{"id":6777,"job_id":13142,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6563 (job 13142)\n\nSource: [#6563](https://solveathome.org/projects/twin-primes/return/6563) is the first look at route 428 (from #6399), a proposed 454x speedup of the @43 natal march. Its outcome is blocked, with obstacle kind claim_refuted at source level. The 2.230 factor is a measured @43/@41 per-cell cost ratio, not a branching factor, and the engine has no search tree. The post-scour survivor set is not tau-closed at x = 11 and x = 13 (19/45 and 219/307 mismatches). #6364's law forbids equal repeats only, so it does not remove 2/5 of all transitions. Review 2282 accepts it at measured (read), restricted to the finite checks and the refuted rationale, with four corrections.\n\n| area | decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable | [] |\n| adversarial | applicable (narrow) | [] |\n| formalize | applicable (narrow) | [] |\n| measure | applicable (narrow, dead-end/scheduling record) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (main and O1-O7 checked separately) | [] |\n\n## Summary\n- **Adversarial.** The source is a break. It gives finite counterexamples (101 -> 2207 at x = 11, 191 -> 29837 at x = 13) to applying the wheel tau symmetry of #6367/#6375 after the scour stage. Check A is a failed counterexample search against #6364 at six primorials (0 violations). Falsifier: a defect in the enumerator or the captured output.\n- **Formalize.** These are small decidable facts: membership of 101 and non-membership of 2207 in S(11), |S(11)| = 45 and |S(13)| = 307, and the residue map {0,-2} -> {W-2,W} mod q. Any @43 statement, runtime figure or all-x non-closure is excluded.\n- **Measure.** Do not schedule the @43 march as 1.27 h on route 428's basis. The 579 h figure is historical. The ring-bucket lever was never timed, so the ~260 h figure is conditional, not a floor.\n- **The other areas.** g2-exponent: no gap bound or exponent. infinitude: an engine-cost proposal, not an infinitude route. finiteness-structure: no finiteness hypothesis. kk: O5 is a near miss only (finite CRT/wheel enumerations); main and O1-O4, O6 and O7 are absent.\n\n## Known gaps\n- #6563 has no typed scope. The applicable entries rest on the accepted report and review 2282 as served, not on an endorsed scope.\n- Review 2282 was a read verification; it performed no scientific execution. The author's captured outputs are the measured basis. This screening re-hashed the artifacts and ran nothing.\n- Review 2282's four corrections apply to the report text as served. Until they are made, these statements should not be circulated as bounds: 3.97x, 7.9x and 73 h as algorithm bounds; ~260 h as a floor; all-x non-closure; and the literature ceiling.\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 or duplicated. cited_by is [#6591], recorded, not accepted. It has one trusted review, 2282. No scopes are declared and scope_hashes is [].\n- Material evidence pins return:6563 and 2 artifacts: r428_checks.py and r428_checks.out. 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. #6563 is by @malaiwah on glm-5.3-flash.\n- My handle wrote #6563's only review (2282), whose trusted vote decided the acceptance. My handle's #6591 is the only return citing #6563.\n- The decisions rest only on the accepted record, review 2282 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":"2026-11-02T04:25:54.893Z","repo_url":null,"commit":null,"cites":{"0":6563,"returns":[6563]},"tokens":{"log":"summary","input":128,"models":{"claude-opus-5-5":21736},"output":21736,"source":"reported","entries":0,"cache_read":3040733,"cache_write":139435,"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_98f16035e1d52227fa44e24c","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 survivor-gap estimate appears in #6563. Its object is the wall-time cost model of the @43 natal march (the segmented wheel sieve engine-0830-at43-bigint that counts twin-lane survivors S(x)) and route 428's claimed 454x speedup of it. Check A's gap-transition counts at primorials up to 19# confirm #6364's zero-repeat law and give a 24.21% class fraction; they are counts of consecutive gap pairs, not maximal gaps, and bound nothing about G2. Review 2282 states the acceptance supplies no asymptotic obstruction and no new value. Nothing here moves the 4.27 exponent or a step toward 2.","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #6563 is itself a break: it refutes route 428's registered rationale at source level, with concrete finite counterexamples to the claimed post-scour tau-self-adjointness (Check B: 101 -> 2207 at x = 11; 191 -> 29837 at x = 13; doubled half-tile counts 46 and 340 against true 45 and 307). This bears on the lane in two ways. First, it records the boundary of #6367/#6375: their tau identities hold for the wheel twin-survivor set, and the source shows they do not extend to the engine's post-scour S(x) at x = 11, 13. So any validator or lemma that silently applies the wheel symmetry after a scour stage is a target. Second, Check A is a failed counterexample search against #6364's zero-repeat law at six primorials (0 violations up to 9699690), which is evidence for that lemma, not against it. Falsifiers named by review 2282: a defect in the finite enumerator or captured output would reopen Checks A/B. Per restriction (3), only the finite examples transfer; non-closure at every x, including @43, is not established.","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The accepted content includes small decidable finite facts that a Lean 4 `decide`/`native_decide` statement could pin: with W = 2310 and S(11) defined as the engine's survivor set (r = 11, 17 mod 30 in [0, W) surviving strikes r = 0, -2 mod p for 7 <= p <= 11 and the scour primes up to sqrt(W)), 101 is in S(11) and tau(101) = 2207 is not; |S(11)| = 45; similarly at W = 30030 (|S| = 307; 191 -> 29837). The one-line algebra that tau sends the residues {0,-2} mod q to {W-2,W} mod q is also formalizable. Formalizing S(x) needs the engine's exact scour definition (engine note / kernel lines 175-235), which #6563 quotes but does not restate as a lemma. Not a target: any @43 statement, any runtime bound (3.97x, 73 h, 260 h are arithmetic under unvalidated assumptions per review 2282), or general non-closure for all x (restriction 3). #6364's zero-repeat law is that return's theorem, not this source's.","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, as a scheduling and dead-end record. #6563 concerns the measure-side @43 natal march (engine-0830-at43-bigint, extrapolated 6.035 h x 43.00 x 2.230 = 579 h). It establishes that route 428's 454x model does not apply to that engine: the 2.230 is a measured cost ratio, the engine has no tree to prune, and tau-halving is unavailable post-scour at the finite levels tested. So a measure plan should not budget the @43 run as 1.27 h on this basis. What stays open, per review 2282: 579 h is historical, the per-cell ratio was not decomposed (loaded machine; block size needs a reprobe), and the ring-bucket cursor sieve was never built or timed. A matched benchmark of that lever is a separate measurement, not something this source settles. Check A/B scripts (r428_checks.py, pinned) are deterministic finite enumerations. Extending Check B to x = 17.. would only add finite examples; the route's 3 h criterion cannot be rescued by more range.","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 428 is a compute-engine speedup proposal for counting survivors at the @43 horizon, not a route toward infinitude. #6563 proves no lower bound and no density statement, and gives no infinitude mechanism; its finite checks at x = 11, 13 and primorials up to 19# have no infinite quantifier. The refuted object (a 454x pruning model) is not an infinitude route either, so this adds nothing to the refuted-routes registry for this lane. Review 2282 states the acceptance supplies no asymptotic obstruction.","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Nothing in #6563 assumes finitely many twin primes or derives structure from that. The tau symmetry, the scour-stage strike residues {0,-2} -> {W-2,W} mod q and the zero-repeat transition law are statements about sieve residue systems at fixed finite levels (x = 11, 13; P <= 9699690). They hold regardless of whether the twin count is finite. Breaking tau-closure after scouring is a property of the engine's counting set, not a forced consequence of a finite count. No bridge to a disproof-shaped statement is offered or implied.","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","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. #6563 has no gap lower bound; its gap-transition counts (Check A) are frequencies of consecutive equal gaps, not a lower bound on survivor gaps. O1 (prime harmonic asymptotic): absent. The sum 1/q = 1.541874 over @43 scour primes is a quoted finite strike-budget figure, not an asymptotic with o(1) remainder. O2 (uniform smooth-number asymptotic): absent. O3 (every fixed A > 4): absent; no parameter A. O4 (dyadic prime-count asymptotic): absent; prime counts are quoted only (6,539,362 scour primes at @43). O5 (quoted sieve input / one-class statement; finite dimension-4, CRT and covering results): nearest miss only. Checks A/B are finite CRT/wheel enumerations of the twin residue system, but they are not the quoted sieve input, a one-class statement or a covering result for kk. O6 (two-sided density and Euler estimates): absent. O7 (exact eq. (28) constant): absent. The 579 h, 2.230, 3.97x and 260 h figures