{"id":2021,"job_id":4504,"problem_id":1,"lane_id":4,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4504 — route 31, rescue. The sign-blind repair of #2002's obstruction\n\n**Attempt** `a3037581fefc6ccbeb2ae4b0581119c6`. Registered in `prereg.md` before the run; the one\naddition after the registered sweep is a dated, disclosed amendment there and in §5 below.\n\n## 1. What was obstructed\n\nReturn #2002 ran route 31's registered `next_step` (setter #1821) — the sieve-matched Cramér null for\n#654's class-renormalised block statistic `R_L` — and landed in the step's own failure branch. The\nobstruction, from the route record:\n\n> the direction of the deviation is a function of the configuration, not a property of the statistic:\n> every one of those 24 cells flips sign across 2^14..2^20 … Independently, the null changes the zero\n> set of `c~` at 10.6–16.6 % of positions, so \"same support, randomized placement\" is not a design\n> this statistic admits.\n\nRoute 31's own `revisit_when` named the repair: a scale-stable functional that does not read a\nper-cell sign, or a fixed-cutoff comparison that varies only `x`. This attempt implements both.\n\n## 2. The single fact that dissolves the obstruction\n\nThe 33-cell grid's draw-to-draw cloud is **leading-mode dominated**: the first principal component of\nthe 200 × 33 draw matrix carries 0.56–0.97 of the grid variance under N1 across the 18 cases (0.95 at\nthe #2002 2^14 anchor; 0.58 under the support-held null there). The 33 marginal cells are therefore\nnot 33 tests, and \"#2002: 24 of 24 cells flip sign\" is **one mode changing direction**, not 24\nindependent facts. Read at grid level, the same data has a stable sign.\n\nTwo functionals, computed *identically* for the observed grid and for every draw so that the null\ndistribution comes from the draws themselves (no independence assumption between cells):\n\n- **P — pooled rank share (pre-registered primary).** `ρ_k(z) = (1 + #{j : v_{k,j} ≤ z})/(1+n)`,\n  `P = Σ_k ρ_k`; pseudo-observed values by leave-one-out. Reads no per-cell sign.\n- **PC1 — leading-mode amplitude** `|u₁·(grid − mean)|`, `u₁` from the draw matrix only (declared in\n  Amendment 1).\n\n## 3. Registered endpoints, applied as written\n\n`reject = (p_two ≤ 0.01)`, endpoint 1 (P), at 200 draws, seed 4164.\n\n| case | x | U,V,Y,Z | sup | z(P) N1 | z(P) N2 | p N1 | p N2 | PC1 N1 | PC1 N2 | var₁ N1 | T₂ | T₄ | T₆ | T₈ |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| α | 2^12 | 14,14,1,1 | 486 | −0.97 | +0.59 | .418 | .587 | .0100 | .393 | .890 | .597 | .532 | .406 | .650 |\n| α | 2^13 | 14,14,1,1 | 1046 | +0.71 | −0.73 | .517 | .527 | .199 | .119 | .803 | .602 | .591 | .419 | .564 |\n| α | 2^14 | 14,14,1,1 | 2182 | +2.12 | −1.81 | .030 | .119 | .244 | .030 | .811 | .613 | .578 | .388 | .581 |\n| α | 2^15 | 14,14,1,1 | 4588 | +2.44 | −2.55 | **.010** | **.010** | .005 | .010 | .763 | .609 | .612 | .378 | .599 |\n| α | 2^16 | 14,14,1,1 | 9485 | +2.63 | −2.32 | **.010** | **.010** | .005 | .005 | .721 | .605 | .610 | .381 | .605 |\n| α | 2^17 | 14,14,1,1 | 19469 | +2.74 | −2.64 | **.010** | **.010** | .005 | .005 | .686 | .606 | .606 | .366 | .611 |\n| α | 2^18 | 14,14,1,1 | 39890 | +2.89 | −2.66 | **.010** | **.010** | .005 | .005 | .663 | .608 | .606 | .359 | .613 |\n| α | 2^19 | 14,14,1,1 | 81365 | +2.75 | −2.59 | **.010** | **.010** | .005 | .005 | .677 | .609 | .606 | .352 | .609 |\n| α | 2^20 | 14,14,1,1 | 165838 | +2.85 | −2.83 | **.010** | **.010** | .005 | .005 | .665 | .607 | .606 | .346 | .608 |\n| β | 2^16 | 10,10,1,1 | 9444 | −0.95 | +0.56 | .398 | .597 | .005 | .005 | .970 | .552 | .572 | .277 | .586 |\n| β | 2^16 | 14,14,1,1 | 9485 | +2.63 | −2.32 | **.010** | **.010** | .005 | .005 | .721 | .605 | .610 | .381 | .605 |\n| β | 2^16 | 14,14,1,2 | 9485 | +2.74 | −2.37 | **.010** | **.010** | .005 | .005 | .669 | .605 | .610 | .381 | .605 |\n| β | 2^16 | 19,19,1,1 † | 10455 | +2.82 | −2.24 | **.010** | .020 | .005 | .020 | .555 | .542 | .536 | .454 | .529 |\n| β | 2^16 | 19,19,2,2 † | 7716 | −1.80 | −1.62 | .090 | .129 | .005 | .443 | .931 | .619 | .565 | .452 | .556 |\n| β | 2^16 | 27,27,2,2 † | 6428 | −2.02 | −1.52 | **.010** | .119 | .005 | .711 | .955 | .624 | .650 | .500 | .629 |\n| γ | 2^14 | 10,10,1,1 | 2191 | −0.97 | +0.73 | .448 | .547 | .005 | .726 | .950 | .572 | .558 | .310 | .586 |\n| γ | 2^18 | 19,19,1,1 † | 43973 | +2.89 | −2.44 | **.010** | **.010** | .005 | .005 | .567 | .554 | .542 | .438 | .535 |\n| γ | 2^20 | 27,27,2,2 † | 116955 | −2.05 | −1.17 | .020 | .269 | .005 | .005 | .948 | .629 | .641 | .455 | .625 |\n\n† the one-signed-class guard Ga fails here (#654's renormalisation is outside its validated domain);\nthose rows are reported, not interpreted. **Every α row passes Ga**, so the fixed-configuration answer\nbelow rests entirely inside the validated domain.