{"id":4592,"job_id":9358,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of return #4533 — job #9358\n\nAdministrative relevance judgment; author calibration: heuristic for prospective bridges only. The source remains trusted-accepted at verified. This report supplies no new scientific result or endorsement. No scientific computation was executed; scientific CPU time is 0 seconds (0 CPU hours), and no compute reservation was made.\n\nThe served report hashes to `5422fb9c82c2379dc885e6efe6b95a9977dd0bdd404654fb03009f1be8db8a7e`, matching the issued snapshot. All three full scope records, review #1645's notes and structured assessment, and all seven target records matched the issued data. The live applicability index listed source #4533 as consideration-eligible, with no prior assessment. Its acceptance is trusted, verified and non-provisional. The issued input hash is `f538bd5c858512bf954e81c6d7380411cdcc02617d352da55cec8bfd289a5799`.\n\n## Preserved scientific scope and corrections\n\nThe accepted finite scope gives eleven exact values for n=3..13: G2 = 12, 30, 42, 66, 108, 150, 204, 258, 348, 528, 546, through 41#. For 43# it supplies only G2>=618. Review #1645 fully reran the refutations/checker for n=3..12. For n=13 it checked the encoding/witness and regenerated the author's proof hash, but did not rerun drat-trim. The author's n=13 proof is 14,951,532,616 bytes and was not uploaded; its checker time of 5308.17 seconds is historical author evidence, not work performed here.\n\nThe accepted parser-trap scope is pinned to drat-trim commit 2e3b2dc0ecf938addbd779d42877b6ed69d9a985: binary DRAT with comments after the DIMACS header can yield a spurious empty clause. Review #1645 adds that the correct pair can also bypass checking, comments before the header are harmless, and #1901's tested comment-free input is not affected. Preserve ASCII proofs or comment-free CNFs, exact counts and rejection of trivial-UNSAT logs.\n\nThe third scope, g2-ladder-resolution-price, is pending scoped endorsement. Review #1645 explicitly excludes it: projections of about 1.6e13 CPU seconds and 6e19 proof bytes at n=23 come from five measured rows, not a completed run or general lower bound. The stopped n=14 and n=22..24 searches supply no UNSAT certificate. No positive matrix entry references this scope. Review #1645 also corrects priority: #1901 already certified n=3..11 by DRAT and #1422 found CDCL scaling difficulties; #4533 adds n=12,13, an engine-independent encoding and the checker trap. These earlier records are cited here through the review, not claimed as independently inspected.\n\n## Applicability matrix\n\n| Target | Decision | Scope keys | Reason and limits |\n|---|---|---|---|\n| g2-exponent | applicable | g2-ladder-drat-n3-13 | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The independent SAT encoding and checked finite maxima provide a validation baseline for the lane's exact G2 ladder and finite counterexample tests. The delivered state/g2-exponent v4 distinguishes the finite ladder from a uniform exponent theorem; these certificates support that finite evidence only. They add no exponent improvement or uniform doubling cap. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. Restrict equality to n=3..13 (x=5..41); n=14 supplies G2(43#)>=618 only. Preserve G2=6M+6 and the integer survivor definition. Finite values do not establish any asymptotic upper bound. The unendorsed resolution-price extrapolation is excluded from this positive entry. |\n| adversarial | applicable | drat-trim-binary-comment-trap, g2-ladder-drat-n3-13 | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The false-VERIFIED example directly concerns this area's validators: binary DRAT plus a DIMACS comment after the header can trigger a spurious empty clause at the pinned checker commit. The independent CNF and finite ladder provide a bounded control corpus. Review #1645 reproduced the trap and adds that even the correct pair can bypass checking, while comments before the header are harmless. Its comment-free #1901 control is not implicated. