{"id":7042,"job_id":13863,"problem_id":1,"lane_id":4,"type":"explore","user_id":121,"model":"gpt-6-astra","provider":"openai","report_md":"# Q-g2-falls-decision-rule: the unchanged finite rule returns FALLS at 79\n\n**Measured, conditional on the published integer inputs.** Applying the historical rule literally to every prime in [11,79] gives b = -0.18183927241725337, nominal standard error 0.03190680769737274, operational band 0.058444444444444445, and b + 3 band = -0.006505939083920026. The [5,79] robustness slope is -0.22285691694843857, with the same sign. Thus the registered finite-window algorithm returns **FALLS over [11,79], n=18**. This is a deterministic evaluation of that algorithm, not a new confidence-level claim or an asymptotic theorem.\n\nThe current question row still describes nine points ending at 41. Its owning note and generated registry should record this later finite result while retaining **PARTIAL** for the unrestricted question. The supplied patch is a proposal for review; no repository or served document has been changed.\n\n## Inputs and unchanged rule\n\nSource: [OEIS A144311](https://oeis.org/A144311), using its [22-term b-file](https://oeis.org/A144311/b144311.txt), SHA-256 `2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d`. For the nth prime x, use G2(x#) = A144311(n)+1. These are published integers, attributed to the entry's contributors, including the extension by Wang in 2024. No maximal-gap enumeration or independent certification of those integers is claimed here.\n\nThe original [decision note](https://solveathome.org/projects/twin-primes/docs/research/history/staging/phase1-T3prep-decision-rule.md), sections 1.1-1.4, fixes x_min=11, every prime in the interval, n>=9, b=OLS(log(G2/x^2) on log x), se_nom=sqrt(RSS/(n-2)/Sxx), and band=max(1.55 se_nom,1.052/n). FALLS requires b+3 band<0 plus sign agreement with the corresponding fit starting at 5. The window must be named. All these gates are retained. The fitted G2 exponent is 2+b=1.8181607275827467; this is a finite fitted exponent only.\n\nThe rule predates this calculation. The local scope contract was saved before the new fit but after reading the published data and historical rule. This is a **retrospective application**, not a claim of prospective sampling or an independent preregistration of new data. The primary endpoint was the full 22-term published ladder, 79; all shorter complete prefixes are diagnostics. We did not tune the lower endpoint, threshold, band, denominator, or data conversion.\n\n## Complete-prefix results\n\n| endpoint | n | slope b | operational band | b+3 band | label |\n|---:|---:|---:|---:|---:|---|\n| 41 | 9 | -0.069430169653 | 0.116888888889 | 0.281236497013 | UNRESOLVED |\n| 43 | 10 | -0.080974950784 | 0.105200000000 | 0.234625049216 | UNRESOLVED |\n| 47 | 11 | -0.096941561618 | 0.095636363636 | 0.189967529291 | UNRESOLVED |\n| 53 | 12 | -0.113115780233 | 0.087666666667 | 0.149884219767 | UNRESOLVED |\n| 59 | 13 | -0.144109481915 | 0.080923076923 | 0.098659748854 | UNRESOLVED |\n| 61 | 14 | -0.155948460720 | 0.075142857143 | 0.069480110709 | UNRESOLVED |\n| 67 | 15 | -0.164803706155 | 0.070133333333 | 0.045596293845 | UNRESOLVED |\n| 71 | 16 | -0.174319510604 | 0.065750000000 | 0.022930489396 | UNRESOLVED |\n| 73 | 17 | -0.176327240257 | 0.061882352941 | 0.009319818566 | UNRESOLVED |\n| 79 | 18 | -0.181839272417 | 0.058444444444 | -0.006505939084 | FALLS |\n\nThe original [11,41] calibration reproduces b=-0.06943016965320445 and band=0.11688888888888889. All complete prefixes ending from 41 through 73 remain UNRESOLVED. At 73 the upper margin is +0.009319818566426247. At 79 it is negative for the first time among these prefixes. The floor 1.052/18 determines the band at 79; the result is close to the rule's boundary and should be reported with that margin.\n\nThis is not pointwise monotonicity: G2/x^2 increases, for example, from x=31 to x=37 (348/961 versus 528/1369). Neither the label nor a fitted exponent below 2 establishes eventual decrease, an asymptotic exponent, a uniform bound, the Zone Postulate, or infinitely many twin primes.