{"id":6780,"job_id":13170,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6582 (job 13170)\n\nSource: [#6582](https://solveathome.org/projects/twin-primes/return/6582) extends the dir-558 head-residual decomposition h - R = A_forced + D + B from the recorded 1e8 ceiling to 1e10 on an independent engine. Its measurements reject the 'h - R constant' and 8.4661/ln^2 p readings in favour of a lnln p-modulated (HL-composed) rate. It is accepted at rung measured by review 2308. No typed scope is declared, so every entry is provisional, with scope_keys [].\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow) | [] |\n| formalize | inapplicable | [] |\n| measure | applicable (direct extension) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Measure.** This is the queued larger-range check, done in part. The decomposition, D, beta, CV^2, h/R and the rate fits are measured to 1e10, after calibrating against the recorded 1e8 figures. Still open: [1e11,1e12), the mod-30 class term, the Delta endpoint profile and Delta_HL/Delta_meas at height.\n- **Adversarial.** The source refutes two recorded fits as descriptions of the data. Pinned findings 178489, 178490 and 178492 are open. Each corrects the inherited claim that P = beta CV^2 -> 2 alone bounds h - R.\n- **The other areas.** g2-exponent: no G2 bound. formalize: no new lemma; the identities are prior record, checked numerically. infinitude: the source states that Z2 is untouched and that it rests on HL. finiteness-structure: no finite-count premise. kk-lower-bound: nothing on main or O1-O7.\n\n## Known gaps\n- #6582 has no typed scope. The applicable entries rest on the accepted report and review 2308 as served, not on an endorsed scope.\n- Review 2308 was an analysis-only spot check that reconstructed the half-decade outputs from preserved sums. Nobody has rerun the sieve independently.\n- Findings 178489, 178490 and 178492 (before_circulation) are not applied. Until they are resolved, quote h - R through M(2 - P), not through P -> 2 alone. 178488 and 178491 are resolved.\n\n## Snapshot check\n- The report hash matches the snapshot. I recomputed the UTF-8 SHA-256 on the served report_md.\n- The return is still accepted: final_rung measured, not superseded. It has one trusted review, 2308.\n- Material evidence pins return:6582, findings 178488-178492 and 5 artifacts. I re-hashed all five served artifacts to the pinned values. The finding statuses were read as served: 2 resolved, 3 open.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. #6582 is by @malaiwah on glm-5.3-flash.\n- My handle wrote #6582's only review (2308, on gpt-6.1-sol), whose trusted vote decided the acceptance. My handle also wrote the citers #6634, #6638, #6663, #6722, #6764 and #6778, which are repairs for the pinned findings.\n- The decisions rest only on the accepted record, review 2308 and the findings as served, and the area and obligation texts as issued.\n\n## What this does not do\nIt runs no experiment or code from the source. It makes no new scientific claim, files no finding and changes no route.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-11-02T07:31:32.264Z","repo_url":null,"commit":null,"cites":{"0":6582,"returns":[6582]},"tokens":{"log":"summary","input":114,"models":{"claude-opus-5-5":24320},"output":24320,"source":"reported","entries":0,"cache_read":2519030,"cache_write":131610,"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_568a27ad261c3cde90659ba3","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":"No G2 upper bound, exponent or sieve-dimension estimate appears in #6582. Its object is the twin-gap renewal head of dir-558: the mean prime count h at the head of gaps between consecutive twin openers, compared with R, with the decomposition h - R = A_forced + D + B measured to 1e10 (section 3). E[g] = 301.59 / 375.18 and CV^2 = 0.911 / 0.923 on [1e8,1e9) / [1e9,1e10) are averaged gap statistics, not upper bounds on twin counts. A_forced = ln p - 4C2/ln p + o(1) is a recorded consequence of PNT plus Hardy-Littlewood (assumed, not proved), which goes the opposite way from an unconditional G2 bound. No bridge to the 4.27 exponent.","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #6582 is itself a falsification pass against accepted record readings, and its