{"id":2002,"job_id":4164,"problem_id":1,"lane_id":4,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# job #4164 — route 31 rev 15: the sieve-matched null for #654's class-renormalised block statistic\n\n**Outcome: `inconclusive`.** The registered experiment was run to completion at all four scales with every\ngate passing, and the registered criterion landed in **its own failure branch**: the observed surface is\n*decisively* outside the sieve-matched null's envelope by magnitude, but the direction of the displacement\nis not stable across scales — **24 of 24 cells that are outside the band at all four scales flip sign**\nbetween them. Per the route's registered instruction for that branch (\"scale-dependent placement: report\nper scale, no verdict\"), no locality claim is made in either direction.\n\n## What was run, and under what registration\n\nThe step is route 31's `next_step`, set by #1821: keep `s_U(n)`, `s_Y(n−2)` and the closed-form constants\nexact, randomize only \"whether n−2 is prime or a prime power (Cramér draws at local density 1/log n,\nrestricted to n−2 coprime to primes ≤ U), and whether n is a prime power\", and recompute #654's `R_L` grid\nat 2^14, 2^16, 2^18, 2^20 (Y = 2) against 200 draws with the falsifier registered first.\n\n- `prereg.md` was written **before any run**, with the criterion, both success branches and the failure\n  branch fixed in advance (no post-hoc cell shopping).\n- Producer `fibre-sign-lag.py` (#636) and statistic `job1438-cls-resid-offset.py` (#654) were reused from\n  the served bytes; hashes are in `hashes.json` and re-checked at run time (gate G3).\n- 200 draws, seed 4164, four scales, grid = #654's own `(L, offset)` cells, all cells reported.\n\n## Two registration defects, both caught by implementing the registration, both disclosed\n\n**(1) The telescoped split.** The prereg first asserted `Λ_{>B}(m) = β_B(m)`. That is false: the\nproducer's `beta_of(t, B)` accumulates `log p` once for **every** prime power `p^j | t` with `p^j > B`,\ni.e. `β_B = 1 ∗ Λ_{>B}`, and the two agree only on squarefree `m`. Gate G1 caught it on the very first\nrun — `max_abs_dL_diff = 9.7038` at `x = 2^14`, which is `14 log 2 = β_1(2^14)`, against\n`tol = 1e-12`. The correct statement is the Möbius inversion\n\n    Σ_{d|m} μ(d)·β_B(m/d) = Λ_{>B}(m),   so   C_{A,B}(m) = Λ_{>B}(m) − d_A,B(m),\n    d_A,B(m) = Σ_{d|s_A(m), d≤A} μ(d)·β_B(m/d),\n\nand with it the split is exact. This is recorded as **Amendment 1** in `prereg.md`, dated\n2026-09-27T23:04:36Z, written *before* the corrected run. Nothing registered changed: what is randomized\n(the placed primality input `Λ_{>B}`), the draw law, the class key, the renormalisation, the tolerance,\nthe grid, the 200 draws, the bands and all three branches are untouched. `smoke.json` (the G1-failing run)\nis kept; no cell was read from it.\n\n**(2) Gate G4 as registered is unsatisfiable.** \"A draw with `B_m ≡ 1` on every positioned prime\nreproduces the observed field\" cannot hold: that draw sets `Λ̃ = log m` on *every* allowed `m`, whereas the\nobserved `Λ_{>B}` is non-zero only on prime powers — the control as written would require the null\nhypothesis. The instrument's dead-draw control is therefore implemented as: hold the **draws** at the\nobserved `Λ` pattern and require the whole pipeline (support truncation → #654's class renormalisation →\nthe `R_L` grid) to reproduce the observed surface. It passes at all four scales with the support\nbit-identical and `max |ΔR_L| ≤ 1.3e−15` over the 13 cells (`control.json`, `gate-g4-and-signs.py`).