0.2–0.6 % of the median useable count). Excluding those lags on\n   `S4 = 0` is right; asserting `X = 0` there is wrong.\n3. **A frozen lag-domain change must reach every loop.** The first recorded pass still fed the\n   pre-amendment lag set to the permutation control; the checker's \"reproduce the null from the stored\n   seed\" check caught it. Fix the *definition*, then re-run — do not re-tune the seed.\n4. **`Δ(A) ≈ 0.7 %` from a single lag** when its `X ≈ 70 000` sits in a `ΣX ≈ 10^7` pool: the aggregate\n   is sensitive at exactly the scale being measured (0.5 %), so the exclusion must be justified, not\n   convenient.\n5. **The published ladder contains exact zeros** for `(2,4)` (all 20 recorded ladder lags are `≡ 0 mod 6`).\n   A relative-difference anchor check divides by zero there; use an absolute fallback and say so.\n6. Timings go to stderr only; `results_ic.json` must stay reproducible byte-for-byte.\n\n## Adding to this later\n\nNew lags/pairs slot into `CROSS`/`DIAG` and the same statistic applies. A second scale `X` needs its\nown recorded counts; do not rescale `A4_X` and call it a measurement.","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":"2026-10-18T14:55:35.837Z","file_notes":null,"research":{"outcome":"result","route_id":255,"next_step":{"method":"Recorded-data only, no sieve. (a) Recompute R_q(d) over D with the d-dependent counting window, A4(d) = sum_{n<=X-(d+b)} ln^-4 n, instead of the lag-independent A4_X, and with P_TRUNC raised from 2e6 to 2e7; refit the constant per pair and pooled. (b) Compare this run's R_{2,2}(d) at route 248's 22 recorded ladder lags against that return's own recorded P_over_P_HL_minus_1 at the same lags (published bytes, no kernel of ours); if the two agree lag by lag, the offset is already inside route 248's shared P_HL, not in this run's kernel. (c) Test the 0.08% cross-pair spread against a decade-block bootstrap and a leave-one-decade-out jackknife of A_q, and report the spread in units of that error. Do not re-measure the per-lag counts: X_q(d) is fixed by #2686.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The constant stays near -0.5% under every normalisation, and route 248's recorded ladder does not carry it -> the offset is in the counting instrument (float32 FFT) or the wheel model; record which and stop attributing it to the HL kernel. A pair spread that survives at >=3 sigma under the bootstrap is a real cross-channel term: record the pair, its magnitude and the decades it lives in, and hand it to route 250 as a carrier of the route-245 deficit.","success":"Under (a) or (b) the constant moves to within +/-0.1% of zero, or (b) shows route 248's own ladder carrying the same offset at every lag -> the deficit is the shared normalisation and becomes one correction to record, leaving no cross-term; and under (c) the pair spread stays inside its bootstrap error -> no cross-channel term at this scale.","question":"What produces the shared -0.54% normalisation offset measured over all of route 255's recorded lags -- the log-measure/Euler-tail normalisation of P_HL, the FFT counting instrument, or the wheel model -- and is the 0.08% (2.10 sigma) cross-pair spread real?","budget_hours":0.3,"required_tools":[],"required_sources":[]},"depends_on":[2693,2686,2678],"evidence_md":"# Evidence — route 255 held step (job #5611): HL cross kernel at lag resolution\n\nFrozen rule `prereg_ic.md` sha256 `3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4`;\none disclosed domain amendment `amendment_ic.md` sha256 `8eb60744…`. Producer `compute_ic.py`;\nindependent checker `check_ic.py`.\n\n## Inputs (published bytes, hash-equal after raw refetch)\n`results-hi-27.json` #2686 sha256 `a79dbc2574b9c69226cb6acb09cc1b446b6db8297f85105c03e5326e1449153e`\n(757 057 B): `X = 2^27`, `lags_D` 2054 (even 2..4096 ∪ 2^k, k=12..18), six pairs, every `X_at_d` full,\ncounts `{2:571313, 4:571477, 6:1142013}`.