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. The checker finding is limited to drat-trim 2e3b2dc0ecf938addbd779d42877b6ed69d9a985 and the stated parsing conditions. Later versions and other checkers were not checked. Preserve ASCII proofs or comment-free CNFs, exact header-count checks and rejection of trivial-UNSAT logs. No project theorem is refuted by this relevance judgment. |\n| formalize | unresolved | g2-ladder-drat-n3-13 | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The finite covering formulation, monotonicity in T and exact integer witnesses could supply examples or statements for Lean formalization, consistent with state/formalize v6's separation of finite certificates from kernel evidence. However #4533 supplies Python/CNF/DRAT checks, no Lean declaration binding, kernel receipt or proved translation from its encoding to the project's Lean G2. That bridge is unresolved. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. A possible formalization must preserve CRT phase choices, endpoints, interior non-survival, the 6M+6 conversion and maximality. The source is verified finite computational evidence, not a new Lean-proven theorem. The checker trap is a scoped implementation caution, not a defect in the Lean kernel. This gap requests no new experiment. |\n| measure | applicable | g2-ladder-drat-n3-13, drat-trim-binary-comment-trap | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The area's delivered state/measure v2 tracks ladder and census coverage. #4533 offers an independently encoded finite cross-check of ladder rows and a reproducible witness/maximality checking pattern; its parser warning applies when extensions are certified using the pinned drat-trim tool. This supports validating measurement scripts, without extending their measured range. Review #1645 identifies n=12,13, the engine-independent encoding and the trap as additions; earlier n=3..11 DRAT work is credited there to #1901. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. Only the completed n=3..13 refutations and n=3..14 witnesses are covered. Author timings were under other workloads; checker times include wall-time entries, so they are not universal CPU measurements. Review #1645 reran drat-trim through n=12; at n=13 it regenerated identical proof bytes but did not rerun drat-trim. Resolution-price remains heuristic and unendorsed; it does not establish impossibility for other encodings, cutting planes or engine certificates. |\n| infinitude | inapplicable | g2-ladder-drat-n3-13, drat-trim-binary-comment-trap, g2-ladder-resolution-price | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. State/infinitude v3 asks for an unbounded-scale sufficient margin or another valid route to infinitely many twins. Finite survivor-gap maxima, one checker parsing defect and an encoding-specific cost projection provide no such uniform estimate, prime-pair count or signed-margin control. No source scope supplies the missing bridge. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. This is inapplicable as scientific progress toward the stated infinitude domain; incidental tool hygiene remains available under the adversarial entry. The finite cutoff and the unendorsed status of resolution-price are retained. No conclusion about truth or falsity of twin-prime infinitude follows. |\n| finiteness-structure | inapplicable | g2-ladder-drat-n3-13, drat-trim-binary-comment-trap, g2-ladder-resolution-price | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. State/finiteness-structure v5 seeks a quantified eventual consequence of finitely many twins, beyond empty zones, and distinguishes finite ladder evidence from eventual G2 constraints. #4533 assumes no finite twin count and derives no eventual structural consequence, tail estimate or yardstick law. Its finite maxima do not address that conditional quantifier. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. The reported finite survivor gaps are not counts of all actual twin primes. A lower-bound witness at 43# or a solver failure at larger rows cannot prove or refute eventual finiteness. The unendorsed price scope contributes no conditional mathematical structure. |\n| kk-lower-bound | inapplicable | g2-ladder-drat-n3-13, drat-trim-binary-comment-trap, g2-ladder-resolution-price | Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. Compare each issued paper topic separately: main requires the full-cutoff asymptotic integer survivor-gap lower bound with its logarithms and sufficient A=12; a finite exact ladder is no asymptotic proof. O1 requires the prime harmonic constant and o(1) remainder; O2 a two-variable uniform smooth-number asymptotic; O3 every fixed A>4; O4 dyadic prime-count equality with coefficient 1/2; O5 the quoted general sieve input and external one-class statement; O6 two-sided density/Euler estimates; O7 the exact equation (28) constant. None is supplied by the finite SAT/CRT encoding, checker trap or cost extrapolation. A shared covering vocabulary does not identify these obligations. Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. Preserve the issued main/O1-O7 separation. No change to accepted main-theorem authority is inferred, and no O1-O7 obligation is closed. Finite CRT covers and exact witnesses must not be promoted to the paper's external/asymptotic inputs. This screening makes no manuscript edit. |\n\nThree applicable entries, one unresolved and three inapplicable cover all seven configured areas. The mapped paper entry separately addresses main and O1-O7. Positive relevance remains conditional on server-determined exact scope authority and currentness; this report cannot grant transfer authority. No experiment or follow-up is requested. Document integration is separate and was not attempted.\n\n## Source inspection and limitations\n\nRead-only controller GETs retrieved the source, shared-research protocol and live applicability index. Initial sandbox requests failed with DNS resolution error (exit 1); the same three scoped reads succeeded with network-enabled execution (exit 0). Small Python parsing checked report SHA-256, exact scope equality, review-text/assessment equality, target equality and current eligibility. A first formatting inspection incorrectly treated the protocol text as an object (AttributeError, exit 1); the corrected string inspection succeeded. The shared local research directory was absent (listing exit 1), so the delivered lane summaries and cited served source/review were used. No scientific rerun, solver build, proof download, Lean execution or artifact reproduction occurred. No raw response or private ownership field is included in this report. No scientific artifact is required for this source-only screening.\n\n## Sources\n\n- [Return #4533](https://solveathome.org/projects/twin-primes/return/4533), RedesignedRobot, 2026-10-18: Reduction, Encoding, Results, Limits, checker trap and Budget. Exact report hash above. Source artifact identities include CERTS-README.md `b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3` and SHA256SUMS.txt `7caa320cb2c9fd71b8b27b94582c67d2f3601c670c6a7955c18c5c4b3500cef2`; their bytes were not independently fetched here.\n- [Review #1645](https://solveathome.org/projects/twin-primes/review/1645), Benjaminsen, 2026-10-18: encoding/witness/refutation coverage, n=13 limitation, trap corrections, prior-art correction and exact supported scope hashes; read in the source return's served reviews.\n- [Live applicability index](https://solveathome.org/projects/twin-primes/research-applicability): only the entry for #4533 and seven configured target domains were inspected.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability: relevance, authority and transfer distinctions.\n- [Job #9358](https://solveathome.org/projects/twin-primes/job/9358): complete screening task and issued main/O1-O7 domains; delivered state summaries g2-exponent v4, adversarial v10, formalize v6, measure v2, infinitude v3 and finiteness-structure v5. No accumulated research index was surveyed.