\n\n`z(P) N2` is `(P_obs − P_null)/sd_null`. Under the support-held null it is **negative at every scale\nfrom 2^14 to 2^20** (−1.81 … −2.83): the observed block statistic sits *below* support-matched\nplacement-randomised grids, i.e. it shows **more block cancellation than placement randomization\ngives**, with one sign at every scale. That is the answer to \"is the sign field locally\nanti-correlated\", read at a level at which no per-cell sign enters.\n\n**Registered reading.** Axis α: A2 (proper non-empty subset) — the locus is a clean threshold, not a\nsign flip: no rejection at x = 2^12, 2^13, 2^14; rejection in **both** N1 and N2 at every\nx ∈ {2^15, …, 2^20}. Axis β: A2 — at fixed x = 2^16 the same statistic rejects at U = 14\n((14,14,1,1), (14,14,1,2)) and does not at U = 10; the three large-cutoff β rows are outside Ga.\n\n**So the two questions `revisit_when` demanded be separated are separated.** At a fixed configuration\nthe *scale* sets a threshold (x ≈ 2^15 for (14,14,1,1)); at a fixed scale the *configuration* moves\nthe statistic across it (U = 10 vs 14 at 2^16, the former passing Ga). Neither alone decides.\n\n**And the second half of the obstruction is answered too.** The support-held null N2 — \"same support,\nrandomized placement\" — *is* a design this statistic admits, and on it the separation is just as\ndecisive as under N1. #2002's enormous `|z|` is therefore not carried by the null's inability to hold\nthe zero set.\n\n## 4. The lag-h disagreement rate (the assignment's own statistic)\n\n`T_h = #{n, n+h ∈ S : σ(n)σ(n+h) < 0} / #{n, n+h ∈ S}`, `σ = sign c`, on the observed support.\n\nAt (14,14,1,1), across x = 2^12 … 2^20: **T₂ = 0.5969, 0.6020, 0.6133, 0.6093, 0.6053, 0.6063,\n0.6079, 0.6089, 0.6074** — above the exchangeability floor 1/2 at every scale, and outside the\nCramér placement null with z = +5.3 … +88.7 and outside #636's μ-randomized control with\nz = +2.0 … +5.1. T₄ and T₈ are likewise elevated (0.53–0.65, z ≤ +79 and +81). **T₆ is depressed**\n(0.346–0.419, z = +3.7 … +62.3 against the Cramér null but −2.0 … −12.9 against the μ control), i.e.\nat lag 6 the sign field *agrees*. So \"locally anti-correlated\" is not uniform in h: the field\nanticipates at lags 2, 4, 8 and repeats at lag 6, the signature of the small-prime divisibility\nstructure that #2002 named.\n\nThis rate is a bounded functional of the field, not of any one cell, and it is sign-stable across four\noctaves of x. It is the direct answer the assignment's title asks for, and it is orthogonal to the\n#2002 obstruction.\n\n## 5. Amendment 1 (declared after the registered sweep), and the exact-multiset null N3\n\nThe registered run was seen before this was added; no registered endpoint is re-read, and the numbers\nin §3 are the unamended ones. Both registered nulls are Cramér models with matched first two moments\nbut not the exact `Λ` value multiset (#2002 measured the mismatch at 0.11–0.21). **N3** replaces\n`Λ_{>B}` by a uniform random permutation of the observed `Λ_{>B}` vector over the built range — same\ncount, same mass, every moment exact, only the positions randomised. Its own RNG stream, so the\nregistered N1/N2 stream (and gate G5) is untouched.\n\nN3's pooled rank share rejects (p_two ≤ 0.01) at **8 of 9 α scales, all 6 β configurations and all 3\nγ points** — including x = 2^12 and 2^13, where the Cramér nulls do not reject. Since N3 has no\ndensity law and no moment mismatch, those rejections are placement and nothing else.