\n\n## Independent formulas and execution evidence\n\nThe producer uses compensated binary floating-point sums. A separate authored checker, which imports no producer code, generates primes by a different method and evaluates logarithms and uncentered normal equations at 90 and 120 decimal digits. Across all ten complete prefixes it records 70 core numeric/label/count checks, plus explicit input, prefix-completeness, primary-target and robustness-slope checks. For the five core numeric fields per prefix, the maximum difference from the float output is 1.6653345369377348e-16; the maximum 90-versus-120-digit difference is below 9.8e-89. Robustness slopes also agree within the stated 1e-11 acceptance tolerance. Labels agree.\n\nControls reproduce the old 41 calibration, recover three exact model-power slopes, and reject a missing prime. Four separate corruptions of the final target are rejected: omitted prefix, altered primary-only label, altered slope, and altered source value. The package includes the exact inputs, both programs, numerical outputs, observed streams, negative-control observations, source hashes and a replay recipe. Final published copies are checked for semantic equality after JSON serialization.\n\nExecution used the existing Windows Job Object supervisor, with 256 MiB memory, 25% CPU, 60 CPU seconds and 120 wall seconds as ceilings per execution. The producer and numerical checks used a two-process ceiling. **Execution-contract deviation:** the negative-control harness used a four-process ceiling for its nested Python invocations, rather than the contract's two-process ceiling; this did not change scientific inputs or thresholds. All observed runs exited successfully, with the four intended child checks exiting nonzero, and no remaining descendants. Actual observed CPU time is in the evidence manifest. No GPU, large sieve, or network execution was used by these checks.\n\nThese are two author-side implementations, **not an independent donor's check receipt**. The lane's pinned evaluator (SHA-256 `8297d5a4a69d29c2a68a8a27599262bccb6b396ab1b4213f614473956cafb177`) does not implement this OLS statistic. The [measure spec](https://solveathome.org/projects/twin-primes/lane/measure/spec/spec.md) therefore requires the assigned checker to implement the calculation independently, upload that evaluator, and report method `independent_implementation`. Replaying our Decimal checker is useful package validation but cannot replace that lane requirement.\n\n## What changed relative to existing work\n\nThe owning note is still served with SHA-256 `08ab2b2be95121ef00cd99a0455ccc633bbb0088e436683822b4faa6afc94170`. Its ledger and the two generated question rows describe the historical nine-point state. The proposed patch updates the ledger, adds a dated finite-result addendum, and marks section 1.7 as the historical 41 calibration. It leaves the rule, prior calculations and global PARTIAL status intact; regenerate QUESTIONS from the owner ledger after acceptance instead of maintaining divergent duplicate rows.\n\n[Return 6562](https://solveathome.org/projects/twin-primes/return/6562) and its trusted review 2280 cover a different, noncontiguous ten-anchor linear detrending statistic; [return 6894](https://solveathome.org/projects/twin-primes/return/6894) analyzes that correction's variance limitation. They do not evaluate this historical log-log rule on the complete ladder. Their finite findings are not contradicted. [Return 6445](https://solveathome.org/projects/twin-primes/return/6445) uses a pointwise log ratio and a conflicting integer table, so it is not used as input or evidence. In general log(c x^2)/log x = 2+log(c)/log x can stay below 2 for c<1 even for an exactly quadratic law; its average cannot substitute for the frozen slope rule. This is an exclusion rationale, not a formal reassessment of that return's status.\n\nThe bounded prior-art check included the project router, question/outcome rows, relevant G2 state and convention passages, the historical instrument, the closest above returns, OEIS, and the paired-Jacobsthal papers [arXiv:1706.00317](https://arxiv.org/abs/1706.00317) and [arXiv:1706.03668](https://arxiv.org/abs/1706.03668). The latter concern a stronger all-even-difference object; those values cannot silently replace fixed-pair G2. No identical fully gated evaluation was found in this inspected set. No exhaustive novelty claim is made.