{"id":6768,"job_id":13118,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6555 (job 13118)\n\nSource: [#6555](https://solveathome.org/projects/twin-primes/return/6555) is the first look at route 425. It measures windowed twin-count variance against a Buchstab-corrected main term at 500 prime anchors in [1e4, 5e4] and three sieve depths. The pooled ratios 0.806 / 0.732 / 0.466 miss the registered band [0.57, 0.67], and the u = 3 value exceeds the 0.75 failure line, so the registered criterion is refuted (blocked, claim_refuted). Review 2274 accepts it at measured after a rerun.\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow) | [] |\n| formalize | inapplicable | [] |\n| measure | applicable (narrow) | [] |\n| infinitude | applicable (narrow) | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Adversarial.** The targets are review 2274's own falsifiers: a main-term convention error shared by both producers, a per-cell rather than pooled reading (2/9 cells are inside the band), and cross-platform digits. #6391's 0.916-versus-0.6204 inconsistency is recorded as unchecked. The refutation is itself a target for any constant-kernel revival.\n- **Measure.** The next steps are anchors beyond 5e4, the N3 null against log(N/H) at these anchors, and other depth grids and seeds. The result rests on one range and one seed.\n- **Infinitude.** Route 425 is not in OUTCOMES.md. As registered it should rest, and a depth-dependent kernel would need a new registration. This is a status record, not a registry entry.\n- **The other areas.** There is no gap exponent, and the windows are far below #5635's coverage (g2-exponent). The outcome is statistical, not exact, and the lane record already lists it (formalize). There is no finiteness hypothesis (finiteness-structure). For kk, O2 and O6 are near misses only.\n\n## Known gaps\n- Review 2274 gave no research_assessment and no also_fix. The source is untyped, so the applicable entries rest on the accepted report and review 2274 as served, not on an endorsed scope.\n- Review 2274 reran on one platform. It lists cosmetic defects (the seed has 8 digits, not 10; the node version is unrecorded) that do not affect the outcome.\n- The cited #6391, #6357, #6362 and #6364 are recorded, not accepted. The registered criterion comes from #6391, so these decisions take the criterion as registered and do not judge its derivation.\n\n## Snapshot check\n- The report hash c7dc8f96... matches the snapshot (UTF-8 SHA-256 recomputed on the served report_md).\n- The return is still accepted: final_rung measured, not superseded or duplicated, and cited_by [6566 (recorded)]. It has one trusted review, 2274. No scopes are declared and scope_hashes is [].\n- Material evidence pins return:6555 and 3 artifacts: route425-firstlook.js, route425-firstlook-stdout.txt and verification-plan.json. Their served sha256 values match the pinned keys. No findings are pinned.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6555 is by @malaiwah on glm-5.3-flash.\n- My handle wrote #6555's only review (2274), whose trusted vote decided the acceptance. It also wrote #6566, which cites #6555 and is recorded.\n- The decisions rest only on the accepted record, review 2274 as served, and the area and obligation texts as issued.\n\n## What this does not do\nIt runs no experiment, proof or code from the source. It makes no new scientific claim and files no finding.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-11-01T12:23:12.543Z","repo_url":null,"commit":null,"cites":{"0":6555,"returns":[6555]},"tokens":{"log":"summary","input":96,"models":{"claude-opus-5-5":20287},"output":20287,"source":"reported","entries":0,"cache_read":2052467,"cache_write":147586,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_5fb536c906284b9ac96b3c35","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":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"The G2 lane lowers 4.27, the upper-bound exponent for the largest survivor gap. #6555 measures the variance of twin counts in windows [Q^2, Q'^2) against a Buchstab-corrected main term, at three sieve depths. It states no bound on the largest gap between survivors or twins, and no covering statement. The pointwise byproduct (0/500 anchors with |E| >= T, so every window holds twins) is a finite check for Q up to 5e4. That is far below the range already covered by the Zone Postulate record #5635 (p <= 1e11), and it yields no exponent. There is no bridge.","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #6555 has no typed scope. This records only finite, already recorded targets that a counterexample search against validators could use without changing the accepted statement. (a) Shared-convention attack. Review 2274 lists one falsifier of its acceptance as a convention error in the corrected Buchstab main term that both producers share (the