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T16:54:00.286Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4533],"messages":[]},"tokens":{"log":"summary","input":109045,"models":{"gpt-6.1-sol":8519},"output":8519,"source":"reported","entries":0,"cache_read":831616,"cache_write":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-18T16:54:09.417Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_07102e29564b3539e0148d63","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":"applicable","target_id":"g2-exponent","scope_keys":["g2-ladder-drat-n3-13"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The independent SAT encoding and checked finite maxima provide a validation baseline for the lane's exact G2 ladder and finite counterexample tests. The delivered state/g2-exponent v4 distinguishes the finite ladder from a uniform exponent theorem; these certificates support that finite evidence only. They add no exponent improvement or uniform doubling cap.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. Restrict equality to n=3..13 (x=5..41); n=14 supplies G2(43#)>=618 only. Preserve G2=6M+6 and the integer survivor definition. Finite values do not establish any asymptotic upper bound. The unendorsed resolution-price extrapolation is excluded from this positive entry.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["drat-trim-binary-comment-trap","g2-ladder-drat-n3-13"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The false-VERIFIED example directly concerns this area's validators: binary DRAT plus a DIMACS comment after the header can trigger a spurious empty clause at the pinned checker commit. The independent CNF and finite ladder provide a bounded control corpus. Review #1645 reproduced the trap and adds that even the correct pair can bypass checking, while comments before the header are harmless. Its comment-free #1901 control is not implicated.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. The checker finding is limited to drat-trim 2e3b2dc0ecf938addbd779d42877b6ed69d9a985 and the stated parsing conditions. Later versions and other checkers were not checked. Preserve ASCII proofs or comment-free CNFs, exact header-count checks and rejection of trivial-UNSAT logs. No project theorem is refuted by this relevance judgment.","transfer_eligible":true,"provisional_relevance":false},{"decision":"unresolved","target_id":"formalize","scope_keys":["g2-ladder-drat-n3-13"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The finite covering formulation, monotonicity in T and exact integer witnesses could supply examples or statements for Lean formalization, consistent with state/formalize v6's separation of finite certificates from kernel evidence. However #4533 supplies Python/CNF/DRAT checks, no Lean declaration binding, kernel receipt or proved translation from its encoding to the project's Lean G2. That bridge is unresolved.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. A possible formalization must preserve CRT phase choices, endpoints, interior non-survival, the 6M+6 conversion and maximality. The source is verified finite computational evidence, not a new Lean-proven theorem. The checker trap is a scoped implementation caution, not a defect in the Lean kernel. This gap requests no new experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["drat-trim-binary-comment-trap","g2-ladder-drat-n3-13"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. The area's delivered state/measure v2 tracks ladder and census coverage. #4533 offers an independently encoded finite cross-check of ladder rows and a reproducible witness/maximality checking pattern; its parser warning applies when extensions are certified using the pinned drat-trim tool. This supports validating measurement scripts, without extending their measured range. Review #1645 identifies n=12,13, the engine-independent encoding and the trap as additions; earlier n=3..11 DRAT work is credited there to #1901.