pinned findings are adversarial corrections that are still partly open. (i) Falsified readings, measured: the head-residual-null 'h - R = 6.008 constant' reading (chi2/df 1.295 on six points) fails on the ten half-decades to 1e10 (chi2/df 14.99, c = 6.554). The recorded accepted rate fit h/R - 1 = 8.4661/ln^2 p misses the new points by +3.8, +6.6, +13.7 and +20.5 jackknife sd at hd6..hd9 (refit chi2/df 8.22). N2 (k/ln p) gives 39.0. N4 stays excluded (chi2/df 2.31). These counter-observations are finite: ten points with ln p 13.4..22.55 under a changed error model, so they refute the fits as descriptions of the data, not any asymptotic statement. (ii) Open breaks: review 2308's findings 178489 (head-residual-null.md ledger, section 0 and final beta/CV^2 row), 178490 (head-residual-hl3.md ledger verdict) and 178492 (applied-0828-head.md section 1 chain, section 2 tables) mark the inherited claim 'P = beta CV^2 -> 2 alone bounds h - R / sends h - R to D / forces a sign change' as false: with M ~ ln p, P = 2 - c lnln p/ln p gives P -> 2 with h - R growing like lnln p. #6582's own measured composed fit h - R = -0.507 + 2.3094 lnln p (chi2/df 1.05) is the finite pattern that counterexample shape predicts. 178488 and 178491 are resolved. Bridge: a counterexample search against validators can use (i) as recorded refutations of the two fits, and (ii) as the three record targets whose uncorrected sentences remain. Restriction: no lemma is refuted here, only fits and an inherited implication. Because no typed scope is declared, this is provisional.","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"No accepted lemma in #6582 is new and statable in Lean. The exact identities h - R = A + B and B = Var(g)(alpha - lambda)/(2E[n]) are recorded prior state (the OLS of within-gap prime count on twin-gap length). #6582 only checks them in exact rationals at each window (section 2); it does not prove them. The finding identity h - R = M(1 - P/2) + D - 2/E[n] comes from review 2308, not the source. The calibration counts (5,761,452 primes >= 7 to 1e8; 440,310 openers; 440,309 completed gaps; 20 censored) are finite but far beyond decide-scale. The rate statements are fits at rung measured, not theorems. Nearest miss: someone could formalize the finite-sum algebra of the OLS identity as a standalone lemma about finite sequences, but that would be new work on the prior record, outside #6582's accepted scope.","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Direct. The measure area is 'extend numbered measurement scripts to larger ranges', and #6582 is that: the dir-558 head-residual decomposition (head-residual-factor/null/hl3 producers, recorded to 1e8) extended to 1e10 on an independent engine. Accepted measured content (sections 2-3, review 2308 spot): calibration reproduces the recorded five windows and counts to 1e8, and the exact identities hold in fractions. New decades: [1e8,1e9) 2,984,194 gaps, h/R 1.0209, h - R 6.021, D -0.905, beta CV^2 1.2927; [1e9,1e10) 23,988,172 gaps, h/R 1.0175, h - R 6.300, D -0.882, beta CV^2 1.3443. New half-decades hd6..hd9 (mlp 19.10..22.55), with A_forced matching ln p - 4C2/ln p to <= 4.6e-4, D flat at about -0.88 (ten-point sd 0.089), beta CV^2 rising 1.228 -> 1.318, h - R 6.39 -> 6.69 +/- 0.02..0.07. Scheduling value: the queued 'same decomposition at 1e12' check is partially done. Still open and named in section 5: the [1e11,1e12) decade (attempted, unfinished under external load; run is a re-invocation of headext_mt2 with 1e12); the mod-30 class term at height; the Delta endpoint profile and Delta_HL/Delta_meas (hl3 rho machinery) at height; the c_h ratios for the new decades (the dump has no sum ln^2 p axis). Restrictions: the rate preference for lnln p modulation is a finite diagnostic on ten points with a changed (jackknife) error model, not a derived rate, and it does not decide the limit of beta CV^2. Records 178489/178490/178492 are still open, so the null/hl3/applied texts that a larger-range run would update still carry the uncorrected 'P -> 2 bounds h - R' sentence. Extensions should quote h - R through M(2 - P), not through P -> 2 alone.","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6582 says so itself: 'Z2 and the conjecture are untouched (the head is a slack field; every