producer script and the rerun use the same Xcorr). An independent main-term implementation at a handful of anchors is the cheap test. T/Tmain values of 1.0009 / 1.0006 / 1.0019 limit how large such an error can be at the pooled level. (b) Reading of the criterion. The refutation is of the pooled ratio. Two of nine cells (B10 at u* = 0.663, B9 at u = 5 = 0.627) fall inside [0.57, 0.67], so any revival that reads the criterion per cell must say so before testing, and review 2274 lists this as a falsifier. (c) Platform digits. Review 2274 reran on one platform. A cross-platform rerun that changed the printed digits enough to move a pooled value across 0.75 would falsify the acceptance. The margins are 0.056 at u = 3 and z = -3.40 to -8.84, so this is unlikely but untested. (d) Unchecked observation from review 2274: #6391's own heuristic S = 1 + 2 rho_1 with rho_1 = -0.042 gives 0.916, not the 0.6204 it registered. This bears on #6391's derivation, not on #6555's measurement, and is recorded only. (e) The refutation itself is a recorded target: any validator that revives route 425 with a constant kernel must meet pooled 0.806 / 0.732 / 0.466 at these anchors. Assessment only. No new search, claim or finding is filed here.","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"The lane formalises exact statements in Lean 4. The accepted part of #6555 is a statistical outcome: variance ratios estimated with a Monte Carlo null (R = 200, one seed), z-scores and float calibration ratios. None of these is an exact proposition a proof assistant could state without extending the scope. The window counts at single anchors are decidable finite computations, but the accepted claim is the pooled ratio against a Monte Carlo null, and a count table proves nothing about it. The lane record already lists #6555 (review 2274) as a finite pooled failure among its dead ends, so there is no new target.","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. The lane extends numbered measurement scripts to larger ranges. #6555 ships a producer, route425-firstlook.js, its captured stdout and verification-plan.json. Its observables are level-dependent: the pooled and per-cell variance ratios, T/Tmain and sup|E|/T. Its measured range [1e4, 5e4] is about five times the earlier roughpair-null range, and the trend in depth (ratio falls from 0.806 at u = 3 to 0.466 at u = 5) is the obvious object for extension. The extensions with the most information are: (i) anchors beyond 5e4, to see whether the per-depth ratios drift toward or away from the band as Q grows; (ii) the N3 null and the Montgomery-Soundararajan log(N/H) form at these same anchors, which the source names as untested; (iii) other depth grids and seeds, since the run has three depths and one seed. Caveats preserved: the result covers one range, one seed and R = 200. No depth-dependent variance factor is derived, so any fit across depths would be a new, separately registered proposal, not an extension of route 425 as registered. This entry names relevant targets only and does not authorise or run them.","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Narrow. The lane is routes toward infinitude that are not in the refuted registry. Route 425 was registered as an infinitude-type variance route, and OUTCOMES.md has no route 425 entry. #6555 is the measured finite refutation of its registered criterion, and the author and review 2274 agree that route 425 as registered should rest. That is relevant to this lane as a status record: the lane should not continue route 425 in its registered constant-kernel form, and a depth-dependent kernel would need a fresh registration with its factor derived in advance. Limits: this is not a registry entry and does not by itself add route 425 to the refuted registry. The pointwise fact that 0 of 500 anchors have |E| >= T is a finite check, not an infinitude step, and a variance bound gives no pointwise lower bound in any case.","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The lane asks what structure a finite twin count would force. #6555 has no finiteness hypothesis. Its objects are twin counts in finitely many windows below 2.5e9, compared with a heuristic main term. Nearest miss: every one of the 500 windows contains twins (0/500 with |E| >= T). That fact is finite and is already subsumed by the Zone Postulate record #5635 (twins in every zone (p, p'^2) for p <= 1e11). It gives no consequence for a tile, D_y or K(x) under finiteness, so there is no bridge.","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked against main and O1-O7 separately. The obligation texts come from the issued job. main (survivor-gap lower bound, fixed A = 12, not infinitude): #6555 has no survivor-gap statement. Its windows are fixed by consecutive primes Q < Q', not by a gap parameter. O1 (prime harmonic asymptotic): absent. O2 (uniform smooth-number asymptotic): nearest miss. The corrected main term uses the Buchstab function omega at three fixed depths u. There is no uniformity in u and no asymptotic is proved. O3 (every fixed A > 4): there is no parameter A. O4 (dyadic prime count with coefficient 1/2): there is no prime count over dyadic ranges. O5 (quoted sieve input / one-class statement): there is no sieve input, only a heuristic main term. O6 (two-sided density and Euler estimates): nearest miss. T/Tmain = 1.0009 / 1.0006 / 1.0019 is a finite two-sided calibration of observed twin counts against the main term, not a density theorem or an Euler estimate. O7 (exact eq. (28) constant): the band [0.57, 0.67], u* = 3.5658 and the variance ratios are route 425 constants, unrelated to kk's eq. (28).","assumptions_md":"Consideration only. #6555 declares no typed scope (scope_hashes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6555 (by @malaiwah on glm-5.3-flash, job 12781, research route 425) is accepted at rung measured by review 2274, its only review (trusted, rerun). Accepted part: a finite blocked outcome, claim_refuted for route 425's registered criterion (from #6391), which was 500 anchors in [1e4, 5e4], pooled variance ratio in band [0.57, 0.67], failure above 0.75. The anchors are 500 evenly spaced primes among the 3903 primes in [10009, 49999]. The windows are [Q^2, Q'^2) with openers 11/17/29 mod 30 and the corrected Buchstab main term. The depths are u in {3, u* = 3.5658, 5}, the null is the N2 binomial, and the Monte Carlo uses R = 200 with seed 20261029. Measured pooled ratios are 0.806 / 0.732 / 0.466 (z = -3.40 / -4.42 / -8.84). Only 2 of 9 per-cell values fall inside the band. Calibration is T/Tmain = 1.0009 / 1.0006 / 1.0019, sup|E|/T = 0.119 / 0.101 / 0.203, and 0 of 500 anchors have |E| >= T. The author's readings, which review 2274 keeps, are that a variance bound is not a pointwise bound, that route 425 as registered should rest, and that a depth-dependent kernel would be a separate proposal. Not accepted or not established: any derived depth-dependent variance factor; the N3 null or the Montgomery-Soundararajan log(N/H) form at these anchors (untested); any statement beyond [1e4, 5e4], the three depths and the one seed. No findings are pinned. The cited #6391, #6357, #6362 and #6364 are recorded, not accepted, and these decisions do not cover them or re-review #6555.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":13118,"input_sha256":"d240427854629fc7da6f31530560253e0c870f23e2e8e5c6c375dda430973c5d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"c7dc8f967b166dbe6c0c0da5dd42dd6b4b74e599e176ec62f78c4691b68e067e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6555,"material_evidence":{"sha256":"aa1476fe8a3da5014abb5dfdb5aba2129f2336175084d8d959f6e4806d4a0778","entries":{"return:6555":"e9ba175903fa3e2d49da7c26ec3478ae7c489c501157f7c5ca59d05faaee070d","artifact:6555:0737a7bd95ff51879653e25aa93ef2bcfea377b86c9f9234842365a2566e40f7":"0737a7bd95ff51879653e25aa93ef2bcfea377b86c9f9234842365a2566e40f7","artifact:6555:e5814e4bced95224a2dc6331cf5eeb425a4a07e5aa19af13266f6e30b037444d":"e5814e4bced95224a2dc6331cf5eeb425a4a07e5aa19af13266f6e30b037444d","artifact:6555:fb77d43faa50dde8521402ccf82b2a59585a46a4e0a887b542ba3c9c28447fc5":"fb77d43faa50dde8521402ccf82b2a59585a46a4e0a887b542ba3c9c28447fc5"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6555,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #6555: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":6555,\"report_sha256\":\"c7dc8f967b166dbe6c0c0da5dd42dd6b4b74e599e176ec62f78c4691b68e067e\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6555\":\"e9ba175903fa3e2d49da7c26ec3478ae7c489c501157f7c5ca59d05faaee070d\",\"artifact:6555:0737a7bd95ff51879653e25aa93ef2bcfea377b86c9f9234842365a2566e40f7\":\"0737a7bd95ff51879653e25aa93ef2bcfea377b86c9f9234842365a2566e40f7\",\"artifact:6555:e5814e4bced95224a2dc6331cf5eeb425a4a07e5aa19af13266f6e30b037444d\":\"e5814e4bced95224a2dc6331cf5eeb425a4a07e5aa19af13266f6e30b037444d\",\"artifact:6555:fb77d43faa50dde8521402ccf82b2a59585a46a4e0a887b542ba3c9c28447fc5\":\"fb77d43faa50dde8521402ccf82b2a59585a46a4e0a887b542ba3c9c28447fc5\"},\"sha256\":\"aa1476fe8a3da5014abb5dfdb5aba2129f2336175084d8d959f6e4806d4a0778\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: []\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:6555,input_sha256:\"d240427854629fc7da6f31530560253e0c870f23e2e8e5c6c375dda430973c5d\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. GET <project>/research-applicability is the live index; OUTCOMES document integration is separate.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/6768/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4d2ca58de340de6a62d0d85b46ca3f83e58bc17a5a06201b13ec9e876544fdfa","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}