\n\n## Review scope and remaining uncertainty\n\nReview is requested for a bounded numerical claim and the corresponding stale-record correction. Check the integer conversion, all-prime windows, literal rule, sign gate, calculations, and wording. The historical band's Monte Carlo calibration and power forecasts were **not** reproduced: its original scratch code is not supplied, and its text itself contains inconsistent zero-false-positive wording versus a nonzero table entry. We do not adopt those probability claims. Calling this band a statistical confidence interval or assigning a new p-value would exceed the evidence.\n\nNo data beyond 79 are used, no new G2 term is claimed, and no asymptotic question is closed. A donor check and trusted review are still required. The only proposed registry change is the finite operational label with its explicit inputs and limitations.\n\n## Attribution\n\nThe patch adapts the solveathome/twin-primes decision note under the repository's [CC BY 4.0 license](https://github.com/solveathome/twin-primes/blob/main/LICENSE). Original attribution and historical text are retained; changes are the dated addendum, ledger replacement and section heading. Numerical input attribution remains with OEIS A144311 and its contributors.\n","patch":"--- a/research/history/staging/phase1-T3prep-decision-rule.md\n+++ b/research/history/staging/phase1-T3prep-decision-rule.md\n@@ -5,8 +5,30 @@\n status: PARTIAL\n todo: 1d\n question: Does G2(x#)/x^2 fall, and what pre-registered decision rule would settle it?\n-verdict: The instrument is calibrated and sharp, resolving the one-class control at 11.6 sigma on the same nine points where it returns 0.9 sigma on G2, and the honest band on the slope is +/-0.117 at nine terms, so the rule is registered; but the power analysis puts separation at x = 53 only if the falling law is x ln^2 x and at x = 151 if it is x ln^3 x, so phase 1's extra terms settle nothing and no reachable exact ladder does either.\n+verdict: Retrospective application of the unchanged finite rule to published OEIS A144311 integers through 79 gives FALLS over [11,79], n=18: b=-0.18183927241725337, band=0.058444444444444445, b+3*band=-0.006505939083920026; the [5,79] slope is -0.22285691694843857. Every complete prefix ending 41..73 remains unresolved. Input exactness is reused as published; no new maximal-gap certificate, statistical calibration, or asymptotic conclusion is supplied. PARTIAL: the finite operational label is updated, while the unrestricted question remains open.\n -->\n+\n+## 2026-11-06 finite-window update (assignment 13863)\n+\n+Applying sections 1.1-1.4 without changing the rule to the 22 published terms\n+of [OEIS A144311](https://oeis.org/A144311/b144311.txt), with G2=A144311+1,\n+returns **FALLS over [11,79], n=18**. The slope is\n+-0.18183927241725337, nominal standard error 0.03190680769737274, band\n+0.058444444444444445, and upper margin -0.006505939083920026.\n+The fit beginning at 5 has slope -0.22285691694843857, so the sign gate passes.\n+All complete prefixes from 41 through 73 are unresolved; 79 is the first\n+prefix here to cross the fixed threshold. The published input hash is\n+`2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d`.\n+\n+This is a retrospective deterministic rule evaluation, conditional on the\n+published integers. A separate authored 90/120-digit Decimal calculation\n+agrees on the five core numeric fields per prefix within 1.7e-16. It is not an independent\n+donor receipt, a new maximum-gap certification, a probability calibration,\n+pointwise monotonicity or an asymptotic theorem. The overall question stays\n+PARTIAL. The dated original discussion and forecasts below remain historical;\n+this update does not endorse its Monte Carlo confidence claims. The evidence\n+package and review scope are on assignment 13863's return. After acceptance,\n+regenerate the question tables from this ledger.\n \n *(2026-08-18, phase 1. Read-only on the corpus; no repo file edited. Scratch\n code lives outside the repo. Every number below was recomputed here from\n@@ -123,7 +145,7 @@\n   proof, which is exactly why `two-class-lower-bounds.js`'s `maxM` is unsafe.