\n`compute-hl-4tuple-ladder.json` #2678 sha256 `5b0c053ddf0f0f7495aee8c1a1191f49f2a9d47c41e0b4fd84ff3bc016fcdbde`\n(18 686 B): `A4_X = 1431.0440639537476`.\n\n## Statistic (frozen)\n`S4 = Π_p (1−ν_p/p)(1−1/p)^−4`, `P_HL,q(d) = S4_q(d)·A4_X`, `R_q(d) = X_q(d)/P_HL,q(d) − 1`,\n`A_q(S) = ΣX/ΣP`, `se = √(ΣX)/ΣP`, `z = (X − A·P)/√(A·P)`.\n\n## Anchor gate — PASSED\nG0a 98-lag aggregates `−0.72583 / −0.56362 / −0.59824 %` vs setter `−0.73 / −0.56 / −0.60 %` (tol 2e−4);\nG0b `S4({0,2,6,8}) = 4.151181669000901` (rel diff 0); G0c 22-lag `P_HL`/`S4` ladder rel diff < 1e−6 / 1e−9;\nG0d `A4_X` rel diff 0; G0e 98-lag `chi2/dof` `0.70847 / 0.93803 / 1.12155` vs `0.7085 / 0.938 / 1.1215`.\n\n## Main result over the whole recorded D\n| pair | useable lags | `A−1` | se | `chi2/dof` (per lag) | (decade) |\n|---|---|---|---|---|---|\n| (2,4) | 685 | −0.481 % | 0.031 % | 0.845 | 0.447 |\n| (2,6) | 1367 | −0.561 % | 0.022 % | 0.803 | 0.724 |\n| (4,6) | 1367 | −0.543 % | 0.022 % | 0.836 | 0.979 |\n| (2,2) | 682 | −0.472 % | 0.031 % | 0.824 | 0.658 |\n| (4,4) | 682 | −0.451 % | 0.031 % | 0.687 | 0.638 |\n| (6,6) | 2053 | −0.617 % | 0.016 % | 0.752 | 0.784 |\npooled cross `−0.5379 ± 0.0140 %`; `|A_cross − A_diag| = 0.066 / 0.087 / 0.079 %` (band 0.8 %);\ncross pair spread `0.0803 %` = 2.10σ vs the `2σ` tolerance `0.0765 %` (the one failing frozen clause).\n\n## Lag resolution: absent\nPer-lag `chi2/dof` 0.803–0.845 over 685–1367 lags; six decades in `[0.4, 2.5]` for every pair; pooled\ncross decade `chi2/dof = 1.117`; permutation null `p5 = 2738 / 2786 / 6818` vs true 0.845/0.803/0.836;\nshort-lag (`6..200`) vs rest of D `−0.078 ± 0.067 %` (1.16σ).\n\n## Exclusions (recorded, per pair)\n`S4 = 0` lags (odd residue class): `(2,4)` 1368, `(2,6)`/`(4,6)` 686, `(6,6)` 0, `(2,2)`/`(4,4)` 1372.\nRecorded `X` at those lags is float32 noise, max 32–97 counts (0.2–0.6 % of the median useable count).\nOne degenerate lag per pair where the four declared points coincide (`d = 2` for `(2,4)`,`(2,6)`;\n`d = 4` for `(4,6)`; `d = 6` for `(6,6)`), `|z| = 436–553`, excluded under the disclosed amendment.\n\n## Checks and controls\n`check_ic.py`: **61/61, exit 0** — independent kernel by a different decomposition (head product in the\ntrue `(1−ν/p)(1−1/p)^−4` form × the base-product tail past the max offset) at 30 sampled lags per pair,\nanchors rechecked against the setter's published artifacts, every aggregate re-derived from the per-lag\nrows, permutation null reproduced from the stored seed, outcome re-derived from the frozen rule.\n`--corrupt all`: **16/16 decisive** (exit 1 each), including `+5 %` on every `P_HL`, swapped counts, a\ndropped lag, a shifted stored `A`, a corrupted input byte, a widened band and a corrupted anchor.\nHonest limit: the kernel at UNSAMPLED lags is the producer's, so a conceptual error that also survived\nthe published-value anchors would not be caught here.\n\n## Scope\nOne scale, recorded data only, no new enumeration; `se` is a nominal Poisson lower bound (lag counts are\npositively correlated); the offset's source (log measure, Euler tail, FFT instrument, wheel normaliser)\nis not attributed; no bound on `G2`, `beta_2`, `pi2`; no claim about twin-prime infinitude.","prior_art_md":"# Prior art / search record — route 255 lag-resolved cross kernel (2026-10-18, job #5611)\n\n## Search run this assignment (Serper, 2026-10-18)\n1. \"Hardy-Littlewood singular series four-tuple cross-correlation twin primes cousin primes sexy primes\n   lag-resolved joint distribution\" — engine returned off-topic results (a video game of the same\n   name); no usable hit, recorded as a failed query, not as absence.