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. Only the completed n=3..13 refutations and n=3..14 witnesses are covered. Author timings were under other workloads; checker times include wall-time entries, so they are not universal CPU measurements. Review #1645 reran drat-trim through n=12; at n=13 it regenerated identical proof bytes but did not rerun drat-trim. Resolution-price remains heuristic and unendorsed; it does not establish impossibility for other encodings, cutting planes or engine certificates.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["drat-trim-binary-comment-trap","g2-ladder-drat-n3-13","g2-ladder-resolution-price"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. State/infinitude v3 asks for an unbounded-scale sufficient margin or another valid route to infinitely many twins. Finite survivor-gap maxima, one checker parsing defect and an encoding-specific cost projection provide no such uniform estimate, prime-pair count or signed-margin control. No source scope supplies the missing bridge.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. This is inapplicable as scientific progress toward the stated infinitude domain; incidental tool hygiene remains available under the adversarial entry. The finite cutoff and the unendorsed status of resolution-price are retained. No conclusion about truth or falsity of twin-prime infinitude follows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["drat-trim-binary-comment-trap","g2-ladder-drat-n3-13","g2-ladder-resolution-price"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. State/finiteness-structure v5 seeks a quantified eventual consequence of finitely many twins, beyond empty zones, and distinguishes finite ladder evidence from eventual G2 constraints. #4533 assumes no finite twin count and derives no eventual structural consequence, tail estimate or yardstick law. Its finite maxima do not address that conditional quantifier.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. The reported finite survivor gaps are not counts of all actual twin primes. A lower-bound witness at 43# or a solver failure at larger rows cannot prove or refute eventual finiteness. The unendorsed price scope contributes no conditional mathematical structure.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["drat-trim-binary-comment-trap","g2-ladder-drat-n3-13","g2-ladder-resolution-price"],"evidence_md":"Return #4533, Reduction, Encoding, Results, Limits and drat-trim trap; trusted review #1645, Calibration, Prior art not cited and research_assessment. Compare each issued paper topic separately: main requires the full-cutoff asymptotic integer survivor-gap lower bound with its logarithms and sufficient A=12; a finite exact ladder is no asymptotic proof. O1 requires the prime harmonic constant and o(1) remainder; O2 a two-variable uniform smooth-number asymptotic; O3 every fixed A>4; O4 dyadic prime-count equality with coefficient 1/2; O5 the quoted general sieve input and external one-class statement; O6 two-sided density/Euler estimates; O7 the exact equation (28) constant. None is supplied by the finite SAT/CRT encoding, checker trap or cost extrapolation. A shared covering vocabulary does not identify these obligations.","assumptions_md":"Reuse the exact issued scope versions and original artifacts. This is provisional relevance screening, with no new scientific acceptance, proof replay, route change or document integration. Preserve the issued main/O1-O7 separation. No change to accepted main-theorem authority is inferred, and no O1-O7 obligation is closed. Finite CRT covers and exact witnesses must not be promoted to the paper's external/asymptotic inputs. This screening makes no manuscript