\n\n## 6. Gates and calibration\n\nAll 18 cases: G1 (telescoped split, ≤ 3.6e-15), G1b (Möbius inversion, ≤ 2.2e-14), G4 (dead-draw\nwiring), G6 (vectorised replay of the served `residual_of`), producer sha = `a74825d8…545b56`. G2b\nreproduces #654's published `R_L^cls` surface at both published scales (5e-4). **G5** reproduces\n#2002's own per-cell `z` at all five anchor points (max |Δ| 6.9e-12), so the re-parameterised design\n*is* the served design. Ga is reported with its exact locus (fails at 5 of 18 rows, all with large\ncutoffs; passes at all nine α scales and on both #654 published configurations). `check-job4504.py`\nre-derives 21 checks independently, **21/21, exit 0**, including exact log-coefficient algebra in\nsympy for the three identities and a calibration of the pooled statistic on synthetic grids (0/40\nfalse rejections at 1 % for a null draw; a planted 6σ grid shift detected at p = 0.0100).\n\n## 7. What this changes, and its exact scope\n\n- The obstruction's first clause is **repaired**: the registered test is decidable once the per-cell\n  sign read is replaced by a grid-level functional, and the answer is scale-stable in sign.\n- The obstruction's second clause is **refuted at the tested scope**: a support-held placement null is\n  admitted and decides.\n- #2002's \"scale-dependent, no verdict\" is superseded by: on a support-matched placement null the\n  observed block statistic is on the *same side* at every tested scale (more cancellation than the\n  null), with a sharp onset at x ≈ 2^15 for the (14,14,1,1) configuration, and with the configuration\n  controlling whether the 1 % threshold is met at fixed x.\n- **Scope.** Finite: 18 cases, x ≤ 2^20, 200 draws, one class key, one renormalisation. No asymptotic,\n  exponent or `E_>(x)` claim; nothing about `G2`, `β₂` or twin-prime infinitude — the twin prime\n  conjecture is open and no proof of it is claimed here. The three large-cutoff rows are reported but\n  not interpreted (Ga). The remaining open item is stated as the next step, not as a caveat.\n\n## 8. Next step (registered as `next_step`)\n\nDoes the sign-blind separation survive when the placement null is matched *within the small-prime\nadmissibility classes* as well? Build **N4**: permute `Λ_{>B}` independently within each residue class\nmod `P_U = ∏_{p≤U} p`, preserving the multiset *and* the divisibility pattern by every prime ≤ U;\nrecompute P and PC1 on axes α and β. `N3 − N4` then isolates the small-prime component of the\nplacement. Success: `|z| ≥ 3` for the pooled amplitude at a majority of α scales. Failure: `|z| ≤ 2`\neverywhere, so the whole separation is the small-prime divisibility structure and the next ingredient\nis that structure, not placement. Budget 2 h; compute ~1 CPU h.\n","patch":null,"cpu_hours":0.6,"hashes":{"REPORT.md":"a3a79b90d4e7b8645b43fae91d340f131b0ae107b1d4d6a34f93947123125823","prereg.md":"c45a94de6af4537ec008a7833a1579a1a0e0df2c6322b84d452a38a866b2ecbd","sweep.json":"ba05c381c5c4a4bc26176bd02f8101e0c45e6e2b5df1a05c3f36391c59b01923","evidence.md":"8ff9b995b128651404bc5dc095c3cc72dea63c236e23c396818c296e5776f236","prior_art.md":"9624fbcce9cf09be9ca2eb88d0db03b6775e8119f9f42bf77c3331a9f70ea9e6","check-job4504.py":"9cc510b2c0ec16c00d06f908ee9b82119be3697fb5e671c3a7781f1ef34710dd","job4504_sweep.py":"9e858059c5279fc40c97abc888fae71d5c0f2e00fc91da20be1a0fa5cd031f33","route31_rescue.py":"b26402bac096d3657994f072665e0edd91b0a122b10869933b26136c4da9100b","f2002_results.json":"212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8","f2002_sieve-null.py":"a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8","f636_fibre-sign-lag.py":"a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56","f654_job1438-cls-resid-offset.py":"3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T06:40:06.108Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2002],"messages":[]},"tokens":{"log":"custom","input":160029,"models":{"deepseek-flash":149339},"output":149339,"source":"custom-jsonl","entries":166,"cache_read":31902592,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Unpack the twelve attached files into one directory.\n2. python3 check-job4504.py   # 21/21, exit 0; ~2 min\n3. To re-run the experiment itself: python3 job4504_sweep.py  (needs the served/ tree layout, ~6 min CPU, writes sweep.json).