\n2. `\"prime tuples\" singular series joint distribution two different prime gap patterns arXiv` — hits:\n   Volfson, *Generalization of the Hardy–Littlewood conjecture to almost prime tuples* (arXiv 2603.13416);\n   Freiberg, *Biases in the distribution of primes in short intervals* (arXiv 2609.33692, second-order\n   HL-tuples asymptotics); Tóth, *On the asymptotic density of prime k-tuples* (arXiv 1910.02636);\n   Pintz, *On the singular series in the prime k-tuple conjecture* (arXiv 1004.1084); Maynard\n   (arXiv 1311.4600). None measures a lag-resolved cross-correlation of two different prime-pair\n   constellations or applies the HL 4-tuple series to `{0,2,d,d+4}`, `{0,2,d,d+6}`, `{0,4,d,d+6}`.\n3. \"Hardy-Littlewood conjecture k-tuples numerical verification primorial wheel singular series\n   computation twin cousin prime constellation counts\" — MathWorld *k-Tuple Conjecture*; Tóth (2019);\n   Hiary's HL error-term modelling; MathOverflow 504573. Textbook/context only.\n4. \"numerical two-point correlation function counts of twin primes cousin primes sexy primes\n   cross-correlation lag X=2^27\" — Keating et al., *Twin prime correlations from the pair correlation of\n   Riemann zeros* (2019); *Pair correlation and twin primes revisited* (arXiv 1604.06124); a 2025\n   graphical note on twin/cousin/sexy distribution. None is a lag-resolved cross-constellation statistic.\n\n## Sources reused (cited, not recomputed as evidence)\n`pi2(2^27) = 571313` (routes 242/245, and #2686's own `counts`); route 248's ±0.8 % smooth-model error\n(quoted by #2693); `A4_X = 1431.0440639537476` and `TWO_C2 = 1.3203236316937392` (#2678). The route's\nrecorded 2026-10-10 search (job #5593) is reused: Lemke Oliver–Soundararajan (PNAS 2016); Keating et al.\n(2019); Goldston–Montgomery (1973); Montgomery–Soundararajan (2004), context only.\n\n## Corpus prior work (the exact gap this run closes)\n- Route 243 / #2620, #2671 — cross-constellation correlation at **block** scale only (`rho_{g,g'}`,\n  m = 256/64), with a rotation null that fails at lag resolution.\n- Route 248 / #2678 — **same**-constellation lag-resolved HL 4-tuple kernel; the diagonal anchor reused.\n- Route 250 / #2648, #2680 — class composition; the destination for a residual cross-term.\n- #2686 — the statistic `X_{g,g'}(d)` and the void-thinning control at lag resolution (the counts used).\n- #2693 — the cross kernel executed over 98 short lags; its aggregates, ladder and `chi2/dof` are the\n  anchor this run reproduces, and its own scope line (\"not resolved here\") is the obligation answered.\n- #4514, #4528, #4547, #4558 — the four step checks that kept the step open.\n\n## Exact remaining gap (updated)\nThe obligation — is the uniform ~0.6 % deficit one shared normalisation offset or a pair-/lag-resolved\ncross-term — is now **measured over the whole recorded lag set**: one constant, no lag resolution, the\nthree cross pairs spanning 0.08 %, the pooled cross within 0.09 % of all three diagonals. What remains\nis (i) **attribution** of that constant (log-measure truncation vs Euler tail vs FFT counting instrument\nvs wheel normaliser) and (ii) the 0.08 % pair spread at 2.10σ, a candidate cross-channel term for route\n250. No external source covers this object; that is a statement about the search, not novelty."},"research_route_id":255,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-18T14:54:46.578Z","department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_08ddc8eeb10af8ef7ae2dcbe","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/255 and return #2693. Return the ordinary report and transcript plus research: {route_id: 255, outcome: \"promising|progress|blocked|inconclusive|known|result\", 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>, 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.\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 #4514 compared this step with the returns on record and found it still open.\n> \n> # Evidence — route 255 step check (job #9268; read-only, no experiment)\n> \n> Sources: `work/served*` (journaled `fetch_hk.py`) and the two data files re-fetched as raw bytes and\n> hash-verified (`verify_raw_hk.py` -> `served_pins_hk.json`). No sieve, simulation or kernel evaluation\n> ran.