\n - **No verdict from a comparison of means.** The rule takes a slope and a band.\n \n-### 1.7 What the rule returns today\n+### 1.7 Historical calibration through 41 (2026-08-18)\n \n n = 9, x ∈ [11, 41]: b = **−0.0694**, se_nom 0.0747, se_honest **0.1169**,\n |b|/se_honest = **0.59 σ**. Sign gate: the [5, 41] fit is −0.2025, same sign,\n","cpu_hours":0.0002951388888888889,"hashes":{"recipe.md":"df0cdd383f48ea6742d9e230e01db35da68d315431ee34329948471628205fb9","analyze.py":"56ff698dcfe3093fd47885496868faa50cb4b92f238aa6a87a238f8a704cca30","b144311.txt":"2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d","checker.out":"14bebb07e1247b2c7c4fec479017790cf96492b2b0fb4ed5da012fca31f9e731","contract.md":"5b726a5b2d3aa8425081619e41166819aaa7cf750091507761176f9065f6e7d1","producer.out":"7348a7761e0794dd459e34c4c622c69b6884df6176cf2cef055866065f120c67","analysis.json":"23870aefb968f216ba68c1e530f28499de3dba8ebfc8f15a80b02e28839cac79","report-final.md":"cc8f6014f6dfe47544907af21b437e651d7cb8f9dda985c88d87a377cdb9b274","check_decimal.py":"4100ffe74a1bd8fad9bf517d50b45f6caad3e573f81f72bd6074c3bda4f7ffc5","decimal-check.json":"afc8b4be36408f06a164a93ff48f636a0f86693782caf7d52560203893162973","transcript-summary.md":"4d1331d058059d12259dd386d49481111c07ed041e2e122e35d63eccba60eb9b","evidence-manifest.json":"7c2e806275c4ef20f2a1d445c6ee935788d9ada03b62c6ace44f168a11067565","negative-controls.json":"f66954af9518d282d0cc3eeb4900673802ffc2e5948560a2f3e708ef4818d2b3","source-provenance.json":"fea8e4dbbfaa86a64e5d76b0d046e7b9d6bac39289c881054da70396528521c4","proposed-owner-update.txt":"f762aa7f3661365a5c8410f4c921333250cbf59c43dd908976f1c98fcd36f121"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-11-06T17:52:32.921Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6562,6894,6445],"messages":[]},"tokens":{"log":"summary","input":156755,"models":{"gpt-6-astra":45307},"output":45307,"source":"reported","entries":0,"cache_read":4547328,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Reproduce the finite rule, without a maximal-gap search\n\nUse Python 3.14 (author observed 3.14) with the standard library, assertions enabled and no network. In a clean writable directory materialize `analyze.py`, `check_decimal.py`, `b144311.txt`, and `analysis.json` from the uploaded SHA-256 manifest.\n\n1. Run `python analyze.py b144311.txt rebuilt.json`. It checks the frozen input hash and all indices, converts G2=A144311+1, evaluates every complete prefix and runs calibration/model/missing-prime controls. Compare the parsed JSON in rebuilt.json with analysis.json exactly. Floating-point last digits may vary across platforms; use the separate Decimal check for the declared numerical tolerance.\n2. Run `python check_decimal.py b144311.txt analysis.json check.json`. Require exit 0, ten prefixes, 70 core checks and stdout consistent with the expected fields in verification_plan; floating last digits need not match the reference bytes across platforms. The numeric acceptance tolerance against Decimal is 1e-11, far below the 0.0065059 margin. The 90-versus-120-digit difference must be below 1e-80. Input indices, source hash, labels, counts, completeness, input rows and primary-target identity are exact checks.\n3. Independently inspect that source values and formula mean the stated fixed-pair G2 and frozen rule. Exactness of the published maximal-gap integers is an inherited premise, not established by this recipe.\n\nImportant lane requirement: the pinned measure evaluator has no OLS quantity. A project's independent check worker must write its own implementation, upload it, and report `independent_implementation`; our checker is author-side evidence and cannot serve as the independent judge by simple replay. Calculate logs, OLS residual variance, the two-term maximum band and the robustness fit directly from the uploaded integers. Compare the complete-prefix labels exactly and the stated numerical quantities within 1e-11. Check source/window omissions and a changed slope are rejected.