{"id":5745,"job_id":11594,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5531 (route 339 census-to-K* transfer)\n\nThis is a provisional consideration screening of accepted return #5531, judging relevance only. #5531 is a scoped negative on route 339. It proves the elementary identities (1)-(5) at fixed P = 17# = 510510:\n- the interval-vacancy identity V_P(ell) = sum_g h_g max(g-ell,0), with V_P(107)=20 and the R3 correction 20/510510 to #4887;\n- the exact CRT inclusion-exclusion count Z_Q(W) of lifts deleting a slot window;\n- the implication from Z_Q = 0 on all L-windows to K* <= L-1;\n- the capacity obstructions (4)-(5).\n\nIt shows that the census of gaps and starts does not supply the window-phase incidence that a K* transfer needs. The census-only K* transfer stays inconclusive. It was accepted at proven, for (1)-(5) only, on one trusted spot vote, review 1979.\n\nI checked the snapshot before screening: report sha256 4d94dba4... matches, the status is accepted with final rung proven, no scopes are declared, and the return is not superseded. Since the snapshot it is cited by #5572 (route 339 rescue) and #5647 (route 217), both recorded, not accepted. So every entry has scope_keys [] and is consideration only.\n\n## Matrix\n| Area | Decision |\n|---|---|\n| g2-exponent | applicable (narrow) |\n| adversarial | applicable (narrow) |\n| formalize | applicable (narrow) |\n| measure | applicable (narrow) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\nWhat transfers from #5531 is a set of exact finite identities on the twin-admissible wheel at 17#, plus a precise statement of the missing input (window-phase incidence) for a census-only K* bound. That matters to:\n- the G2 lane, as a finite K* criterion and a negative on uniform capacity;\n- adversarial checks of (1)-(5);\n- formalizing (1)-(5);\n- measurement, as a formula and check target, with no script.\n\nIt lowers no exponent and has no infinitude, finiteness or kk content. For kk o5 it is one of the finite CRT/covering results to keep separate from the general sieve input.\n\n## Known gaps\n- #5531 declares no scopes, so every entry is consideration of relevance, not a validated scoped transfer.\n- The acceptance rests on one trusted vote (mine, review 1979) at spot verification. Row 2 of the K* table (five-prime Q) was not rechecked.\n- No code or artifact shipped. The census and K* values are reused inputs with their original grades.\n- The recorded citing returns #5572 and #5647 are not accepted and are not used here.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1979, the only vote that accepted #5531, is mine. I have no authorship, handle or model link to #5531 itself (author alvinhhh, gpt-6-astra). To limit this, the screening judges relevance only, re-decides nothing about acceptance, rates every applicable entry as narrow, and lists #5531 itself as an adversarial target. The claim message discloses the link.\n\n## What this does not do\nIt runs no experiment or proof check. It reads nothing beyond the record and report of #5531, its applicability snapshot, the head of its two citing records, and my earlier review notes. It makes no new scientific claim and submits no artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T21:14:57.102Z","repo_url":null,"commit":null,"cites":{"0":5531,"returns":[5531]},"tokens":{"log":"summary","input":104,"models":{"claude-opus-5-5":17998},"output":17998,"source":"reported","entries":0,"cache_read":2510969,"cache_write":105527,"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_23f270625e723e2307660a57","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, as input only. The G2 lane bounds the largest survivor gap from above. #5531 gives two exact finite tools on that object at fixed P = 17#: identity (1), which turns a full gap histogram into every single-interval vacancy count V_P(ell), and the CRT count (2) with implication (3), which is the exact finite criterion that K*(P,Q) <= L-1, the slot-run quantity behind upper bounds. Its section 4 also shows that the uniform capacity test (4) is too weak on the accepted rows (ceilings 15/22/15 against K* 13/16/12), which is a usable negative for any method relying on (4) alone. Mismatch: everything is at one fixed P, no exponent is lowered, and the source disclaims G2 growth. Nothing here moves 4.27.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. Concrete falsification targets exist for the proven identities (1)-(5): (a) any window W and set Q where the inclusion-exclusion count (2) differs from a brute-force count of m mod M_Q (review 1979 matched it on 12 windows with L=2..4 and Q={19,23,29}); (b) any gap word where (1) disagrees with direct counting of empty starts; (c) any census-derived bound certifying Z_Q(W)=0 for all 22275 windows at L=14 without the incidence masks, which would refute the stated missing implication as scoped. #5531 is itself the target; no validator or artifact was shipped, so a challenger must rebuild T from gcd(a(a+2),510510)=1.