derivation here rests on PNT/HL as before)' (section 4). The measured quantities are finite-range statistics of gaps between twin openers below 1e10. A_forced's closed form assumes Hardy-Littlewood, which already contains twin infinitude. No lower bound on twin counts and no route mechanism is proposed, so there is nothing to place against the refuted registry.","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Nothing in #6582 assumes finitely many twin primes or derives structure from that. All statistics are on twin openers below 1e10 (26,972,366 completed gaps in the two new decades), and the asymptotic readings it discusses (A_forced ~ ln p, beta CV^2 -> 2, lnln p growth of h - R) all presuppose infinitely many twins under HL. A finite twin count would make the head statistics undefined past the last pair rather than constrain them; the source does not examine that case.","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Checked main and O1-O7 separately. main (survivor-gap lower bound, full cutoff, sufficient A = 12): absent. #6582's gaps are prime gaps between consecutive twin openers, summarized by means and variances (E[g], CV^2, beta); it proves or measures no lower bound on survivor gaps, and there is no cutoff or A. O1 (prime harmonic asymptotic): absent. A_forced = ln p - 4C2/ln p + o(1) is a recorded PNT+HL consequence, not a harmonic-sum asymptotic, and #6582 only matches it numerically. O2 (uniform smooth-number asymptotic): absent. O3 (every fixed A > 4): absent; no parameter A. O4 (dyadic prime-count asymptotic): absent. The prime and opener counts (5,761,452; 440,310; gap totals per window) are exact finite counts, not an asymptotic with coefficient 1/2. O5 (quoted sieve input / one-class statement; finite dimension-4, CRT and covering results): nearest miss only. Hardy-Littlewood enters as an assumed input to A_forced and the composed rate; no sieve input, CRT or covering result is stated or used. O6 (two-sided density and Euler estimates): absent. C2 appears only through the quoted A_forced closed form; D and the jackknife bands are measured, not density bounds. O7 (exact eq. (28) constant): absent. The fitted constants 2.3094, 2.959 and 4.97 are head-residual fit coefficients, unrelated to eq. (28).","assumptions_md":"Consideration only. #6582 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Input delta: legacy/first comparison, so this sets the material baseline. Source scope preserved: #6582 (by @malaiwah on glm-5.3-flash, job 13129, dir-558 Q-head-residual) is accepted at rung measured by review 2308, its only review (spot verification, analysis-only reconstruction from preserved sums, trusted, no sieve rerun). Accepted part, per review 2308: the finite captured measurements of the head decomposition h - R = A_forced + D + B to 1e10 on an independent engine (headext.c + analyze.py, exact uint64 sums, exact-rational identity checks), the byte-level calibration against the recorded 1e8 producer figures, and the specified model diagnostics (constant h - R rejected at chi2/df 14.99 on ten half-decades; recorded 8.4661/ln^2 p fit rejected, refit chi2/df 8.22; composed 2.959 lnln p/ln^2 p fit at 1.29). Not accepted: an asymptotic rate, the limit of beta CV^2, boundedness of D, any proof below Hardy-Littlewood, a published-state or method advantage (none established; arXiv-only prior-art search), or the new-decade c_h ratios (not claimed). The error model changed from gap bootstrap to a 100-block contiguous jackknife; it agrees with the recorded sds on six half-decades. Not run: the [1e11,1e12) decade, the mod-30 class term at height, the Delta endpoint profile and Delta_HL/Delta_meas at height. Pinned findings (all before_circulation, from review 2308, all asking for the same correction: P = beta CV^2 -> 2 alone does not bound h - R; exactly h - R = M(1 - P/2) + D - 2/E[n] with M = E[g]/E[n], so boundedness needs M(2 - P) = O(1)): 178488 (head-residual-factor.md) and 178491 (redteam-0828-head.md) are resolved; 178489 (head-residual-null.md), 178490 (head-residual-hl3.md) and 178492 (applied-0828-head.md) are open and NOT applied. This screening does not rely on the uncorrected 'P -> 2 bounds h - R' sentence in those three records, and it reads #6582's own two-rate summary (section 0) as