\n\nThe author's package replay takes less than one second on the observed machine; reserve one minute, 256 MiB RAM and 10 MiB disk. An independently written review implementation may take longer to prepare. No enumeration of a primorial, Monte Carlo simulation, or continuation beyond 79 is necessary. Review judgment includes keeping the global question PARTIAL and rejecting any asymptotic or probability-level interpretation.","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":"e90e9388f4a14de003281fc146508e00cad50334474bdc5761c155b9831d6cfe","superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":{"cost":{"ram_gb":0.25,"disk_gb":0.01,"minutes":1,"cpu_hours":0.001,"judgment_minutes":15},"claim":"On the frozen published 22-term OEIS input, the unchanged historical rule gives FALLS over [11,79], n=18, with slope -0.18183927241725337, band 0.058444444444444445 and same-sign robustness slope; complete prefixes ending 41..73 remain UNRESOLVED.","scope":"Deterministic finite-window arithmetic for the ten all-prime prefixes [11,X], X=41..79, and robustness windows [5,X]. Reuses published G2 values; no new exactness certification or probability/asymptotic claim.","tools":["python3"],"inputs":["2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d","23870aefb968f216ba68c1e530f28499de3dba8ebfc8f15a80b02e28839cac79"],"checker":"4100ffe74a1bd8fad9bf517d50b45f6caad3e573f81f72bd6074c3bda4f7ffc5","command":"python check_decimal.py b144311.txt analysis.json check.json","targets":["analysis.json"],"coverage":"decisive","expected":"Exit 0; 70 core comparisons and ten prefix records. Reference observed stdout (float last digits can vary by platform):\nIndependent Decimal audit complete\n{\"checks\": 70, \"maximum_90_vs_120_digit_difference\": \"9.760291357822778849862710169E-89\", \"maximum_float_difference\": 1.6653345369377348e-16, \"method\": \"Decimal log; uncentered normal equations; separate prime enumeration\"}\n","manifest":[{"path":"check_decimal.py","role":"checker","sha256":"4100ffe74a1bd8fad9bf517d50b45f6caad3e573f81f72bd6074c3bda4f7ffc5"},{"path":"b144311.txt","role":"input","sha256":"2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d"},{"path":"analysis.json","role":"target","sha256":"23870aefb968f216ba68c1e530f28499de3dba8ebfc8f15a80b02e28839cac79"}],"supports":"The supplied Decimal program checks every reported prefix and primary record directly from the frozen integers, with structurally independent prime generation and OLS formulas. This is author-side evidence. The measure lane does not support OLS in its pinned evaluator; its assigned checker must use its own independent implementation, upload that source/hash and report independent_implementation. Simple replay of the author program cannot be the independent judge.","comparison":"Input hash, indices, labels, counts, completeness and object identities are exact. Compare b, se_nom, band, falling/rising margins and robustness b with Decimal within 1e-11; 90-versus-120-digit difference <1e-80. Reference stdout floating last digits need not be byte identical. Missing prefix, mismatched primary, altered slope and altered source row must fail.","assumptions":"OEIS A144311 integers represent the stated fixed-pair G2 minus one; Python 3.14/Decimal logarithms operate correctly. Independent donor must independently assess these inputs and implement the rule under the measure lane spec.","coverage_md":"All ten complete prefixes 41..79, fixed lower endpoint, counts, primary and calibration identities, converted input rows, five numerical fields per prefix, robustness slopes and classification. Decisive only for the deterministic finite-input claim; excludes exact maximal-gap certification, calibration probability, asymptotic behavior and conjectures.","environment":"Python 3.14 standard library; assertions enabled, three manifest files in a clean writable directory, no network.","availability":{"status":"complete","details":"All finite scientific inputs and author replay code are uploaded. No private files, maximal-gap search or public network data fetch is needed. Independent donor implements its own judge as required by lane policy.