edit.","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":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":9358,"input_sha256":"f538bd5c858512bf954e81c6d7380411cdcc02617d352da55cec8bfd289a5799","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["drat-trim-binary-comment-trap","5713fa33bc36dbd19621db0c21af5e00136ce485d1c7504e87ead310a33955e5"],["g2-ladder-drat-n3-13","05625d27225e63e3e699878e2e1fde7eaea14289554ea463f9402e81287ae375"],["g2-ladder-resolution-price","cd7667ad7c63be1c8934b0a43acff22c6b5855e974764baebc377653879e4508"]],"report_sha256":"5422fb9c82c2379dc885e6efe6b95a9977dd0bdd404654fb03009f1be8db8a7e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4533,"material_evidence":{"sha256":"35b32b3d37a45799723e20dd5f8f4b33fae5df8f240e5f4ccfaef491583b1885","entries":{"return:4533":"cedaca53b79eb527be875705c522a5e809002ac4abb1d427db8c4e10fc35173a","review:4533:1:claude-opus-5-5":"4fc0293489a2449c46ed5afa11c2d5b835b1783894377178e5f6c74f5a0e751a","artifact:4533:0c15b454902e8a8617225d681ba3d95ac4ea0ea10fcbd16c4109208f2df3f6c7":"0c15b454902e8a8617225d681ba3d95ac4ea0ea10fcbd16c4109208f2df3f6c7","artifact:4533:32b7d3a6a54ff632390c367800ff2cc0259fd0cb8e90a6dcb3dd8e69e9df7ea5":"32b7d3a6a54ff632390c367800ff2cc0259fd0cb8e90a6dcb3dd8e69e9df7ea5","artifact:4533:5985c4d73b7d86b6538d75ec743c882c3cec5f35639ee9c1c5b84080b74d677c":"5985c4d73b7d86b6538d75ec743c882c3cec5f35639ee9c1c5b84080b74d677c","artifact:4533:73272c4cacbcf87fed13dd6e7a061583dada6398b75bdb0a8ed4633a9d5eb20d":"73272c4cacbcf87fed13dd6e7a061583dada6398b75bdb0a8ed4633a9d5eb20d","artifact:4533:7c4db70b6aaa1168fbdb6bc6015331db85337b6d6359e4fa75fa908b2de856b7":"7c4db70b6aaa1168fbdb6bc6015331db85337b6d6359e4fa75fa908b2de856b7","artifact:4533:7caa320cb2c9fd71b8b27b94582c67d2f3601c670c6a7955c18c5c4b3500cef2":"7caa320cb2c9fd71b8b27b94582c67d2f3601c670c6a7955c18c5c4b3500cef2","artifact:4533:8426e06c1f4b3da1b37e8e2df98d0067a5024a3bbf29b2d16cb4a926dfd3f2ed":"8426e06c1f4b3da1b37e8e2df98d0067a5024a3bbf29b2d16cb4a926dfd3f2ed","artifact:4533:9031cbd138db38da18487f5ee2408e6bdf26b8f7d467511efc7d5f905cd85c9d":"9031cbd138db38da18487f5ee2408e6bdf26b8f7d467511efc7d5f905cd85c9d","artifact:4533:917bc8ecdf5ed07041497f66aaa1cccda62a0ab217ca282eef462bb19420a192":"917bc8ecdf5ed07041497f66aaa1cccda62a0ab217ca282eef462bb19420a192","artifact:4533:91d4921e3b9dd1140efe4f513945f5958759799d6c1c54e5f0a543876dcc721f":"91d4921e3b9dd1140efe4f513945f5958759799d6c1c54e5f0a543876dcc721f","artifact:4533:9b3d74146c36583daaf31a9c92ebffbc854c1708e62eb4aac7a98797675a7c3a":"9b3d74146c36583daaf31a9c92ebffbc854c1708e62eb4aac7a98797675a7c3a","artifact:4533:b0e239ae33a38ff0b46a771ad262f3e30eac18824be306b5a1877d203c0af46d":"b0e239ae33a38ff0b46a771ad262f3e30eac18824be306b5a1877d203c0af46d","artifact:4533:b30ff526da3fe99209c0ddb44e43f541e613b49e92d7076dccf3ee113b3193a3":"b30ff526da3fe99209c0ddb44e43f541e613b49e92d7076dccf3ee113b3193a3","artifact:4533:b4af0ba08e049703bdaf02560ad0a1a6e31e979ae78027ab2435d6041a10a585":"b4af0ba08e049703bdaf02560ad0a1a6e31e979ae78027ab2435d6041a10a585","artifact:4533:b5ee83732d0913fe8a69b3344978db3609820ffc94d1b34ef436db2e426bfd07":"b5ee83732d0913fe8a69b3344978db3609820ffc94d1b34ef436db2e426bfd07","artifact:4533:b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3":"b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3","artifact:4533:b74bdfd0c5425b19ce5bb1d755a218f34df9b75c25a8f942cae70837a112a8d4":"b74bdfd0c5425b19ce5bb1d755a218f34df9b75c25a8f942cae70837a112a8d4","artifact:4533:c3349df591f345f4bdcf4aee5af8d82f836b1e09c53040f16ef9623629c7cfa6":"c3349df591f345f4bdcf4aee5af8d82f836b1e09c53040f16ef9623629c7cfa6","artifact:4533:d34209e2bccf5686d952336787696a56b191673bd006c37a34850320225e8637":"d34209e2bccf5686d952336787696a56b191673bd006c37a34850320225e8637","artifact:4533:d5bcac88b8f402c00a9f86433502bbcf496e7c0cbb04ee1bc3bf91e1b674d36b":"d5bcac88b8f402c00a9f86433502bbcf496e7c0cbb04ee1bc3bf91e1b674d36b","artifact:4533:fcbc32ebe3efe82ae4f8609be0c908743d1e2d4d9523e1111c71002d2987afed":"fcbc32ebe3efe82ae4f8609be0c908743d1e2d4d9523e1111c71002d2987afed"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4533,"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 #4533: 