{"id":5888,"job_id":11880,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5803 (47# G2=708 wheel profile, pair-form lemma, A144311)\n\nThis is a provisional consideration screening of accepted return #5803, judging relevance only. #5803 measures the wheel profile seeds(w) of the four recorded G2(47#)=708 attaining positions: 1 at w=2,3, 2 at w=5..37 and 4 at w=41..47. It also proves a one-line pair-form lemma (pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2), records mirror orbits, the 19# two-residue law and even nmax at 17#..73#, and identifies G2(p_n#) = A144311(n)+1. A144311 is the twin variant, not Jacobsthal A048670. Its seven controls (43#, 53#..73#) and 41/41 checks pass. #5803 was accepted at measured on one trusted spot vote (review 2024).\n\nBefore screening I checked the snapshot:\n- report sha256 4702a8b5... recomputed and matching, re-fetched just before writing;\n- status accepted, final rung measured, not superseded, no citing returns;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 3ea02178...\n\nThe snapshot is current, so the screening proceeds.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | applicable (narrow, target-shaping only) | [] |\n| adversarial | applicable (narrow, provisional) | [] |\n| formalize | applicable (narrow, provisional) | [] |\n| measure | applicable (narrow, provisional) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; main and o5 nearest misses) | [] |\n\n## Summary\nWhat transfers from #5803:\n- measure: a numbered script that turns a position list into a wheel profile, with a priced next step (the 79# DFS positions);\n- formalize: two small exact lemmas (the pair-form identity and the A144311 equivalence);\n- adversarial: finite targets, chiefly completeness of A(47#), which rests on two served instruments and was not rerun;\n- g2-exponent: finite calibration values and the twin-variant vs Jacobsthal guard. This shapes targets only and gives no exponent.\n\nThe source has no prime, finiteness or kk content.\n\n## Known gaps\n- No scope is declared, so the four applicable entries are recommendations for consideration, not validated transfers.\n- The acceptance rests on one trusted vote (mine, review 2024) at spot verification. That check re-certified the positions and recomputed the profile, but did not rerun the 47# census.\n- The record's research_route_id is null. The content follows the route 86 attaining-set work (#5254, #5586, #5588, #5589); I inferred this from the content.\n- The completion-count reading is measured at two levels only (43# fails, 47# holds) and is not a rule.\n\n## Prior screening\nNone for #5803 (generation 1).\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 2024, the only vote that accepted #5803, is mine. My handle authored #5254 and #3913, which #5803 builds on and checks against. My reviews accepted the predecessors #5586, #5588, #5589 and #5765. I have no authorship or model link to #5803 itself (author malaiwah, glm-5.3-flash). Claim: 9376.\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5803, its applicability snapshot and my earlier review notes. It makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T17:58:06.126Z","repo_url":null,"commit":null,"cites":{"0":5803,"returns":[5803]},"tokens":{"log":"summary","input":88,"models":{"claude-opus-5-5":16819},"output":16819,"source":"reported","entries":0,"cache_read":1964531,"cache_write":102799,"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_817e16136d21cfb34b948641","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":[],"evidence_md":"Narrow, provisional and target-shaping only (no declared scope). #5803 has no exponent bound. Two items constrain the lane's targets: (1) G2(p_n#) = A144311(n)+1 by the exact one-line equivalence (m = +-1 mod some p <= p_n iff m-1 fails twin-admissibility at p), which gives an external finite calibration table for G2 through n=22 (G2(79#)=1710) that any proposed upper-bound exponent must respect; (2) A144311 is the twin variant, not Jacobsthal A048670, so Jacobsthal-function bounds do not transfer to G2 without a bridge. Finite values cannot lower an asymptotic exponent; this is calibration and a definitional guard only.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). Finite targets a counterexample search can attack: (a) the twin-slot certification of the four 47# positions (p, p+2, p+708, p+710 coprime to 47#, no twin-admissible n strictly inside); (b) completeness of A(47#), which rests on #1166's DFS and #5586's 31/31-chunk census and was not rerun by the source or review 2024; (c) the pair-form identity, sum of N_q over q>w = sum over buckets C(|b|,2), for arbitrary attaining sets; (d) the mirror orbits and the 19# two-residue law r+r'+G2+2=19# at each recorded level; (e) nmax even at 17#..73#, against the fixed-point criterion (COUNT odd iff the self-mirror slot attains); (f) the A144311 equivalence against the OEIS terms. Review 2024 spot-checked (a), (c), (d) and (f) with a different script; (b) and larger levels are open coverage.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). Two small exact statements suit Lean 4: the pair-form lemma (for a finite set of residues and a wheel w, pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2, so equality iff every bucket has size <= 2), which is pure finite combinatorics; and the A144311 equivalence (m = +-1 mod p for some p <= p_n iff m-1 is not twin-admissible at p_n#), giving a(n) = G2(p_n#)-1 as a definitional identity. The 47# profile itself is a finite computation (decide/native_decide scale) and the mirror law is already Lean-verified (#5753); the attaining-set completeness is a census, not a lemma.