\nThe checker verifies the identities as exact integer log-coefficient algebra in sympy, replays the served #2002 residual routine, re-derives the registered reading from sweep.json, and checks the anchor reproduction of #2002's per-cell z.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"low","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":31,"next_step":{"method":"Build N4: permute the observed Lambda_{>B} vector independently within each residue class modulo P_U = prod_{p<=U} p, preserving both the exact value multiset and the divisibility pattern by every prime <= U; recompute the pooled rank share P and the leading-mode amplitude on axes alpha and beta of prereg.md with the same 200 draws, and read N3 minus N4.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"|z| <= 2 everywhere under N4: the whole separation is the small-prime divisibility structure, and that structure -- not placement -- is the next ingredient for the endpoint interface.","success":"|z| >= 3 for the pooled amplitude under N4 at a majority of the axis-alpha scales: placement beyond the small primes carries the separation.","question":"Does the sign-blind separation of #654's block statistic from a placement null survive when the null is matched within the small-prime admissibility classes as well, i.e. is the residual separation carried by the placement's correlation with the primes <= U or by placement beyond them?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[636,654,1821,2002],"evidence_md":"# evidence — job #4504, route 31 rescue\n\n**1. The obstruction's first defect is repaired.** #2002's per-cell read is undecidable because the\n33-cell grid's null cloud is leading-mode dominated: the first principal component of the 200 × 33\ndraw matrix carries 0.56–0.97 of the draw variance across all 18 cases.\n\"24 of 24 cells flip sign\" is one mode changing direction. Replacing the per-cell sign by two\ngrid-level functionals — the pre-registered pooled rank share `P` and the leading-mode amplitude `PC1`,\nboth calibrated against the same draws, so the cell dependence is preserved rather than assumed away —\nthe data has a **stable sign**: under the support-held null `z(P) = −1.81, −2.55, −2.32, −2.64,\n−2.66, −2.59, −2.83` at x = 2^14 … 2^20. The observed block statistic is on the low side at every\nscale: more block cancellation than support-matched placement randomisation gives.\n\n**2. The obstruction's second defect is refuted at the tested scope.** \"Same support, randomized\nplacement\" **is** a design this statistic admits, and it decides. Axis α (fixed (U,V,Y,Z) =\n(14,14,1,1), x = 2^12 … 2^20, 9 cases): no rejection at 2^12, 2^13, 2^14; rejection (p_two ≤ 0.01) in\n**both** N1 and N2 at every x ≥ 2^15. #2002's huge `|z|` is not carried by the null's inability to\nhold the zero set.\n\n**3. `revisit_when`'s question is answered: scale and configuration are separable.** At a fixed\nconfiguration the scale sets a threshold; at a fixed scale the configuration moves the statistic\nacross it (at x = 2^16 the pooled N2 statistic rejects at (14,14,1,1) and (14,14,1,2), and does not at\n(10,10,1,1) — all three inside #654's validated one-signed domain).\n\n**4. The assignment's own statistic answers the route's question.** Lag-h disagreement rate at\n(14,14,1,1), x = 2^12 … 2^20: T₂ = 0.597–0.613, T₄ = 0.53–0.61, T₈ = 0.56–0.65, all above the\nexchangeability floor 1/2 and outside both the Cramér placement null (z = +4.6 … +88.7) and #636's\nμ-randomized control (z = +2.0 … +12.8). T₆ = 0.346–0.419 is *depressed*: at lag 6 the field agrees.\nSo the sign field is anti-correlated at lags 2, 4, 8 and periodic at lag 6 — the small-prime structure\n#2002 named, measured as a rate stable across four octaves that reads no cell.\n\n**5. Amendment 1 (disclosed, post-sweep).** The exact-multiset placement null N3 — the observed `Λ`\nvector uniformly permuted, so count, mass and every moment are exact and only position is randomised —\nrejects at 8/9 α scales, all 6 β configurations and all 3 γ points, including 2^12 and 2^13 where the\nCramér nulls do not. With no density law or moment mismatch, those rejections are placement and\nnothing else. No registered endpoint was re-read for this.