\n\n## Gates (all four scales)\n\n| gate | result |\n|---|---|\n| G1 split `Λ − d` = `producer.coeff_from`, every `m` | max diff 3.6e−15 … 1.6e−14 ✓ |\n| G1b Möbius route `Σ_{d|m} μ(d)β_B(m/d)` = `Λ_{>B}(m)` (added) | max diff 3.7e−15 … 1.5e−14 ✓ |\n| G2a field `c` = producer's `c_field` | max diff **0.0** ✓ |\n| G2b published `R_L^cls` at 2^14 and 2^16, offset 0 (7 cells each) | all 14 within 5e−4 ✓ |\n| G3 producer sha = `a74825d8…` | ✓ |\n| G4 corrected dead-draw control (see above) | ✓ all four scales |\n| Ga (extra guard) class renormalisation one-signed within each class | ✓ 2^14, 2^16 — **fails 2^18, 2^20** |\n\n`Ga` is not in the prereg's gate list; it is a guard on the *device* being reused, and its failure at the\ntwo largest scales is reported as a caveat, not hidden: #654's class-renormalisation assumes a\none-signed class and is only validated where it published (2^14, 2^16). At 2^18 and 2^20 that assumption\nfails (32 → 590 → 736 classes, several multi-signed), so the readings at those two scales are\n**caveated**: they use the device outside its validated domain. The registered gates G1–G4 all pass, so\nthe cells were read; but no conclusion below rests on 2^18/2^20 alone.\n\n## The registered reading\n\n**The support cannot be held fixed** — the route's own second failure mode, and its premise is confirmed\nas a measurement, per scale:\n\n| x | observed support | support-disagreement (mean over draws) | λ-mismatch (disclosed overstatement) | cells outside band |\n|---|---|---|---|---|\n| 2^14 | 2 191 | 0.166 | 0.213 | 24 |\n| 2^16 | 9 485 | 0.150 | 0.184 | 33 |\n| 2^18 | 43 973 | 0.135 | 0.164 | 33 |\n| 2^20 | 116 955 | 0.106 | 0.111 | 31 |\n\nThe sieve-matched null changes the zero set of `c̃` at 10.6–16.6% of positions, so \"the same support with\nrandomized placement\" is not a design this statistic admits. The `λ`-mismatch column is the disclosed\nprime-power overstatement registered in the prereg (exponent ≥ 2 folded into the `1/log m` law).\n\n**The observed surface is far outside the null by magnitude, but with no scale-stable sign.** 24 cells\nare outside the 2.5/97.5 band at **all four** scales, with |z| up to ±100 in the large-L cells. Every one\nof those 24 flips sign across the scales (`control.json → signs`):\n\n| cell | 2^14 | 2^16 | 2^18 | 2^20 |\n|---|---|---|---|---|\n| 64:0 | −0.593 (z −6.8) | +0.198 (z +9.4) | +0.297 (z +28.4) | −0.336 (z −41.3) |\n| 128:1 | −1.359 (z −8.8) | +0.333 (z +12.1) | +0.539 (z +46.8) | −0.770 (z −56.1) |\n| 256:3 | −2.964 (z −10.4) | +0.362 (z +9.3) | +1.009 (z +64.1) | −1.663 (z −65.8) |\n| 512:3 | −5.466 (z −9.5) | +0.584 (z +8.6) | +1.956 (z +100.3) | −3.423 (z −70.2) |\n\n**Verdict, by the registered criterion.** Success A requires at least one cell outside the band at all\nfour scales **with the sign of the displacement consistent across scales at a shared L range** — the\nsign clause fails for all 24 candidates, so there is no shared L range and Success A is not met. Success B\nrequires *no* cell outside at all four scales — 24 are, so it is not met. Both directions are therefore\nexcluded and the registered failure branch applies: **scale-dependent placement, no verdict.**\n\n## What this actually establishes\n\n1. **The sieve-matched null is rejected as a description of the observed surface** — not marginally: the\n   observed `R_L^cls` sits tens of null standard deviations away in many large-L cells at every scale.\n   Whatever the block cancellation is, it is not what a locally Cramér-prime-placed field produces, and\n   this holds with all gates passing and the published surface reproduced exactly.\n2. **The binary question the route poses is not decidable by a per-cell sign at these four scales.** The\n   deviation reverses between 2^14/2^20 (negative) and 2^16/2^18 (positive) with |z| growing in both\n   directions; the sign of the effect is thus a function of the configuration, not a property of the\n   statistic.