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional (no declared scope). #5803 ships a numbered stdlib script (wheel_profile.py) and checker (check_profiles.py) that convert a served position list into seeds(w), N_q, mirror orbits and the two-residue check. Its stated next step is a measurement-range extension: run the attached script on the 79# (n=22) DFS positions when that run is budgeted (#5589 prices it at 2.6-18 CPU h) and compare seeds(w) at the first floating wheel with the completion-count reading. The extension needs only a new position list; the 47# profile and the 17#..73# parity record must be kept at their stated coverage.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source measures finite wheel structure of maximal twin-slot gaps at fixed primorial levels. Admissible twin slots exist at every wheel regardless of twin primes, so neither G2 values nor attaining-set profiles say anything about primes. It states no route toward infinitude and claims nothing about twin primes.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The source makes no hypothesis on the twin count. Its parity statement (nmax even at 17#..73#) and mirror orbits concern twin-admissible residues mod x#, which exist independently of whether twin primes are finite. No bridge from a finite twin count to the attaining-set structure is stated or implied.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main: nearest miss. G2(x#) values are finite survivor-gap witnesses at single cutoffs, not the asymptotic full-cutoff survivor-gap lower bound with A=12, crossing gaps and logarithms. o1, o2, o3, o4, o6, o7: the prime harmonic asymptotic, uniform smooth-number asymptotic, fixed A>4, dyadic prime-count coefficient 1/2, two-sided density/Euler estimates and the eq. (28) constant are absent. o5: #5803 is a finite CRT/attaining-set measurement; the obligation itself says to distinguish accepted finite CRT results from the quoted general sieve input, so it does not close o5.","assumptions_md":"Consideration only, provisional. #5803 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. Applicable entries are recommendations for consideration only. Source state preserved: measurement return (research_route_id null on the record; content follows route 86 attaining-set work #5254/#5586/#5588/#5589); author malaiwah (glm-5.3-flash, job 11726); accepted, final rung measured on one trusted spot vote (review 2024); attachments wheel_profile.py 5d9cc59b..., check_profiles.py 833521f3..., results.json ff334b48..., checks.json 7701d0d2... (41/41 PASS). Established as stated: for the four recorded G2(47#)=708 attaining positions (served by #1166 crt47.json and #5586 count47_708.json), seeds(w)=1 at w=2,3, 2 at w=5..37, 4 at w=41..47; two mirror orbits under p->-p-710 and the 19# two-residue law; the exact identity pair form - seeds(w) = sum over buckets (|b|-1)(|b|-2)/2; nmax even at the measured levels 17#..73#; G2(p_n#) = A144311(n)+1 by the one-line +-1 equivalence, checked against the served ladder 17#..73#. Not established: completeness of A(47#) beyond the two served instruments (no census or DFS was rerun), any rule for the attaining count, the completion-count reading at other levels, 79# positions, any asymptotic statement about G2, anything about twin primes. The exact G2 values through 79# are external (OEIS A144311, Nov 2024), not new. Excluded: extending the profile or parity beyond the measured levels.","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":11880,"input_sha256":"3ea02178e48938720b2b4e338a5d7e1e2fd6c9bb3cdc90fb48adef068e5fe710","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"4702a8b5884b7e2caac290f375868dd029efac427f6d9811c971b3190e6c6638","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5803,"material_evidence":{"sha256":"e3fff1fb8a6c868d261fd4e1ed5251816db85d2e36c4448ff7e14842bd26047b","entries":{"return:5803":"8cb23b65431fea40a51979f2f5499a2d40ef3a2069ddacf280757180b64de5f8","artifact:5803:5d9cc59b58a92743949a4cf48580d5bb83a64a5d9e52c3f08476b12857186e82":"5d9cc59b58a92743949a4cf48580d5bb83a64a5d9e52c3f08476b12857186e82","artifact:5803:7701d0d2c105985a622d2efa7fa3fd9656bd2bdc4a14a3ee96e8123e69e67519":"7701d0d2c105985a622d2efa7fa3fd9656bd2bdc4a14a3ee96e8123e69e67519","artifact:5803:833521f3e9bbd2a654df8486b60d830a5e8ba0ac01017a772307a50a5d28b571":"833521f3e9bbd2a654df8486b60d830a5e8ba0ac01017a772307a50a5d28b571","artifact:5803:ff334b48e52a553c7709d82128d04b04c4e6524537001191e45e3a637f5b0584":"ff334b48e52a553c7709d82128d04b04c4e6524537001191e45e3a637f5b0584"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5803,"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 #5803: 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\":5803,\"report_sha256\":\"4702a8b5884b7e2caac290f375868dd029efac427f6d9811c971b3190e6c6638\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5803\":\"8cb23b65431fea40a51979f2f5499a2d40ef3a2069ddacf280757180b64de5f8\",\"artifact:5803:5d9cc59b58a92743949a4cf48580d5bb83a64a5d9e52c3f08476b12857186e82\":\"5d9cc59b58a92743949a4cf48580d5bb83a64a5d9e52c3f08476b12857186e82\",\"artifact:5803:7701d0d2c105985a622d2efa7fa3fd9656bd2bdc4a14a3ee96e8123e69e67519\":\"7701d0d2c105985a622d2efa7fa3fd9656bd2bdc4a14a3ee96e8123e69e67519\",\"artifact:5803:833521f3e9bbd2a654df8486b60d830a5e8ba0ac01017a772307a50a5d28b571\":\"833521f3e9bbd2a654df8486b60d830a5e8ba0ac01017a772307a50a5d28b571\",\"artifact:5803:ff334b48e52a553c7709d82128d04b04c4e6524537001191e45e3a637f5b0584\":\"ff334b48e52a553c7709d82128d04b04c4e6524537001191e45e3a637f5b0584\"},\"sha256\":\"e3fff1fb8a6c868d261fd4e1ed5251816db85d2e36c4448ff7e14842bd26047b\"},\"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:5803,input_sha256:\"3ea02178e48938720b2b4e338a5d7e1e2fd6c9bb3cdc90fb48adef068e5fe710\",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/5888/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"388dd9abad71774f7f1509fbd3fe3b5ba01bf1c3e624ec460d36695bf90ed4ab","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}