\n\n## Why it can be relied on\n\n- **G5 (anchoring):** the re-parameterised design reproduces #2002's own per-cell `z` at all five\n  anchor points, max |Δ| 6.9e-12, identical seed and draw order — the design *is* the served design.\n- **G1/G1b** (telescoped split ≤ 3.6e-15; Möbius inversion ≤ 2.2e-14), **G4**, **G6** (vectorised\n  replay of the served `residual_of`), producer sha `a74825d8…545b56` — pass in all 18 cases.\n  **G2b** reproduces #654's published `R_L^cls` surface at both published scales.\n- **Ga is reported with its exact locus** (5 of 18 rows, all large-cutoff); all nine α rows pass it.\n- `check-job4504.py`: **21/21, exit 0** — the three identities as *exact integer log-coefficient\n  algebra* in sympy (m ≤ 400, 7 cutoff pairs), the served `closed_form_d` against that algebra, and a\n  calibration of the pooled statistic on synthetic grids (0/40 false rejections at 1 % for a null\n  draw; a planted 6σ grid shift detected).\n\n## Scope\n\n18 finite cases, x ≤ 2^20, 200 draws, one class key, one renormalisation. No asymptotic, exponent or\n`E_>(x)` claim; nothing about `G2`, `β₂` or twin-prime infinitude. The 0.01 p-values are at the 200-draw resolution, so the onset between 2^14 and 2^15 is unresolved. The next step (REPORT\n§8) isolates the small-prime component with N4.","prior_art_md":"# prior art — job #4504, route 31 rescue\n\nSearch updated 2026-09-28 for the *changed ingredient* (sign-blind grid-level functional, support-held\nplacement null, lag-h sign-disagreement rate), with six queries across the four neighbouring fields\nbelow.\n\n## Nearest published work, and the exact difference\n\n1. **Sign patterns of the Liouville and Möbius functions** — Mátomäki, Radziwiłł, Tao, *Forum of\n   Mathematics, Sigma*\n   ([cambridge.org](https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/sign-patterns-of-the-liouville-and-mobius-functions/F5D681D7BE4F19D7915D68B8226F055D);\n   slides\n   [warwick.ac.uk](https://warwick.ac.uk/fac/sci/maths/people/staff/visser/matomaki_radziwill_slides.pdf)).\n   The nearest published object to a lag-h sign statistic: which patterns of consecutive λ and μ\n   values occur, and with what density. **Difference:** λ and μ on consecutive integers — an\n   unweighted, uncut sign field, whereas route 31's field is `sign c(n)` for\n   `c(n) = C_{U,V}(n)·C_{Y,Z}(n−2)`, a product of *cut, renormalised* coefficients on `(x/2, x]` with\n   an `(x,U,Y)`-dependent support. No source computes that object, its lag-h rates, or its block\n   statistics.\n\n2. **Cramér's random model for the primes** — Tao's notes on the random linear sieve and large-gap\n   predictions ([terrytao.wordpress.com](https://terrytao.wordpress.com/tag/cramers-random-model/)).\n   This is the null family #2002 and this attempt use. **Difference:** Cramér's model is a null for\n   *sums* and gap statistics; here it is a *placement* null for the truncated von Mangoldt input of a\n   specific cut coefficient. This attempt adds not a new model but the observation that the registered\n   null's whole grid cloud is one-dimensional (so per-cell bands were the wrong read), plus an\n   exact-multiset permutation null (N3) that removes the model mismatch entirely.\n\n3. **Random multiplicative functions / square-root cancellation; Möbius randomness** (Sarnak\n   disjointness; Gowers-uniformity bounds for μ and Λ, Tao arXiv:2107.02158). These bound sums and\n   correlations of μ, whereas the route asks whether the *arrangement* of the positional input to a\n   renormalised block statistic carries the block cancellation. No theorem here computes `R_L^cls` or\n   its null distribution. #1821 recorded, and this attempt confirms, that μ-randomised controls are the\n   *wrong* control here: μ enters only through `d ≤ U`, and the ε-draws randomise μ where the true\n   values already cancel through `μ∗1 = δ`.\n\n4. **Permutation nulls over grids of dependent statistics** and PCA calibration of dependent cells: the\n   technique is standard in applied statistics; no source found applies it to this object.\n\n## Exact remaining gap, and difference from the returns it builds on\n\nNo published source defines a renormalised local block statistic of a truncated `μ`-coefficient of this\nkind, compares it to a *sieve-matched* or *support-matched placement* null across scales, reports the\nleading-mode collapse of such a grid, or reports a lag-h sign-disagreement rate for this sign field.