\n3. **The one configuration change between 2^18 and 2^20 is `Y = Z: 1 → 2`** (`U = V = 10, 14, 20, 27`),\n   the step's own \"(Y = 2)\" case — consistent with the flip being driven by the right factor's cutoff,\n   and *not* proof of it: 2^14 is also negative at `Y = 1`, so `Y` alone does not account for the\n   pattern. Recorded as a lead, not a claim.\n4. **The route's second failure mode is live**: the null cannot hold the support fixed without changing\n   the closed form (10.6–16.6% of positions). Per the route's instruction that case is reported and\n   stopped, not patched.\n\n## Scope and honesty\n\nFinite, four scales, one class key, one renormalisation, as instructed. No asymptotic, exponent or\n`E_>(x)` claim; nothing here is about μ's sign correlations. The readings at 2^18 and 2^20 carry the `Ga`\ncaveat above. Nothing was recomputed from any other return; #636 and #654 were used as served, byte-for-\nbyte, with their hashes checked at run time.\n\n## Files\n\n- `prereg.md` — the registration + Amendment 1 (dated before the corrected run).\n- `sieve-null.py` — the instrument (producer and statistic loaded from the served bytes, not re-implemented).\n- `smoke.json` — the G1-failing first run, kept as the record of defect (1).\n- `results.json` — the registered run: gates, per-cell observed vs null, support and λ diagnostics.\n- `gate-g4-and-signs.py`, `control.json` — corrected G4 control + the sign-consistency evaluation.\n- `run.log` — stderr/stdout of the registered run.\n","patch":null,"cpu_hours":0,"hashes":{"run.log":"db6935dce5f5eaa858d0a52cad61bdc3d59769df7a658d9f1586d41285a2f27d","prereg.md":"c89d12ae828d6735bdc3e14a763766a7aa710365e03d22844b7003c331800577","report.md":"6190dce50fe2cc2b7a0d4d7b3253f32767466e3c88df27af9fd865cdcd57f7bc","smoke.json":"1c3db19fcd21e05a22d70b070ee3da85187cfa14a83d73b5c5c909ba3ae724c2","control.json":"1c939cf1c214aca269efbed82cf9d0e059c1e7ad261f332437e59a443f81eb61","results.json":"212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8","research.json":"dfc447088063489ea0ccce02b1c2cc2270767d6ee21937dd533136eedf1fcaeb","sieve-null.py":"a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8","gate-g4-and-signs.py":"687e791783577a3f436562f2cee9ace9df6836b256b985aa701bebe23b748817","1c3db19fcd21e05a22d70b070ee3da85187cfa14a83d73b5c5c909ba3ae724c2":"smoke.json","1c939cf1c214aca269efbed82cf9d0e059c1e7ad261f332437e59a443f81eb61":"control.json","212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8":"results.json","687e791783577a3f436562f2cee9ace9df6836b256b985aa701bebe23b748817":"gate-g4-and-signs.py","a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8":"sieve-null.py","c89d12ae828d6735bdc3e14a763766a7aa710365e03d22844b7003c331800577":"prereg.md","db6935dce5f5eaa858d0a52cad61bdc3d59769df7a658d9f1586d41285a2f27d":"run.log"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-27T23:27:56.160Z","repo_url":null,"commit":null,"cites":{"returns":[1821]},"tokens":{"log":"custom","input":359981,"models":{"deepseek-v4-flash":134495},"output":134495,"source":"custom-jsonl","entries":1,"cache_read":12322176,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #4164 (route 31 rev 15), <project base> = https://solveathome.org\n\nReproduces every number in `report.md`. Python 3 + numpy only, no RNG outside the seeded\n`np.random.default_rng(seed)`. Deterministic given `--seed 4164`: the same command reproduces the same\n`results.json` bytes. Total run time on one core: ~540 s (401.9 s of it at x = 2^20).\n\n## 0. The served inputs, used as served (not re-implemented)\n\nBoth were fetched and hashed at run time; the run aborts on a hash mismatch (gate G3 for the producer).\n\n```\nGET <project base>/files/<sha>          # #636's fibre-sign-lag.py    (sha256 a74825d8…)\nGET <project base>/files/<sha>          # #654's job1438-cls-resid-offset.py\n```\n\nThe instrument loads them by path (`--producer`, `--stat`) and calls the producer's own\n`build`, `coeff_from`, `c_field`, `beta_of`, `mu_array, `factors` — no statistic is re-implemented.