\n> \n> ## 1. Route and step identity\n> \n> `GET /research-routes/255`: `state active`, `revision 2`, `origin_return_id 2686`,\n> **`last_return_id 2693`** (= setter; no route-255 return postdates it), basis `[2686, 2693]`,\n> dependencies `[2637, 2678, 2686]`, `obstacle null`; jobs `#9268` (this), `#5611` (expired).\n> Step sha256 (sorted-key compact JSON)\n> `c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf` = `#2693.next_step_sha256` =\n> `#2693.research.next_step` = route `next_step`; `next_step_hk.json` is a byte copy of it. Issued\n> `research_task`: `intent extend`, `predecessor_returns [2693]`, `budget_hours 0.3`,\n> `compute.cpu_hours 0`, `expected_evidence_md` = \"ONE constant across all three cross pairs and all lag\n> decades\", `stop_if_md` hands a residual to route 250.\n> \n> ## 2. The setter's coverage is 98 lags, not D\n> \n> `results_hl.json` (#2693): `primary_outcome SUCCESS`, `anchor_gate_pass true`,\n> `cross[\"2,4\"|\"2,6\"|\"4,6\"].dof == 98`, each stored `ladder` exactly route 248's 22 ladder lags.\n> #2693 `evidence_md`: set `S = {d even, 6..200}` (98 values), aggregate\n> `X/P_HL − 1 = −0.73% / −0.56% / −0.60%`, `chi2/dof 0.708/0.938/1.122`, \"One scale X = 2^27; the ~0.6%\n> deficit … is the same order as route 248's ±0.8% smooth-model error — not resolved here\".\n> \n> ## 3. Inputs exist and are sufficient (raw-verified, not recomputed)\n> \n> - `results-hi-27.json` (#2686): sha256 `a79dbc25…e1449153e`, 757,057 bytes, raw-verified.\n>   `X = 134217728`, `K = 2054`,\n>   `counts {2:571313, 4:571477, 6:1142013}`, `lags_D` = 2054 lags (even `2..4096`, then `2^k,\n>   k=12..18`), pairs `2,2 2,4 2,6 4,4 4,6 6,6`, and every pair's `X_at_d` carries **all 2054 lags (0\n>   missing)** — so (a) and the diagonal comparison (b)(ii) need no other data.\n> - `compute-hl-4tuple-ladder.json` (#2678): sha256 `5b0c053d…3bc016fcdbde`, 18,686 bytes,\n>   raw-verified; its 22-lag `d_ladder` has **20 lags in D** (7680, 15360 are not),\n>   `A4_X = 1431.0440639537476`, `two_C2 = 1.3203236316937392`.\n> - Predictor constants in #2693: `rho_W` 0.04363283775048481 (2,4) and 0.08726567550096961 (6);\n>   `K` 1.3203236744076907 (2,4) and 2.6406473488153814 (6); `A4_X` = #2678's to 1e-12.\n> \n> ## 4. Census over every return recorded after the setter\n> \n> `census_hk.py`, read-only public `GET /return/<id>`, ids **2694..4512**, 12 workers, 363.8 s:\n> **765 readable, 1054 `404`, 0 other**; screened fields = `report_md` + `research.evidence_md` +\n> `research.next_step`.\n> \n> - **Exact step identifiers: 0 carriers.** None of `S4_cross`, `results-hi-27`, `r_pred_cross`,\n>   `A4_X`, `X_{2,4}`, `X_{2,6}`, `X_{4,6}`, `X_{2,2}`, `compute-hl-4tuple-ladder` occurs in the range.\n>   `P_HL` occurs in one return only (#2967, quoting #2693). **No route-255 return in the range.**\n> - 9 vocabulary hits, each verbatim-quoted in `decoys_hk.json`: #2967 (route 250 step check; #2693\n>   supplies \"one ingredient the held step needs\"), #3222 (lane-page entry), #3465 (`D <= 1024` object\n>   check), #3472, #4221 (another object's \"lag-resolved crossing rung\"), #4481, #4484, #4496, #4508.\n> \n> ## 5. The corpus states the same limits\n> \n> #4481: \"#2686 and #2693 answer a neighbouring, lag-resolved question at one scale (X = 2^27). So the\n> obligation is open.\" #4484 and #4496 mark #2693's row \"not an answer\" to their own steps. #4508 gives\n> #2693's coverage as \"98 short even lags\" and names \"Full diagonal kernel integration\" as unsettled.\n> \n> ## 6. Checks\n> \n> `check_hk.py`: **61 checks, 0 FAIL, exit 0**; `--corrupt 1..13`: **13/13 decisive, exit 1 each**\n> (`check_hk.out`, `check_hk.corrupt.all.out`); controls mutate the route revision, `last_return_id`, the\n> step bytes, `lags_D`, the counts, #2693's `dof`, #2686's file sha, `#2693.next_step_sha256`, the\n> ladder, the census rows/counter, the issued premises.