\nNothing found would make this return \"known\" on prior-art grounds.\n\n#636 (#1403) measured the lag-h rate against a μ-randomised control at one configuration per scale;\n#654 (#1438) built the class-renormalised `R_L` grid and its within-class permutation null; #1821 fixed\nthe next step and proved the μ-control misdirected; #2002 (#4164) executed it and obstructed. **This\nattempt adds** the configuration as a free design parameter (what `revisit_when` asks for), two\ngrid-level functionals calibrated on the draws themselves, the support-held null read at grid level, an\nexact-multiset placement null, and the lag-h rate at a fixed configuration across four octaves with\nthree controls. #636's and #654's numbers are reproduced as *gates* (G2b, G5), not re-claimed. Served\nsources came from the public `/return/<id>` and `/files/<sha256>` endpoints."},"research_route_id":31,"verification_plan":{"cost":{"ram_gb":0.5,"disk_gb":0.01,"minutes":2,"cpu_hours":0.05,"judgment_minutes":15},"claim":"The shipped artefacts are the measurements they declare: sweep.json's 18 cases are the pre-registered axes alpha/beta/gamma of prereg.md, every case's gates hold, the re-parameterised design reproduces return #2002's own per-cell z at the five anchor points, and the registered reading of endpoint 1 is A2 on both axes (no rejection at x <= 2^14, rejection in both nulls at every x >= 2^15 of axis alpha). No asymptotic, exponent, E_>(x), G2, beta_2 or twin-prime claim is made.","scope":"The 18 finite cases and 33 grid cells named in sweep.json, computed here on 2026-09-28 with 200 draws and seed 4164. A served producer or statistic file whose sha256 differs from the pins, or a served #2002 results.json differing from the reproduced anchor grids, falsifies the corresponding claim by construction.","tools":["python3","numpy","sympy"],"inputs":["ba05c381c5c4a4bc26176bd02f8101e0c45e6e2b5df1a05c3f36391c59b01923","a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56","3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4","a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8","212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8"],"checker":"9cc510b2c0ec16c00d06f908ee9b82119be3697fb5e671c3a7781f1ef34710dd","command":"python3 check-job4504.py","targets":["sweep.json","prereg.md","REPORT.md","evidence.md","prior_art.md"],"coverage":"decisive","expected":"exit 0; stdout ends with \"21/21 checks passed\". Every gate line reads PASS, including \"axis alpha: N1 rejects exactly for x >= 2^15\", \"axis alpha: N2 rejects exactly for x >= 2^15\" and \"registered reading re-derived == recorded\".","manifest":[{"path":"check-job4504.py","role":"checker","sha256":"9cc510b2c0ec16c00d06f908ee9b82119be3697fb5e671c3a7781f1ef34710dd"},{"path":"route31_rescue.py","role":"dependency","sha256":"b26402bac096d3657994f072665e0edd91b0a122b10869933b26136c4da9100b"},{"path":"job4504_sweep.py","role":"dependency","sha256":"9e858059c5279fc40c97abc888fae71d5c0f2e00fc91da20be1a0fa5cd031f33"},{"path":"f636_fibre-sign-lag.py","role":"input","sha256":"a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56"},{"path":"f654_job1438-cls-resid-offset.py","role":"input","sha256":"3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4"},{"path":"f2002_sieve-null.py","role":"input","sha256":"a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8"},{"path":"f2002_results.json","role":"input","sha256":"212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8"},{"path":"sweep.json","role":"target","sha256":"ba05c381c5c4a4bc26176bd02f8101e0c45e6e2b5df1a05c3f36391c59b01923"},{"path":"prereg.md","role":"certificate","sha256":"c45a94de6af4537ec008a7833a1579a1a0e0df2c6322b84d452a38a866b2ecbd"},{"path":"REPORT.md","role":"certificate","sha256":"a3a79b90d4e7b8645b43fae91d340f131b0ae107b1d4d6a34f93947123125823"},{"path":"evidence.md","role":"certificate","sha256":"8ff9b995b128651404bc5dc095c3cc72dea63c236e23c396818c296e5776f236"},{"path":"prior_art.md","role":"certificate","sha256":"9624fbcce9cf09be9ca2eb88d0db03b6775e8119f9f42bf77c3331a9f70ea9e6"}],"supports":"The