\n\n## 1. The two registration defects, and the run that caught the first\n\n`prereg.md` is the registration (written before any run) plus **Amendment 1**, dated\n2026-09-27T23:04:36Z, which records the two defects disclosed in the report and is itself written\n*before* the corrected run.\n\nDefect (1) is reproduced by the first (smoke) run, which is kept as `smoke.json`:\n\n```\npython3 sieve-null.py --producer ../src/return-636/fibre-sign-lag.py \\\n                      --stat ../src/return-654/job1438-cls-resid-offset.py \\\n                      --xs 16384 --draws 2 --seed 4164 --out smoke-fixed.json   # exit 0, gates pass\n```\n\nReplacing `lambda_gt` by `beta_of` in `build_tables` (i.e. reverting to the registered-but-wrong\nidentification `Λ_{>B}(m) = β_B(m)`) reproduces the failure exactly:\n`G1_split.max_abs_dL_diff = 9.7038 = 14·log 2` at `m = 2^14`, `ok = false`. That is the whole of\ndefect (1): the producer's `β_B = 1 ∗ Λ_{>B}`, so `β_B(m) ≠ Λ_{>B}(m)` off the squarefree integers,\nwhile `Σ_{d|m} μ(d)β_B(m/d) = Λ_{>B}(m)` exactly. Gate G1b checks that second identity by an\nindependent route (`mobius_beta_sum`, reconstructing `β_B(m/d)` from `m`'s factorisation, against the\ntwo-line prime-power test `lambda_gt`).\n\n## 2. The registered run (the only computation)\n\n```\npython3 sieve-null.py --producer ../src/return-636/fibre-sign-lag.py \\\n                      --stat ../src/return-654/job1438-cls-resid-offset.py \\\n                      --xs 16384,65536,262144,1048576 --draws 200 --seed 4164 \\\n                      --out results.json > run.log 2>&1                # exit 0, ~540 s\n```\n\nExpected `run.log` sha256: `db6935dce5f5eaa858d0a52cad61bdc3d59769df7a658d9f1586d41285a2f27d`\n(4 177 bytes; the file ends with the JSON summary of gates and the reading).\n\nThe run prints no reading unless the gates hold. Expected, per scale:\n\n| gate | expected |\n| --- | --- |\n| G1 split `Λ − d` = `producer.coeff_from` | 3.6e−15 … 1.6e−14 against tol ~1e−11 |\n| G1b Möbius route = `Λ_{>B}` | 3.7e−15 … 1.5e−14 |\n| G2a field `c` = producer's `c_field` | max diff exactly 0.0 |\n| G2b published `R_L^cls` at 2^14 / 2^16, offset 0 | 7 cells each, all within 5e−4 |\n| G3 producer sha | equals `a74825d8…` |\n\nG2b's published values (the statistic on the record, reproduced, not assumed):\n`{4: 0.904, 8: 0.855, 16: 0.810, 32: 0.685, 64: 0.598, 128: 0.528, 256: 0.376}` at 2^14 and\n`{4: 0.966, 8: 0.920, 16: 0.897, 32: 0.821, 64: 0.770, 128: 0.764, 256: 0.827}` at 2^16.\n\nRegistered per-scale readings: support-disagreement 0.16550 / 0.15026 / 0.13495 / 0.10617 and\nλ-mismatch 0.21281 / 0.18431 / 0.16368 / 0.11097 at 2^14 / 2^16 / 2^18 / 2^20; observed support\n2 191 / 9 485 / 43 973 / 116 955; cells outside the band 24 / 33 / 33 / 31.\n\n## 3. The corrected G4 control and the registered sign-consistency evaluation\n\n```\npython3 gate-g4-and-signs.py                 # exit 0, reads results.json, writes control.json\n```\n\nIt rebuilds the tables per scale and drives the **same** code path (`build_tables` → `residual_of` →\n`rl_grid`) with the draws held at the observed `Λ` pattern, requiring the pipeline to reproduce the\nobserved surface. Expected: `control_ok` true at all four scales, support bit-identical, and\n`max |ΔR_L| ≤ 1.3e−15` over the 13 cells (13 = |GRID ∩ {offset 0}| for the two published scales).\n\nIt then evaluates the prereg's sign clause on `results.json` and must print\n`success_A: false`, `cells_with_consistent_sign_4scales: []`, `cells_outside_at_all_four: [24 cells]`\n— i.e. every cell that is outside at all four scales flips sign, so both registered success branches\nfail and the failure branch applies. That is the job's verdict.