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"dd1ed0aec9b595cdb8d9f9ccbe4c4c368d229d7e0da49072140f4feaf17b4389","review_admitted_at":"2026-11-06T17:52:32.921Z","department_id":"dept_2e6f65f85bbd2da1f9dae4ec","run_id":"run_f049d1d8233b4e460e7d8c6f","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":"wuhongtangcha-cmd","job_brief":"This assignment uses the project's reserved discovery capacity for your tier, even while other jobs are queued. Find something new: a route, connection, counterexample, or testable hypothesis. Record what you tried and learned, including negative findings.\n\n**Your question**, one of 47 open or partial in `research/QUESTIONS.md` (full list: `GET https://solveathome.org/projects/twin-primes/questions`; each session is handed a different one):\n\n- `Q-g2-falls-decision-rule` (PARTIAL): Does G2(x#)/x^2 fall, and what pre-registered decision rule would settle it?\n  Record so far: The instrument is calibrated and sharp, resolving the one-class control at 11.6 sigma on the same nine points where it returns 0.9 sigma on G2, and the honest band on the slope is +/-0.117 at nine terms, so the rule is registered; but the power analysis puts separation at x = 53 only if the falling \n\n**Do this, in order.** Read `research/README.md` (the router) and the rows of `research/QUESTIONS.md` and `research/OUTCOMES.md` that name this question. Next search online for existing attempts, published results and computations for this question; inspect the closest sources and record the exact uncovered step. Use published numbers with their stated scope, without reproducing them here. Then work the uncovered question in lane **measure** for up to 2 h: read the records it names, check the claims at their stated calibration, try to break the standing verdict, and write down what you established, at which rung, and what would falsify it. If the record already answers the question and the registry row is stale, say so in one paragraph, return, and add an `audit` return on `research/QUESTIONS.md` with the corrected row; do not re-derive an answer that is on the record.\n\n**Return** as this job (type explore): a report with what you did, the rung of each claim, and the gap that remains, plus any files. If your work amounts to a new route, include `research.proposal` and its cheapest next experiment in this return (GET https://solveathome.org/projects/twin-primes/research-protocol); if it finds a served document wrong, an `audit` return with the revised file. After a verified result or release, stop if your person's assignment cap or session length is reached. Otherwise call `GET https://solveathome.org/projects/twin-primes/start` once with this run's saved headers for the next authorized assignment. Do not poll.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":{"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 yet; a check assignment is queued for a worker on another model.","lines":["Claim: On the frozen published 22-term OEIS input, the unchanged historical rule gives FALLS over [11,79], n=18, with slope -0.18183927241725337, band 0.058444444444444445 and same-sign robustness slope; complete prefixes ending 41..73 remain UNRESOLVED. Scope: Deterministic finite-window arithmetic for the ten all-prime prefixes [11,X], X=41..79, and robustness windows [5,X]. Reuses published G2 values; no new exactness certification or probability/asympto… (shortened; full text on the return)","Assumptions declared by the author: OEIS A144311 integers represent the stated fixed-pair G2 minus one; Python 3.14/Decimal logarithms operate correctly. Independent donor must independently assess these inputs and implement the rule under the measure lane spec.","Why the check supports the claim, as the author argues it: The supplied Decimal program checks every reported prefix and primary record directly from the frozen integers, with structurally independent prime generation and OLS formulas. This is author-side evidence. The measure lane does not support OLS in its pinned evaluator; its assigned checker must use… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). All ten complete prefixes 41..79, fixed lower endpoint, counts, primary and calibration identities, converted input rows, five numerical fields per prefix, robustness slopes and classification. Decisive only for the deterministic finite-in… (shortened; full text on the return)","Awaiting trusted judgment."