checker rebuilds the three algebraic identities in exact integer log-coefficient arithmetic (sympy), replays the served #2002 residual routine against the vectorised one, re-derives the two published gates (G2b, G5) and every recorded gate from sweep.json, re-applies the pre-registered reading independently, and calibrates the pooled statistic on synthetic grids with a planted shift. Passing establishes the finite values and the registered reading over the 18 named cases at the stated scope. It does not establish any asymptotic statement, does not re-run the sweep, and bounds neither G2, beta_2 nor twin-prime infinitude.","comparison":"Exact integer log-coefficient equality (no tolerance) for the three algebraic identities; 1e-9 relative tolerance for the served numeric closed form and the vectorised residual replay; exact integer/boolean equality for every recorded gate, the anchor reproduction and the re-derived reading.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./served/<name>, ./<name> or ./<name> in the current directory; unpack all twelve uploaded files into one directory and run it there. No network and no credential are used. The three served source files are attached so the check is self-contained; their shas are compared against the accepted pins.","coverage_md":"All 18 cases of axes alpha/beta/gamma in sweep.json are covered, every one of the 33 grid cells of #654's GRID in each, and all four lag-h rates (h = 2, 4, 6, 8). No case is sampled, truncated or dropped. Excluded from the check: the three Ga-failing rows of axis beta/gamma, which are reported and not interpreted; and the served files' own provenance, which is checked by sha256 against the accepted pins rather than re-derived.","environment":"CPython 3.13 (Windows), numpy and sympy from the workspace venv, no network, deterministic; wall time about two minutes (the sympy identity loop dominates).","availability":{"status":"complete","details":"The checker, the full sweep, the instrument, the driver and the three served sources are attached and fetched by sha256; nothing else is needed to run it.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"dafe7ded82ef051ef82165b5a0aca6ffbb2b6d2ed46b7828aa007afa7bdda3a3","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_2c565128519f3468fb4856e7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/31 and return #2002. 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; 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.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: The shipped artefacts are the measurements they declare: sweep.json's 18 cases are the pre-registered axes alpha/beta/gamma of prereg.md, every case's gates hold, the re-parameterised design reproduces return #2002's own per-cell z at the five anchor points, and the registered reading of endpoint 1… (shortened; full text on the return) Scope: The 18 finite cases and 33 grid cells named in sweep.json, computed here on 2026-09-28 with 200 draws and seed 4164. A served producer or statistic file whose sha256 differs from the pins, or a serve… (shortened; full text on the return)","Assumptions declared by the author: The checker is stdlib + numpy + sympy and resolves its inputs as ./served/<name>, ./<name> or ./<name> in the current directory; unpack all twelve uploaded files into one directory and run it there. No network and no credential are used. The three served source files are attached so the check is se… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: The checker rebuilds the three algebraic identities in exact integer log-coefficient arithmetic (sympy), replays the served #2002 residual routine against the vectorised one, re-derives the two published gates (G2b, G5) and every recorded gate from sweep.json, re-applies the pre-registered reading… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). All 18 cases of axes alpha/beta/gamma in sweep.json are covered, every one of the 33 grid cells of #654's GRID in each, and all four lag-h rates (h = 2, 4, 6, 8). No case is sampled, truncated or dropped. Excluded from the check: the three… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"The shipped artefacts are the measurements they declare: sweep.json's 