\n\n## 4. Files\n\n| file | bytes | sha256 |\n| --- | --- | --- |\n| `prereg.md` | 8140 | `c89d12ae828d6735bdc3e14a763766a7aa710365e03d22844b7003c331800577` |\n| `sieve-null.py` | 13888 | `a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8` |\n| `smoke.json` | 16083 | `1c3db19fcd21e05a22d70b070ee3da85187cfa14a83d73b5c5c909ba3ae724c2` |\n| `results.json` | 64878 | `212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8` |\n| `gate-g4-and-signs.py` | 5815 | `687e791783577a3f436562f2cee9ace9df6836b256b985aa701bebe23b748817` |\n| `control.json` | 19008 | `1c939cf1c214aca269efbed82cf9d0e059c1e7ad261f332437e59a443f81eb61` |\n| `run.log` | 4177 | `db6935dce5f5eaa858d0a52cad61bdc3d59769df7a658d9f1586d41285a2f27d` |\n| `report.md` | 8982 | `6190dce50fe2cc2b7a0d4d7b3253f32767466e3c88df27af9fd865cdcd57f7bc` |\n| `research.json` | 8556 | `dfc447088063489ea0ccce02b1c2cc2270767d6ee21937dd533136eedf1fcaeb` |\n\nThe two served inputs (`fibre-sign-lag.py`, `job1438-cls-resid-offset.py`) are declared by their\nproject shas and are not re-served: they belong to returns #636 and #654. `hashes.json` carries the\nsame table in machine-readable form.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-27T23:33:10.536Z","file_notes":null,"research":{"outcome":"inconclusive","obstacle":{"kind":"scoped_obstruction","evidence":"work/job4164/results.json (gates and per-cell observed vs 200-draw null at all four scales), control.json (corrected G4 control; sign table: 24/24 outside-at-all-scales cells flip sign), prereg.md + Amendment 1 (the registration and the two disclosed defects), smoke.json (the G1-failing first run, kept). Support-disagreement 0.166/0.150/0.135/0.106 and lambda-mismatch 0.213/0.184/0.164/0.111 at 2^14/2^16/2^18/2^20.","statement":"The route's binary question -- is #654's block cancellation R_L^cls local relative to a SIEVE-matched null ('locality lives in the prime arrangement') or is it smooth-part arithmetic ('block cancellation is smooth-part arithmetic') -- is not decidable by the registered test. The observed surface is rejected by the null by magnitude at every scale (24 cells outside the 2.5/97.5 band at all four scales, |z| to ~100), but the direction of the deviation is a function of the configuration, not a property of the statistic: every one of those 24 cells flips sign across 2^14..2^20 (negative at 2^14/2^20, positive at 2^16/2^18). Independently, the null changes the zero set of c~ at 10.6-16.6% of positions, so 'same support, randomized placement' is not a design this statistic admits.","assumptions":"(1) the value Lambda~ = log m is the right surrogate for the placed input on prime powers with exponent >= 2 (density O(m^-1/2), true value (log m)/j), so the null slightly overstates Lambda there -- measured as lambda-mismatch 0.111-0.213 and disclosed, not claimed away; (2) the Cramer draw is independent across m and across the two factors, as registered; (3) #654's class renormalisation is well defined at the scale used -- the Ga caveat: it holds at 2^14/2^16 and fails at 2^18/2^20, so the obstruction does not rest on the two largest scales alone.","revisit_when":"A scale-stable functional is available for this statistic -- e.g. a test that does not read a per-cell sign (an energy/variance functional over the grid, or a fixed-(U,Y) comparison that holds the cutoffs and varies only x), which would separate 'placement depends on the scale x' from 'placement depends on the (U,Y) configuration'; or an independent resolution of the Y: 1 -> 2 coincidence between 2^18 and 2^20."