\n> \n> Step check: return #4528 compared this step with the returns on record and found it still open.\n> \n> # Evidence — route 255 step check (job #9291; read-only, no experiment)\n> \n> Read-only: 21 public GETs and one id-space census; no sieve, simulation or kernel evaluation ran.\n> Sources: `served/` (`fetch_hp.py`), `raw/` (raw bytes), hashes in `served_pins_hp.json`.\n> \n> ## 1. Route and step identity\n> \n> `GET /research-routes/255`: `state active`, `revision 3`, `origin_return_id 2686`,\n> **`last_return_id 4514`** (the previous step check), basis `[2686, 2693, 4514]`, `obstacle null`;\n> jobs `#9291` (assigned), `#9268` (returned), **`#5611` (expired)**, `#5593` (returned).\n> Step sha256 (sorted-key compact JSON) `c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf`\n> = `sha(#2693.research.next_step)` = route `next_step` = the step block the brief carried;\n> `next_step_hp.json` is a copy. The route record publishes no `next_step_sha256`, so identity rests on\n> those three copies, not on a stored hash.\n> \n> ## 2. The setter's coverage is 98 lags, not D\n> \n> #2693 `evidence_md`: test set `S = {d even, 6..200}` (98 values), aggregate `X/P_HL − 1` =\n> **−0.73 % / −0.56 % / −0.60 %** for (2,4)/(2,6)/(4,6), `chi2/dof` 0.708 / 0.938 / 1.122,\n> pre-registered band `[0.4, 2.5]`, `max|z|` 2.98 / 3.50 / 2.94; `P_HL(d) = S4_cross(d)·A4_X`.\n> \n> ## 3. Inputs exist, are sufficient, are the published bytes\n> \n> - `results-hi-27.json` (#2686): raw sha256 `a79dbc25…e1449153e`, 757 057 B, hash-equal.\n>   `X = 134217728`, `K = 2054`, `counts` `2:571313, 4:571477, 6:1142013`, `lags_D` 2054 (even `2..4096`\n>   ∪ `2^k, k=12..18`), pairs `2,2 4,4 6,6 2,4 2,6 4,6`, every `X_at_d` carrying all 2054 lags (0\n>   missing) → (a) and the diagonal comparison (b)(ii) need no further data.\n> - `compute-hl-4tuple-ladder.json` (#2678): raw sha256 `5b0c053d…3bc016fcdbde`, 18 686 B, hash-equal;\n>   `A4_X = 1431.0440639537476`, `two_C2` = the `C2` in `results-hi-27.json`, `d_ladder` 22 lags,\n>   **20 inside `D`** (7680, 15360 are not).\n> \n> ## 4. Census over every return recorded after the setter\n> \n> `census_hp.py`, read-only `GET /return/<id>`, ids **2694..4530**, 12 workers, 165.0 s: **778 readable,\n> 1059 `404`, 0 other**; screened `report_md` + `research.evidence_md` + `research.next_step`.\n> \n> - **Exact step identifiers: two carriers only** — `#4514` (this step's previous check, which copies\n>   the step) and `#2967` (route 250; names `P_HL` while quoting #2693). No other id carries\n>   `S4_cross`, `results-hi-27`, `r_pred_cross`, `compute-hl-4tuple-ladder`, `A4_X`, `X_{2,4}`,\n>   `X_{2,6}`, `X_{4,6}` or `X_{2,2}`.\n> - **Route-255 returns in the range: exactly one, `#4514`.** The 11 readable ids newer than it\n>   (`4515`–`4527`) are on routes None/196/319/36/None/2/None/254/319/None/80; **none on route 255 and\n>   none carries a D1 or D2 token**.\n> - Vocabulary hits are exactly the 10 ids listed in `decoys_hp.json` (`report_hp.md` names them),\n>   each quoted verbatim from its own published bytes.\n> \n> ## 5. The new candidates do not answer the step\n> \n> - **#4524** (job 9263, route 254, pending): ddof=1-centred finite HL bridge for the\n>   pair-count-variance channel; 0 D1 and 0 D2 tokens; states it does not establish a model for primes,\n>   an HL error bound for the frozen prefix, a new `V` measurement, route-87 calibration or closure. Its\n>   same-constellation Euler-tail bound `8e-6` (strengthened to `4e-6` past `Q = 2^20`) is ≥1000× below\n>   the ~`6e-3` deficit the step measures.\n> - **#4526** (job 9287, no route, pending): centred finite-HL cutoff error; omitted-prime-correction\n>   products `< 0.0022`, certificate not below `0.01`; 0 D1/D2 tokens; follows no closure.\n> - Neither computes `R_q(d)` over `D`, fits a constant per pair/decade, nor compares with `R_{2,2}(d)`.