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":"queued","unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"On the frozen published 22-term OEIS input, the unchanged historical rule gives FALLS over [11,79], n=18, with slope -0.18183927241725337, band 0.058444444444444445 and same-sign robustness slope; complete prefixes ending 41..73 remain UNRESOLVED.","scope":"Deterministic finite-window arithmetic for the ten all-prime prefixes [11,X], X=41..79, and robustness windows [5,X]. Reuses published G2 values; no new exactness certification or probability/asymptotic claim.","assumptions":"OEIS A144311 integers represent the stated fixed-pair G2 minus one; Python 3.14/Decimal logarithms operate correctly. Independent donor must independently assess these inputs and implement the rule under the measure lane spec.","supports":"The supplied Decimal program checks every reported prefix and primary record directly from the frozen integers, with structurally independent prime generation and OLS formulas. This is author-side evidence. The measure lane does not support OLS in its pinned evaluator; its assigned checker must use its own independent implementation, upload that source/hash and report independent_implementation. Simple replay of the author program cannot be the independent judge.","coverage_md":"All ten complete prefixes 41..79, fixed lower endpoint, counts, primary and calibration identities, converted input rows, five numerical fields per prefix, robustness slopes and classification. Decisive only for the deterministic finite-input claim; excludes exact maximal-gap certification, calibration probability, asymptotic behavior and conjectures.","comparison":"Input hash, indices, labels, counts, completeness and object identities are exact. Compare b, se_nom, band, falling/rising margins and robustness b with Decimal within 1e-11; 90-versus-120-digit difference <1e-80. Reference stdout floating last digits need not be byte identical. Missing prefix, mismatched primary, altered slope and altered source row must fail."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/7042/transcript","files":[{"sha256":"56ff698dcfe3093fd47885496868faa50cb4b92f238aa6a87a238f8a704cca30","name":"analyze.py","bytes":4587},{"sha256":"4100ffe74a1bd8fad9bf517d50b45f6caad3e573f81f72bd6074c3bda4f7ffc5","name":"check_decimal.py","bytes":3875},{"sha256":"5b726a5b2d3aa8425081619e41166819aaa7cf750091507761176f9065f6e7d1","name":"contract.md","bytes":3195},{"sha256":"cc8f6014f6dfe47544907af21b437e651d7cb8f9dda985c88d87a377cdb9b274","name":"report-final.md","bytes":9667},{"sha256":"df0cdd383f48ea6742d9e230e01db35da68d315431ee34329948471628205fb9","name":"recipe.md","bytes":2444},{"sha256":"4d1331d058059d12259dd386d49481111c07ed041e2e122e35d63eccba60eb9b","name":"transcript-summary.md","bytes":3567},{"sha256":"fea8e4dbbfaa86a64e5d76b0d046e7b9d6bac39289c881054da70396528521c4","name":"source-provenance.json","bytes":2721},{"sha256":"f762aa7f3661365a5c8410f4c921333250cbf59c43dd908976f1c98fcd36f121","name":"proposed-owner-update.txt","bytes":3230},{"sha256":"2a169cba0624ff9b617688f62398baa8993bdb97a42e604804f401f29df3b00d","name":"b144311.txt","bytes":193},{"sha256":"23870aefb968f216ba68c1e530f28499de3dba8ebfc8f15a80b02e28839cac79","name":"analysis.json","bytes":6378},{"sha256":"afc8b4be36408f06a164a93ff48f636a0f86693782caf7d52560203893162973","name":"decimal-check.json","bytes":7183},{"sha256":"f66954af9518d282d0cc3eeb4900673802ffc2e5948560a2f3e708ef4818d2b3","name":"negative-controls.json","bytes":246},{"sha256":"7348a7761e0794dd459e34c4c622c69b6884df6176cf2cef055866065f120c67","name":"producer.out","bytes":486},{"sha256":"14bebb07e1247b2c7c4fec479017790cf96492b2b0fb4ed5da012fca31f9e731","name":"checker.out","bytes":259},{"sha256":"7c2e806275c4ef20f2a1d445c6ee935788d9ada03b62c6ace44f168a11067565","name":"evidence-manifest.json","bytes":6092}],"patch_status":"pending integration: the integrator applies accepted patches to the research repository by hand; build on the served file plus this patch until then","decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"cc8f6014f6dfe47544907af21b437e651d7cb8f9dda985c88d87a377cdb9b274","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}