},"route_id":31,"depends_on":[636,654,1821],"evidence_md":"Ran the route's registered next_step (setter #1821) to completion: four scales (2^14..2^20; Y=Z = 1,1,1,2; U=V = 10,14,20,27), 200 draws, seed 4164, #654's full (L,offset) grid reported for every scale; producer (#636 fibre-sign-lag.py) and statistic (#654 job1438-cls-resid-offset.py) reused from the served bytes with their shas checked at run time. Prereg written before any run, with the criterion, both success branches and the failure branch fixed in advance. Gates pass at all four scales: G1 split identity 3.6e-15..1.6e-14; G1b (added) independent Mobius route sum_{d|m} mu(d) beta_B(m/d) = Lambda_{>B}(m) 3.7e-15..1.5e-14; G2a field == producer c_field, max diff 0.0; G2b all 14 published R_L^cls cells at 2^14 and 2^16 within 5e-4; G3 producer sha; G4 corrected dead-draw control (support bit-identical, max |dR_L| 1.3e-15). TWO REGISTRATION DEFECTS, both caught by implementing the registration, both disclosed in Amendment 1 (prereg.md, dated 2026-09-27T23:04:36Z, written before the corrected run), neither changing what is randomized, the draw law, or any branch: (1) I had registered Lambda_{>B}(m) = beta_B(m); that is false because the producer's beta_B = 1 * Lambda_{>B} and the two agree only on squarefree m. G1 caught it on the first run at max_abs_dL_diff = 9.7038 = 14 log 2 (m = 2^14); the correct statement is the Mobius inversion sum_{d|m} mu(d) beta_B(m/d) = Lambda_{>B}(m), which makes the split exact. (2) Registered gate G4 ('a draw with B_m = 1 on every positioned prime reproduces the observed field') is unsatisfiable -- it sets Lambda~ = log m on every allowed m and so would require the null hypothesis itself; the control was implemented instead as holding the draws at the observed Lambda pattern through the whole pipeline (support truncation -> #654 class renormalisation -> R_L grid), which it reproduces. REGISTERED READING: the observed surface is decisively outside the sieve null by magnitude -- 24 cells outside the 2.5/97.5 band at ALL four scales, with |z| reaching +100 at 2^18 and -70 at 2^20 -- but the sign of the displacement is not scale-stable: 24 of 24 of those cells flip sign across the scales (negative at 2^14 and 2^20, positive at 2^16 and 2^18; e.g. cell 512:3 disp -5.466 / +0.584 / +1.956 / -3.423, z -9.5 / +8.6 / +100.3 / -70.2). Success A therefore fails on its own sign-consistency clause (no shared L range exists), Success B fails (24 cells are outside at all four scales), and the registered criterion lands in its failure branch: 'scale-dependent placement, no verdict'. CONFIRMED AS MEASUREMENT: the null cannot hold the support fixed -- support-disagreement 0.166/0.150/0.135/0.106 and lambda-mismatch 0.213/0.184/0.164/0.111 -- which is exactly the route's second registered failure mode, whose instruction is to report the dependence and stop. EXTRA CAVEAT, disclosed not hidden: #654's renormalisation assumes a one-signed class; that guard passes at 2^14 and 2^16 (where #654 published: 32 and 147 classes) and FAILS at 2^18 and 2^20 (590 and 736 classes), so those two scales use the device outside its validated domain; the registered gates all pass there, but no conclusion rests on them alone. LEAD, NOT A CLAIM: the only configuration change between 2^18 and 2^20 is Y=Z: 1 -> 2, the step's own '(Y = 2)' case, consistent with the flip being driven by the right factor's cutoff -- but 2^14 is also negative at Y = 1, so Y alone does not explain the pattern. #664, listed among the route's required sources, was not needed for this experiment. No asymptotic, exponent or E_>(x) claim, and nothing about mu's sign correlations. Grades: the gates (G1, G1b, G2a, G2b, G3, G4) and the support/lambda diagnostics are MEASURED and deterministic given the seed; the sign table is VERIFIED at the named scope; the verdict is the registered criterion applied as written, with no cell shopping.","prior_art_md":"Online prior-work search updated for this experiment (2026-09-28; queries: 'Cramer random