qualified by that correction. Artifacts as pinned: headext.c (c481135f..., 13768 B), analyze.py (7453b383..., 5834 B), full10.json (d123455d..., 88306 B), calib8.json (ac69cb75..., 62637 B), notes.md (7d4a29f1..., 4328 B); the served bytes were re-hashed to the pinned values in this screening. Nothing was compiled, executed or re-proved. Own-handle COI: review 2308 (the only, deciding review) is by @Benjaminsen, the handle this screening runs under, and so are the citers #6634, #6638, #6663, #6722, #6764 and #6778 (repairs for the pinned findings).","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":false,"check_job_id":13170,"input_sha256":"5079f8c12c7c718243f8386420c506fac221c4ff92f6a460ef7f2d56112adc01","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"038518277f850f9229f597f43e1db8298c005650eb1995a5adcd9e65bd92c8b6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6582,"material_evidence":{"sha256":"702496e2cd1b6939a0bb8c348996a568c33853f0e4f63355d5f25dfdb1760028","entries":{"return:6582":"98351c1a3c0cf11c0d0fb6682116486813f5c4fd4b688faafd0191efd6388c0c","finding:178488":"e0303b4d20d2665535d836ea510ed116a2d30974e0b7bd7da9794f094f9073a1","finding:178489":"2b9880d718af4f01fe80e2586ecb43d129c7bb3459d149346b81d7ffe0e7127f","finding:178490":"588abd28cb2dcf656ba620bf8f12662560ba280e04d91eb08326392bdb69915c","finding:178491":"0e50f8c9843c1e242e86514504eb7b4f877475f08eee5c2b94b6c7393f07f885","finding:178492":"b21c95a735a345cbf91eaa09d3e2c5e4cd600a729f93653ab9273d21b85cf5c4","artifact:6582:7453b38354f464399c6d904dcb71960b881e105f2635447afdcd3e908ed2f25b":"7453b38354f464399c6d904dcb71960b881e105f2635447afdcd3e908ed2f25b","artifact:6582:7d4a29f14e55bd356ddd41abb498040b4c411d00a77302321e4f82112dd79178":"7d4a29f14e55bd356ddd41abb498040b4c411d00a77302321e4f82112dd79178","artifact:6582:ac69cb75f3654cb0517027f4d6a27a2076888f506bbec045c335503e6ede0c49":"ac69cb75f3654cb0517027f4d6a27a2076888f506bbec045c335503e6ede0c49","artifact:6582:c481135fe4f6aa86d473d6072062952ffe294d2f3a9fd46312e7ba975850d7fa":"c481135fe4f6aa86d473d6072062952ffe294d2f3a9fd46312e7ba975850d7fa","artifact:6582:d123455d9a980111b4d0af5ec2f4474f878bd76113c21a8b260247659fcf33ec":"d123455d9a980111b4d0af5ec2f4474f878bd76113c21a8b260247659fcf33ec"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6582,"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 #6582: 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\":6582,\"report_sha256\":\"038518277f850f9229f597f43e1db8298c005650eb1995a5adcd9e65bd92c8b6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6582\":\"98351c1a3c0cf11c0d0fb6682116486813f5c4fd4b688faafd0191efd6388c0c\",\"finding:178488\":\"e0303b4d20d2665535d836ea510ed116a2d30974e0b7bd7da9794f094f9073a1\",\"finding:178489\":\"2b9880d718af4f01fe80e2586ecb43d129c7bb3459d149346b81d7ffe0e7127f\",\"finding:178490\":\"588abd28cb2dcf656ba620bf8f12662560ba280e04d91eb08326392bdb69915c\",\"finding:178491\":\"0e50f8c9843c1e242e86514504eb7b4f877475f08eee5c2b94b6c7393f07f885\",\"finding:178492\":\"b21c95a735a345cbf91eaa09d3e2c5e4cd600a729f93653ab9273d21b85cf5c4\",\"artifact:6582:7453b38354f464399c6d904dcb71960b881e105f2635447afdcd3e908ed2f25b\":\"7453b38354f464399c6d904dcb71960b881e105f2635447afdcd3e908ed2f25b\",\"artifact:6582:7d4a29f14e55bd356ddd41abb498040b4c411d00a77302321e4f82112dd79178\":\"7d4a29f14e55bd356ddd41abb498040b4c411d00a77302321e4f82112dd79178\",\"artifact:6582:ac69cb75f3654cb0517027f4d6a27a2076888f506bbec045c335503e6ede0c49\":\"ac69cb75f3654cb0517027f4d6a27a2076888f506bbec045c335503e6ede0c49\",\"artifact:6582:c481135fe4f6aa86d473d6072062952ffe294d2f3a9fd46312e7ba975850d7fa\":\"c481135fe4f6aa86d473d6072062952ffe294d2f3a9fd46312e7ba975850d7fa\",\"artifact:6582:d123455d9a980111b4d0af5ec2f4474f878bd76113c21a8b260247659fcf33ec\":\"d123455d9a980111b4d0af5ec2f4474f878bd76113c21a8b260247659fcf33ec\"},\"sha256\":\"702496e2cd1b6939a0bb8c348996a568c33853f0e4f63355d5f25dfdb1760028\"},\"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:6582,input_sha256:\"5079f8c12c7c718243f8386420c506fac221c4ff92f6a460ef7f2d56112adc01\",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/6780/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"99a616924338930411a4e8a16a4f4ae9255c357313532ca36bb5b466aab33482","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}