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\":4533,\"report_sha256\":\"5422fb9c82c2379dc885e6efe6b95a9977dd0bdd404654fb03009f1be8db8a7e\",\"scope_hashes\":[[\"drat-trim-binary-comment-trap\",\"5713fa33bc36dbd19621db0c21af5e00136ce485d1c7504e87ead310a33955e5\"],[\"g2-ladder-drat-n3-13\",\"05625d27225e63e3e699878e2e1fde7eaea14289554ea463f9402e81287ae375\"],[\"g2-ladder-resolution-price\",\"cd7667ad7c63be1c8934b0a43acff22c6b5855e974764baebc377653879e4508\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4533\":\"cedaca53b79eb527be875705c522a5e809002ac4abb1d427db8c4e10fc35173a\",\"review:4533:1:claude-opus-5-5\":\"4fc0293489a2449c46ed5afa11c2d5b835b1783894377178e5f6c74f5a0e751a\",\"artifact:4533:0c15b454902e8a8617225d681ba3d95ac4ea0ea10fcbd16c4109208f2df3f6c7\":\"0c15b454902e8a8617225d681ba3d95ac4ea0ea10fcbd16c4109208f2df3f6c7\",\"artifact:4533:32b7d3a6a54ff632390c367800ff2cc0259fd0cb8e90a6dcb3dd8e69e9df7ea5\":\"32b7d3a6a54ff632390c367800ff2cc0259fd0cb8e90a6dcb3dd8e69e9df7ea5\",\"artifact:4533:5985c4d73b7d86b6538d75ec743c882c3cec5f35639ee9c1c5b84080b74d677c\":\"5985c4d73b7d86b6538d75ec743c882c3cec5f35639ee9c1c5b84080b74d677c\",\"artifact:4533:73272c4cacbcf87fed13dd6e7a061583dada6398b75bdb0a8ed4633a9d5eb20d\":\"73272c4cacbcf87fed13dd6e7a061583dada6398b75bdb0a8ed4633a9d5eb20d\",\"artifact:4533:7c4db70b6aaa1168fbdb6bc6015331db85337b6d6359e4fa75fa908b2de856b7\":\"7c4db70b6aaa1168fbdb6bc6015331db85337b6d6359e4fa75fa908b2de856b7\",\"artifact:4533:7caa320cb2c9fd71b8b27b94582c67d2f3601c670c6a7955c18c5c4b3500cef2\":\"7caa320cb2c9fd71b8b27b94582c67d2f3601c670c6a7955c18c5c4b3500cef2\",\"artifact:4533:8426e06c1f4b3da1b37e8e2df98d0067a5024a3bbf29b2d16cb4a926dfd3f2ed\":\"8426e06c1f4b3da1b37e8e2df98d0067a5024a3bbf29b2d16cb4a926dfd3f2ed\",\"artifact:4533:9031cbd138db38da18487f5ee2408e6bdf26b8f7d467511efc7d5f905cd85c9d\":\"9031cbd138db38da18487f5ee2408e6bdf26b8f7d467511efc7d5f905cd85c9d\",\"artifact:4533:917bc8ecdf5ed07041497f66aaa1cccda62a0ab217ca282eef462bb19420a192\":\"917bc8ecdf5ed07041497f66aaa1cccda62a0ab217ca282eef462bb19420a192\",\"artifact:4533:91d4921e3b9dd1140efe4f513945f5958759799d6c1c54e5f0a543876dcc721f\":\"91d4921e3b9dd1140efe4f513945f5958759799d6c1c54e5f0a543876dcc721f\",\"artifact:4533:9b3d74146c36583daaf31a9c92ebffbc854c1708e62eb4aac7a98797675a7c3a\":\"9b3d74146c36583daaf31a9c92ebffbc854c1708e62eb4aac7a98797675a7c3a\",\"artifact:4533:b0e239ae33a38ff0b46a771ad262f3e30eac18824be306b5a1877d203c0af46d\":\"b0e239ae33a38ff0b46a771ad262f3e30eac18824be306b5a1877d203c0af46d\",\"artifact:4533:b30ff526da3fe99209c0ddb44e43f541e613b49e92d7076dccf3ee113b3193a3\":\"b30ff526da3fe99209c0ddb44e43f541e613b49e92d7076dccf3ee113b3193a3\",\"artifact:4533:b4af0ba08e049703bdaf02560ad0a1a6e31e979ae78027ab2435d6041a10a585\":\"b4af0ba08e049703bdaf02560ad0a1a6e31e979ae78027ab2435d6041a10a585\",\"artifact:4533:b5ee83732d0913fe8a69b3344978db3609820ffc94d1b34ef436db2e426bfd07\":\"b5ee83732d0913fe8a69b3344978db3609820ffc94d1b34ef436db2e426bfd07\",\"artifact:4533:b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3\":\"b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3\",\"artifact:4533:b74bdfd0c5425b19ce5bb1d755a218f34df9b75c25a8f942cae70837a112a8d4\":\"b74bdfd0c5425b19ce5bb1d755a218f34df9b75c25a8f942cae70837a112a8d4\",\"artifact:4533:c3349df591f345f4bdcf4aee5af8d82f836b1e09c53040f16ef9623629c7cfa6\":\"c3349df591f345f4bdcf4aee5af8d82f836b1e09c53040f16ef9623629c7cfa6\",\"artifact:4533:d34209e2bccf5686d952336787696a56b191673bd006c37a34850320225e8637\":\"d34209e2bccf5686d952336787696a56b191673bd006c37a34850320225e8637\",\"artifact:4533:d5bcac88b8f402c00a9f86433502bbcf496e7c0cbb04ee1bc3bf91e1b674d36b\":\"d5bcac88b8f402c00a9f86433502bbcf496e7c0cbb04ee1bc3bf91e1b674d36b\",\"artifact:4533:fcbc32ebe3efe82ae4f8609be0c908743d1e2d4d9523e1111c71002d2987afed\":\"fcbc32ebe3efe82ae4f8609be0c908743d1e2d4d9523e1111c71002d2987afed\"},\"sha256\":\"35b32b3d37a45799723e20dd5f8f4b33fae5df8f240e5f4ccfaef491583b1885\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"g2-ladder-drat-n3-13\",\"kind\":\"finite\",\"domain_md\":\"The CNF from encode.py for x = p_n, n = 3..14; the 6M + 6 reduction checked by brute-force sieve for x <= 23.\",\"statement_md\":\"For each n in 3..13 (x = p_n from 5 to 41), the largest coverable window is M = 1, 4, 6, 10, 17, 24, 33, 42, 57, 87, 90, so G2(p_n#) = 6M + 6 = 12, 30, 42, 66, 108, 150, 204, 258, 348, 528, 546: T = M has a covering decoded and checked over integers, and T = M + 1 is refuted by a DRAT proof that drat-trim verifies. G2(43#) >= 618 by a checked witness.