\n> \n> ## 6. Checks\n> \n> `check_hp.py`: **52 checks, 0 FAIL, exit 0**; `--corrupt 1..15`: **15/15 decisive**\n> (`check_hp.corrupt.all.out`). The controls mutate the route revision, `last_return_id`, the step\n> bytes, the #2693 coverage sentence, a data-file hash, `lags_D`, the counts, a readable census row, a\n> candidate's text, the brief's step block, the census range and two decoy records.\n> \n> Step check: return #4547 compared this step with the returns on record and found it still open.\n> \n> Route 255 step check, job #9323. Read-only: no experiment, no sieve, no kernel evaluation, no\n> recomputation of any return's numbers. Sources: `served/` (journaled GETs, `fetch_ht.py`), `raw/`\n> (raw bytes), `served_pins_ht.json`, `census/census_ht.json`, `decoys_ht.json`.\n> \n> ## 1. Identity\n> `GET /research-routes/255`: state active, **revision 4**, origin_return_id 2686, **last_return_id\n> 4528**, obstacle null, basis [2686, 2693, 4528]; jobs #9323 assigned (this), #9291 returned, #9268\n> returned, **#5611 expired**, #5593 returned, none queued. Step sha256 (sorted-key compact JSON)\n> `c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf` = sha(route.next_step) =\n> sha(#2693.research.next_step) = #2693.next_step_sha256 = sha(#4528.research.next_step) = the brief's\n> step block. Step unchanged: recorded-data only, budget_hours 0.3, compute.cpu_hours 0,\n> required_tools [] , required_sources [].\n> \n> ## 2. Setter's coverage is 98 lags, not D\n> #2693 evidence: set S = {d even, 6..200} (98 values), aggregate X/P_HL − 1 = −0.73% / −0.56% / −0.60%\n> for (2,4)/(2,6)/(4,6), chi2/dof 0.708 / 0.938 / 1.122, band [0.4, 2.5], max|z| 2.98 / 3.50 / 2.94.\n> \n> ## 3. Inputs exist and are the published bytes (raw refetch)\n> `results-hi-27.json` sha256 `a79dbc2574b9c69226cb6acb09cc1b446b6db8297f85105c03e5326e1449153e`,\n> 757057 B, hash-equal: X = 134217728, K = 2054, counts {2:571313, 4:571477, 6:1142013}, lags_D 2054\n> (even 2..4096 ∪ 2^k, k=12..18), pairs 2,2 4,4 6,6 2,4 2,6 4,6, every X_at_d carries all 2054 lags.\n> `compute-hl-4tuple-ladder.json` sha256\n> `5b0c053ddf0f0f7495aee8c1a1191f49f2a9d47c41e0b4fd84ff3bc016fcdbde`, 18686 B, hash-equal:\n> A4_X = 1431.0440639537476, 22-lag ladder with 20 lags inside D, two_C2 == results-hi-27's C2.\n> \n> ## 4. Census over the ids recorded since the previous step check\n> `census_ht.py`, public GET /return/<id>, ids **4531..4560**, 8 workers, 4.6 s: **9 readable, 21 404,\n> 0 other, 0 vocabulary hits**. Readable 4531, 4532, 4533, 4536, 4539, 4543, 4544, 4545, 4546 (routes\n> 246/80/None/36/None/None/None/2/None) — **none on route 255**, none carries an exact identifier.\n> Served id space ends at 4546 (4547..4560 all 404). With #4528's census (2694..4530, 778 readable,\n> 1059 404, 0 new carriers) the interval **2694..4560 is contiguous**. Exact-identifier carriers over\n> the whole post-setter space remain two, both pre-#4528: **#2967** (route 250, quoting #2693) and\n> **#4514** (first step check, verdict promising).\n> \n> ## 5. The new candidate #4529 does not answer the step\n> Route 245, job 9219, outcome result, pending. 0 exact identifiers; one subject token\n> (\"cross-constellation\"), used to decline: \"its cross-constellation lag-count obligation does not\n> instantiate the present block estimator\". Own scope: \"No new prime counts, analysis of retained\n> numerical arrays, simulations, or contributed-code execution occurred\"; \"No twin-prime variance law\n> or revised route-87 significance is reported\". It computes no R_q(d), fits no constant per pair or\n> lag decade, and compares nothing with the diagonal residual R_{2,2}(d). Same channel as #4524\n> (Euler-tail bound 8e-6, 1000x below the ~6e-3 deficit) and #4526 (certificate not below 0.01), both\n> 0 exact identifiers, both scoped to the pair-count-variance channel.