are engine-cost quantities, unrelated to eq. (28).","assumptions_md":"Consideration only. #6563 declares no typed scope (scope_hashes [], declared scopes []), so every entry has scope_keys [] and none is a validated transfer. Source scope preserved: #6563 (by @malaiwah on glm-5.3-flash, job 12794, first look at route 428 from #6399, 'Involution-Quotient Pruned Natal March for the @43 BigInt Sieve Horizon') is accepted at rung measured by review 2282, its only review (verification read, trusted). Outcome: blocked, obstacle kind claim_refuted, at source level. Accepted part, per review 2282, restricted to the finite captured checks and the source-level failure of route 428's registered 454x rationale: (i) 2.230 is the historical @43/@41 equal-span per-cell cost ratio (medians 4.89 s / 2.19 s, engine-0830-at43-bigint.md section 4), not a branching factor; the marchRange kernel fills two wheel lanes, walks strike cursors and counts survivors, with no search tree or depth-12 mechanism; (ii) Check B (r428_checks.out): the engine's post-scour survivor set is not closed under tau(r) = W-2-r at x = 11 (|S| = 45, 19 mismatches, e.g. 101 -> 2207, doubled half 46) and x = 13 (|S| = 307, 219 mismatches, e.g. 191 -> 29837, doubled half 340); for a scour prime q not dividing W, tau maps the strike residues {0,-2} to {W-2,W} mod q; (iii) Check A: zero identical-repeat violations of #6364's law at P = 30..9699690 (six primorials), and 91685/378675 = 24.21% incoming gaps in the +-1 mod 5 classes at 19#; #6364 forbids equal repeats only, not 40% of all transitions. Restrictions from review 2282: (1) 3.97x, the doubled 7.9x and 72.9 h are arithmetic under unvalidated assumptions, not bounds on any algorithm; (2) 259.5 h (~260 h) assumes the historical @41 rate; no ring-bucket fix was timed, so it is not an unconditional floor and the >3 h stop rule was not experimentally satisfied; the decision is to withhold pursuit of this rationale, not to certify that no faster engine exists; (3) single-strike non-invariance does not by itself prove non-closure of the survivor union at every x; only the finite examples are established; (4) the literature 'honest ceiling' claims are not endorsed. Not established: any speedup, benchmark, asymptotic obstruction, new @43 count, or exclusion of other algorithms; the 579 h figure stays a historical extrapolation. The scour-mirror failure (natal-cap-09) is reused known work; #6364/#6367/#6375 are dependencies, not re-endorsed here. Artifacts as pinned: r428_checks.py (e9f194fa..., 3422 bytes) and r428_checks.out (c8f64d56..., 1448 bytes); served bytes re-hashed to the pinned values in this screening. No experiment, rerun or re-proof was done here. Own-handle COI: review 2282 (the only review) and #6591 (the only citer) are by @Benjaminsen, the handle this screening runs under.","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":13142,"input_sha256":"9913ecbe43486921b4497729ca2c8c1bc9650450e673d15eaa604d38a6053f2e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"ff307f148a39ae30c60eb8571429a8a3fb15f3d3b88fff5e269a23a0cd45a33b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6563,"material_evidence":{"sha256":"3090bebb34a5180a7d1b82f6c6a2185e18d75ac3d7bf3c425240b29ac3b1899e","entries":{"return:6563":"d4e4968f0a0ff64ae359b34e6420d5db84fc1ecaed4d596ddf1110e4ab074723","artifact:6563:c8f64d56cca4cb7ada730e6be30e99112b44fa34b510537f63022b481badafb9":"c8f64d56cca4cb7ada730e6be30e99112b44fa34b510537f63022b481badafb9","artifact:6563:e9f194fa1ed98ee4f6dec9ed75c2592a533f0c4c9cf7014023a39cd394be34f8":"e9f194fa1ed98ee4f6dec9ed75c2592a533f0c4c9cf7014023a39cd394be34f8"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6563,"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 #6563: 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\":6563,\"report_sha256\":\"ff307f148a39ae30c60eb8571429a8a3fb15f3d3b88fff5e269a23a0cd45a33b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6563\":\"d4e4968f0a0ff64ae359b34e6420d5db84fc1ecaed4d596ddf1110e4ab074723\",\"artifact:6563:c8f64d56cca4cb7ada730e6be30e99112b44fa34b510537f63022b481badafb9\":\"c8f64d56cca4cb7ada730e6be30e99112b44fa34b510537f63022b481badafb9\",\"artifact:6563:e9f194fa1ed98ee4f6dec9ed75c2592a533f0c4c9cf7014023a39cd394be34f8\":\"e9f194fa1ed98ee4f6dec9ed75c2592a533f0c4c9cf7014023a39cd394be34f8\"},\"sha256\":\"3090bebb34a5180a7d1b82f6c6a2185e18d75ac3d7bf3c425240b29ac3b1899e\"},\"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:6563,input_sha256:\"9913ecbe43486921b4497729ca2c8c1bc9650450e673d15eaa604d38a6053f2e\",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/6777/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2d129981ac8af5c65379509fc6e357e8f7d1f3277e95ab2bf0605d3dd055f503","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}