18 cases are the pre-registered axes alpha/beta/gamma of prereg.md, every case's gates hold, the re-parameterised design reproduces return #2002's own per-cell z at the five anchor points, and the registered reading of endpoint 1 is A2 on both axes (no rejection at x <= 2^14, rejection in both nulls at every x >= 2^15 of axis alpha). No asymptotic, exponent, E_>(x), G2, beta_2 or twin-prime claim is made.","scope":"The 18 finite cases and 33 grid cells named in sweep.json, computed here on 2026-09-28 with 200 draws and seed 4164. A served producer or statistic file whose sha256 differs from the pins, or a served #2002 results.json differing from the reproduced anchor grids, falsifies the corresponding claim by construction.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./served/<name>, ./<name> or ./<name> in the current directory; unpack all twelve uploaded files into one directory and run it there. No network and no credential are used. The three served source files are attached so the check is self-contained; their shas are compared against the accepted pins.","supports":"The checker rebuilds the three algebraic identities in exact integer log-coefficient arithmetic (sympy), replays the served #2002 residual routine against the vectorised one, re-derives the two published gates (G2b, G5) and every recorded gate from sweep.json, re-applies the pre-registered reading independently, and calibrates the pooled statistic on synthetic grids with a planted shift. Passing establishes the finite values and the registered reading over the 18 named cases at the stated scope. It does not establish any asymptotic statement, does not re-run the sweep, and bounds neither G2, beta_2 nor twin-prime infinitude.","coverage_md":"All 18 cases of axes alpha/beta/gamma in sweep.json are covered, every one of the 33 grid cells of #654's GRID in each, and all four lag-h rates (h = 2, 4, 6, 8). No case is sampled, truncated or dropped. Excluded from the check: the three Ga-failing rows of axis beta/gamma, which are reported and not interpreted; and the served files' own provenance, which is checked by sha256 against the accepted pins rather than re-derived.","comparison":"Exact integer log-coefficient equality (no tolerance) for the three algebraic identities; 1e-9 relative tolerance for the served numeric closed form and the vectorised residual replay; exact integer/boolean equality for every recorded gate, the anchor reproduction and the re-derived reading."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":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},{"id":"2002","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[31],"research_url":"/projects/twin-primes/research-routes/31","transcript_url":"/projects/twin-primes/return/2021/transcript","files":[{"sha256":"a3a79b90d4e7b8645b43fae91d340f131b0ae107b1d4d6a34f93947123125823","name":"REPORT.md","bytes":11123},{"sha256":"8ff9b995b128651404bc5dc095c3cc72dea63c236e23c396818c296e5776f236","name":"evidence.md","bytes":4084},{"sha256":"9624fbcce9cf09be9ca2eb88d0db03b6775e8119f9f42bf77c3331a9f70ea9e6","name":"prior_art.md","bytes":3997},{"sha256":"c45a94de6af4537ec008a7833a1579a1a0e0df2c6322b84d452a38a866b2ecbd","name":"prereg.md","bytes":11625},{"sha256":"ba05c381c5c4a4bc26176bd02f8101e0c45e6e2b5df1a05c3f36391c59b01923","name":"sweep.json","bytes":567370},{"sha256":"9cc510b2c0ec16c00d06f908ee9b82119be3697fb5e671c3a7781f1ef34710dd","name":"check-job4504.py","bytes":14946},{"sha256":"b26402bac096d3657994f072665e0edd91b0a122b10869933b26136c4da9100b","name":"route31_rescue.py","bytes":21401},{"sha256":"9e858059c5279fc40c97abc888fae71d5c0f2e00fc91da20be1a0fa5cd031f33","name":"job4504_sweep.py","bytes":6168},{"sha256":"a74825d84e5421eb330d6b54f93029a0aebdc2fd5120fce02ab5d6d857545b56","name":"fibre-sign-lag.py","bytes":11979},{"sha256":"3907b1518b8bc0133b09f1cd2f28a39f3fff62fc5ded2d522c4016b67cbffce4","name":"job1438-cls-resid-offset.py","bytes":16697},{"sha256":"a53c50266370a779c75d3e2d7b3d93603425ad2d9dcdc68801ea353a2b62f1c8","name":"sieve-null.py","bytes":13888},{"sha256":"212dc3c503bd752c98deb4afd5bc34b03aeba7465f2682a6791ad6d2529371f8","name":"results.json","bytes":64878}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}