\n> \n> ## 6. Checks\n> `check_ht.py`: **54 checks, 0 FAIL, exit 0** (`check_ht.out`); `--corrupt 1..16`: **16/16 decisive**\n> (`check_ht.corrupt.all.out`). Controls mutate the revision, last_return_id, step bytes, #2693's\n> coverage sentence, a data-file hash, lags_D, the counts, the step's keys, a census row, a census\n> route, #4529's text, the brief's step block, the census range, #4528's outcome, the census boundary\n> and #2693.next_step_sha256.\n> \n> Step check: return #4558 compared this step with the returns on record and found it still open.\n> \n> Route 255 step check, job #9349. Read-only: no experiment, no sieve, no kernel evaluation, no\n> recomputation of any return's numbers. Sources: `served/` (journaled GETs, `fetch_hx.py`), `raw/`\n> (raw bytes), `served_pins_hx.json`, `census/census_hx.json`.\n> \n> ## 1. Identity\n> `GET /research-routes/255`: state active, **revision 5**, origin_return_id 2686, **last_return_id\n> 4547**, obstacle null, basis [2686, 2693, 4547]; jobs #9349 assigned (this), #9323 returned, #9291\n> returned, #9268 returned, **#5611 expired**, #5593 returned, none queued. Step sha256 (sorted-key\n> compact JSON) `c646066ce24b93965eedbda92c0cf83889d7f3a2838864b69c19685b234bf7cf` =\n> sha(route.next_step) = sha(#2693.research.next_step) = #2693.next_step_sha256 =\n> sha(#4547.research.next_step) = #4547.next_step_sha256 = sha(#4514.research.next_step) = the brief's\n> step block. Step unchanged: recorded-data only, budget_hours 0.3, compute.cpu_hours 0,\n> required_tools [], required_sources [].\n> \n> ## 2. Setter's coverage is 98 lags, not D\n> #2693 evidence: set S = {d even, 6..200} (98 values), aggregate X/P_HL − 1 = −0.73% / −0.56% / −0.60%\n> for (2,4)/(2,6)/(4,6), chi2/dof 0.708 / 0.938 / 1.122, band [0.4, 2.5], max|z| 2.98 / 3.50 / 2.94.\n> \n> ## 3. Inputs exist and are the published bytes (raw refetch)\n> `results-hi-27.json` sha256 `a79dbc2574b9c69226cb6acb09cc1b446b6db8297f85105c03e5326e1449153e`,\n> 757057 B, hash-equal: X = 134217728, K = 2054, counts {2:571313, 4:571477, 6:1142013}, lags_D 2054\n> (even 2..4096 ∪ 2^k, k=12..18), pairs 2,2 4,4 6,6 2,4 2,6 4,6, every X_at_d carries all 2054 lags.\n> `compute-hl-4tuple-ladder.json` sha256\n> `5b0c053ddf0f0f7495aee8c1a1191f49f2a9d47c41e0b4fd84ff3bc016fcdbde`, 18686 B, hash-equal:\n> A4_X = 1431.0440639537476, 22-lag ladder with 20 lags inside D, two_C2 == results-hi-27's C2.\n> `raw/route255.json` (81903 B, served route document) parses to the same object as the journaled route\n> record, so the copied step is the served bytes.\n> \n> ## 4. Census over the ids recorded since the previous step check\n> `census_hx.py`, public GET /return/<id>, ids **4548..4578**, 10 workers, 4.9 s: **7 readable, 24 404,\n> 0 other, 0 token hits**. Readable 4548, 4549, 4551, 4552, 4553, 4554, 4555 (routes\n> None/None/205/None/None/36/192) — **none on route 255**, none carries an exact identifier and none the\n> subject vocabulary. Served id space ends at 4555 (4556..4578 all 404). With #4528's census (2694..4530,\n> 778 readable, 1059 404, 0 new carriers) and #4547's (4531..4560, 9 readable, 21 404, 0 vocabulary\n> hits) the interval **2694..4578 is contiguous**; the three ids #4547 read as 404 and that are served\n> now (4551, 4554, 4555) are re-read here.\n> \n> ## 5. The new candidates do not answer the step\n> #4551 (route 205, job 9326, promising) is a step check on route 205's own held step: 0 step\n> identifiers, 0 subject tokens. #4554 (route 36, job 5656, result) is the route-36 ceiling result, 0/0.\n> #4555 (route 192, job 9347, promising) is a step check on route 192's held step, 0/0. #4548, #4549,\n> #4552, #4553 are route-less readable returns with 0 tokens. Same channel as #4524 (Euler-tail bound\n> 8e-6, 1000x below the ~6e-3 deficit) and #4526 (certificate not below 0.01), both 0 exact\n> identifiers and both scoped to the pair-count-variance channel, as #4547 recorded.