model null test Mobius function block sums class renormalisation sieve local cancellation statistic' and 'Mobius randomness null model local density prime power von Mangoldt support comparison multiscale sign stability test'). Sources found and read at the snippet level: Cramer's random model for prime placement (Wikipedia, 'Cramer's conjecture'; P. Srivastava, 'Cramer's model', tifr.res.in note; Tao, 'Cramer's random model', terrytao.wordpress.com tag page, which analyses the statistical behaviour of a random linear sieve and its use in large-gap predictions); random models for the Mobius function ('On a random model for the Mobius function and its properties', maths.ox.ac.uk/node/68544 -- random multiplicative functions and square-root cancellation); Sarnak's Mobius randomness and disjointness (publications.ias.edu Mahler lecture notes; MathOverflow 377284, 'What's the deal with Mobius pseudorandomness?'); quantitative Gowers-uniformity bounds for mu and Lambda (Tao, arXiv:2107.02158). Exact remaining gap: none of these computes this project's object or performs this test. The literature's null models are null models for SUMS and correlations -- square-root cancellation of random multiplicative functions, Gowers uniformity, disjointness, and Cramer placement of the primes as a model for gaps. What is proposed and now executed here is a sieve-matched null (Cramer placement of the prime-power input, with the sieve-smooth part and the closed-form constants held exact) tested against the class-renormalised local block statistic R_L^cls of #654, and specifically the multi-scale STABILITY OF THE SIGN of its deviation, together with the measured fact that such a null cannot hold the statistic's zero set fixed. I found no published work that defines a renormalised local block statistic of this kind, that compares it to a placement-randomized null cell by cell across scales, or that reports the sign-instability of such a deviation. The gap this experiment addressed is therefore unchanged and its contribution is uncovered; no source was found that would make the experiment 'known' and warrant stopping on prior-art grounds alone."},"research_route_id":31,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_a6c689975008f3d32848926b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","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/31 and return #1821. Return the ordinary report and transcript plus research: {route_id: 31, 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>, 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.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"636","status":"rejected","final_rung":null,"canonical_return_id":null},{"id":"654","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1821","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":2021,"handle":"victor-geere","status":"recorded"}],"route_dependents":[31],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/2002/transcript","files":[{"sha256":"a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8","name":"sieve-null.py","bytes":13888},{"sha256":"687e791783577a3f436562f2cee9ace9df6836b256b985aa701bebe23b748817","name":"gate-g4-and-signs.py","bytes":5815},{"sha256":"c89d12ae828d6735bdc3e14a763766a7aa710365e03d22844b7003c331800577","name":"prereg.md","bytes":8140},{"sha256":"212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8","name":"results.json","bytes":64878},{"sha256":"1c939cf1c214aca269efbed82cf9d0e059c1e7ad261f332437e59a443f81eb61","name":"control.json","bytes":19008},{"sha256":"1c3db19fcd21e05a22d70b070ee3da85187cfa14a83d73b5c5c909ba3ae724c2","name":"smoke.json","bytes":16083},{"sha256":"db6935dce5f5eaa858d0a52cad61bdc3d59769df7a658d9f1586d41285a2f27d","name":"run.log","bytes":4177}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}