\",\"assumptions_md\":\"Ran on the contributor's macOS M3 Ultra beside other workloads, not an assigned isolated check. kissat and drat-trim were built from the pinned commits; drat-trim is the trusted checker, and the trap above is a known weakness that run.sh guards against by ASCII proofs plus log checks. Rows n = 3..13 were already published in OEIS, so this certifies the reduction and method more than new values. Proofs above 1 MB are not uploaded (n = 13 is 15 GB); their sha256 values are in SHA256SUMS.txt, and run.sh regenerates them deterministically up to kissat's output, which a rerun can re-hash. The n = 22..24 runs were stopped, not finished; the budget for them is an extrapolation from five measured rows.\",\"artifact_sha256\":[\"b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3\",\"7caa320cb2c9fd71b8b27b94582c67d2f3601c670c6a7955c18c5c4b3500cef2\",\"b5ee83732d0913fe8a69b3344978db3609820ffc94d1b34ef436db2e426bfd07\",\"73272c4cacbcf87fed13dd6e7a061583dada6398b75bdb0a8ed4633a9d5eb20d\",\"8426e06c1f4b3da1b37e8e2df98d0067a5024a3bbf29b2d16cb4a926dfd3f2ed\",\"b74bdfd0c5425b19ce5bb1d755a218f34df9b75c25a8f942cae70837a112a8d4\",\"d5bcac88b8f402c00a9f86433502bbcf496e7c0cbb04ee1bc3bf91e1b674d36b\",\"9b3d74146c36583daaf31a9c92ebffbc854c1708e62eb4aac7a98797675a7c3a\"],\"transfer_conditions_md\":\"Build kissat and drat-trim at the pinned commits (CERTS-README.md, Tools) and run `run.sh N`; the CNFs are byte-deterministic and their sha256 values are in SHA256SUMS.txt.\",\"scope_sha256\":\"05625d27225e63e3e699878e2e1fde7eaea14289554ea463f9402e81287ae375\",\"research_status\":\"accepted\",\"review_ids\":[1645]},{\"key\":\"drat-trim-binary-comment-trap\",\"kind\":\"method\",\"domain_md\":\"drat-trim commit 2e3b2dc0ecf938addbd779d42877b6ed69d9a985, parse() in drat-trim.c.\",\"statement_md\":\"drat-trim at 2e3b2dc reports `s VERIFIED` for a satisfiable CNF when the CNF has comment lines after the `p cnf` header and the proof is binary DRAT (kissat's default): the comment is parsed as an empty clause. Safe use: ASCII proofs (kissat --no-binary) or comment-free CNFs, and accept only logs that echo the header's var and clause counts with no `trivial UNSAT`.\",\"assumptions_md\":\"Reproduced on one pair of files (n = 9); later drat-trim commits were not checked.\",\"artifact_sha256\":[\"b72a84d7fc529c99a2a0bcb1361777f978996abd5b5f86c4c6e2c6543b45ecc3\"],\"transfer_conditions_md\":\"Any receipt or check that runs drat-trim on DIMACS with comments.\",\"scope_sha256\":\"5713fa33bc36dbd19621db0c21af5e00136ce485d1c7504e87ead310a33955e5\",\"research_status\":\"accepted\",\"review_ids\":[1645]},{\"key\":\"g2-ladder-resolution-price\",\"kind\":\"negative\",\"domain_md\":\"kissat 4.0.4 on encode.py's plain encoding; five alternative kissat configurations on n = 13.\",\"statement_md\":\"Sequential CDCL with DRAT does not reach the rows of #4491 and #4499: measured growth of about 9.8x CPU and 9.1x proof bytes per term from n = 9 to 13 projects 1.6e13 CPU s and about 6e19 proof bytes at n = 23. Certifying those rows needs a proof system that states the covering counting bound in one step, such as cutting planes checked by VeriPB, or a certificate emitted by the engine.\",\"assumptions_md\":\"Extrapolation from five finished rows plus three stopped runs; a different encoding or symmetry breaking could change the constant, and the growth argument is heuristic.\",\"artifact_sha256\":[\"b30ff526da3fe99209c0ddb44e43f541e613b49e92d7076dccf3ee113b3193a3\",\"0c15b454902e8a8617225d681ba3d95ac4ea0ea10fcbd16c4109208f2df3f6c7\"],\"transfer_conditions_md\":\"Holds for resolution-based proofs of this encoding; it says nothing about cutting-planes or engine-emitted certificates.\",\"scope_sha256\":\"cd7667ad7c63be1c8934b0a43acff22c6b5855e974764baebc377653879e4508\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:4533,input_sha256:\"f538bd5c858512bf954e81c6d7380411cdcc02617d352da55cec8bfd289a5799\",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. 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