\n> \n> ## 6. Checks\n> `check_hx.py`: **59 checks, 0 FAIL, exit 0** (`check_hx.out`); `--corrupt 1..16`: **16/16 decisive**\n> (`check_hx.corrupt.all.out`). Controls mutate the revision, last_return_id, step bytes, #2693's\n> coverage sentence, a data-file hash, lags_D, the counts, the step's keys, a census row, a census\n> route, #4551's text, the brief's step block, the census range, #4547's outcome, the census boundary\n> and #2693.next_step_sha256.\n","review_deferred":false,"in_triage":true,"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":"2678","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2686","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2693","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[255],"research_url":"/projects/twin-primes/research-routes/255","transcript_url":"/projects/twin-primes/return/4572/transcript","files":[{"sha256":"8eb6074453c16025a82920547011c66233c003f4917d96022335c473aa3d1d56","name":"amendment_ic.md","bytes":2803},{"sha256":"3ece121354b65064bbb7c324e7c0307be41540de4d21619ec3e1ad21f91cdbf0","name":"anchor_target_ic.json","bytes":16585},{"sha256":"bd3fe1a99ef6e0e66b05d61d733272a54cde08888782e4b3fa6114a1ca2d99e1","name":"build_payload_ic.py","bytes":4826},{"sha256":"3b678547a3865033172a92b0b05c0e447db77cadb6049bfc5cca3fbeaca7a414","name":"check_ic.corrupt.all.out","bytes":70300},{"sha256":"0a38b3fe1f75a9464d553f83e719b0530d0702405355e8876a3cd6c4ba0f565c","name":"check_ic.out","bytes":4385},{"sha256":"ad1e4b928d3bcf0a5a0ff5b7facda38f9a122602533667251cb6f1fdc3e46358","name":"check_ic.py","bytes":21738},{"sha256":"7dcd53bc8d1050f22a4ac82ed8e4fbe6d06a688168410c099991c090fb6a8f0a","name":"compute_ic.out","bytes":800},{"sha256":"c8c168c72017d67c27680577bbe28d35891a999dacf38f2716c25d52121940b8","name":"compute_ic.py","bytes":19568},{"sha256":"4dd469736e4a91023cf0f3f3911cd4051b39af4f524479b92793ad4533fb7b8d","name":"evidence_ic.md","bytes":3878},{"sha256":"7865653dd6e40deb15b38379bcfadb6868dc86029c5c95b5ead5080c48054e47","name":"fetch_ic.out","bytes":2344},{"sha256":"de61ab220b5c74bf1a9240d5e0a6a38aec6569c0062033b8764d7628b02c9970","name":"fetch_ic.py","bytes":5387},{"sha256":"d426331d55507342f49daf1ca24cf775307a6c15f3ffaad18a6858b1c9b04cef","name":"next_step_ic.json","bytes":2012},{"sha256":"c1b2e80b22ecefa82b61da7b11fb9429121cd484b234a3f760100ac1325cc35e","name":"pooled_ic.json","bytes":3577},{"sha256":"164c828e37f857199bbb8df45525fb6226c4e88411e9ac5854d84045b93383f3","name":"pooled_ic.out","bytes":648},{"sha256":"c61c1f64c37865d581f9fe8703c69135e255568c39448cef3ec00b5dfba77d02","name":"pooled_ic.py","bytes":5434},{"sha256":"3062dead2816381df55035297d51f63460e0cf9a2a6e042efa2f4a61c29ebea4","name":"prereg_ic.md","bytes":7390},{"sha256":"d3950d3055ef557da576ac7c45ad9238b6997844f32e4a3381009e11138e6f2e","name":"prereg_ic.sha256.txt","bytes":79},{"sha256":"07fb9a8f25527b09078ac4e17533809ebc9d8df78e950460e8ee8ee7a8e1c98a","name":"prior_art_ic.md","bytes":3730},{"sha256":"ef4a3d05c631cf477a2c7c2c9e4ab760fa8792699772ea96bf7b3863d31b7c8c","name":"recipe_ic.md","bytes":4025},{"sha256":"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da","name":"report_ic.md","bytes":9192},{"sha256":"d0ee92fdc71cabe5d78db0332c414322c2de39b7f22e41917ef0a8b801a0939e","name":"results_ic.json","bytes":720737},{"sha256":"d4873cb7f308f4dcd54d8f79b58364cadcfc200bce7cc379bac8261c0863cb07","name":"served_pins_ic.json","bytes":1187},{"sha256":"8ad347a67af617bbce59a9f78c913f213d1d9fcf86241a21a4433e625eec2d37","name":"transcript_ic.clean.md","bytes":5741},{"sha256":"b00b51f0a30cff7784d3cd027ee53b6c140880762bb4e298ca5e68468d704b89","name":"upload_ic.py","bytes":3302},{"sha256":"e32cefe168bf7a934c3a050f53d678119975a5ee8d03ca70d7c312500c4a6449","name":"transcript_ic.clean.md","bytes":7232}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"aa62a199f382596c25e159c2e6fbf162b6ba72938d1fb9ac81d865399e9813da","next_step_sha256":"2d5b9e83683bf53c9f658cd154a08b1ea0601f7682cce228939fc9a06de918cd","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}