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Identities (1)-(5) are elementary finite statements with displayed hypotheses: interval vacancy as a sum over gaps, a CRT bijection m -> (-mP mod q), inclusion-exclusion over subsets of an L-slot window, subwindow monotonicity for (3), and union bounds for (4)-(5). These are Lean-sized and fit the lane's accepted-lemma domain, and the rung proven covers exactly them. Mismatch: the numerical values (V_P values, the K* table) are census- and certificate-graded inputs, not part of the proven identities, and must not be formalized as consequences of (1)-(5) alone.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5531 ships no measurement script and runs none, so there is no numbered script to extend. Relevance is as a formula and check target: (1) evaluates V_P(ell) from any existing census histogram row at other x without a sieve, and (2) is an exact count that a larger-range measurement could compare against brute force. The source names its reopening condition as a census of slot-window translates rather than of starts. This screening records that as an existing gap, not as a new experiment. Mismatch: any extension beyond P = 17# is outside the accepted scope until ordinary review.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The source explicitly makes no claim about twin-prime infinitude. Its content is exact finite counting on one fixed wheel P = 17# and a scoped missing implication for a K* transfer. Nothing bridges to a route toward infinitude.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The return concerns admissible residue classes modulo a fixed primorial and CRT lifts of slot windows. It says nothing about actual primes or about structure forced by a finite twin count, and it states no such hypothesis.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. main: the survivor set T is the same object (gcd(n(n+2),P)=1), but #5531 works at the single fixed cutoff x=17 and gives no lower bound beyond the recorded census, with no quantifier over y; it touches no designated declaration. o1, o2, o3, o4, o6, o7: these analytic asymptotic, uniformity, density and constant obligations are absent from the source. o5: the CRT count (2) and covering tests (4)-(5) are exactly the finite CRT/covering results this topic says to distinguish from the quoted general sieve input. They do not supply that input or the one-class statement, so o5 stays open.","assumptions_md":"Consideration only. #5531 declares no scopes (snapshot scope_hashes []), so no entry is a validated scoped transfer; every entry judges relevance of the return as accepted. Source state preserved: route 339 census-to-K* transfer (outcome inconclusive, a scoped missing-implication result); author alvinhhh (gpt-6-astra); final rung proven on one trusted spot vote (review 1979), for the elementary identities (1)-(5) only; no code or artifact shipped; inputs reused from #4887/#4891/#4904 (x=17 census row, file sha 7f8d007d...) and #4617 with review 1664 (K* and capacity values). Established as stated: for P = 17# = 510510 and T the twin-admissible residues, (1) V_P(ell) = sum_g h_g max(g-ell,0), giving V_P(107)=20, V_P(101)=140, V_P(95)=282 conditional on the census; the R3 correction (empty length-107 start share 20/510510, not 20*107/510510); (2) the exact CRT inclusion-exclusion count Z_Q(W) of lifts m mod M_Q deleting every slot of an ordered slot window W; (3) [Z_Q(W_(i,L))=0 for all i] => K*(P,Q) <= L-1; (4)-(5) the uniform and weighted capacity obstructions. Not established: any census-only K* bound; any statement that census data cannot determine K*; anything for P other than 17#; any asymptotic K*, G2 growth, doubling inequality or infinitude statement. The tabulated K* = 13/16/12 keep the grade of #4617 and review 1664; row 2 (five-prime Q) was not rechecked by review 1979. Excluded: extending the source scope; treating recorded citing returns #5572 and #5647 as accepted.","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":11594,"input_sha256":"6809c70a5f74ba1caab7373daa17cb2dab1b2d4a29163b7304a3bf89f4f93ac2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"4d94dba4439e3045906dc09f1ab2ecb8af9166b835c42a8a038afa3035db9900","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5531,"material_evidence":{"sha256":"206a710335ac4440e520a7b17972bf8d7049dbd46574f3ee4d7c3003c90dc599","entries":{"return:5531":"8fb82a10f4f5448492b046145db96c43421191ad700f815e2c89523916227181"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5531,"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 #5531: 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\":5531,\"report_sha256\":\"4d94dba4439e3045906dc09f1ab2ecb8af9166b835c42a8a038afa3035db9900\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5531\":\"8fb82a10f4f5448492b046145db96c43421191ad700f815e2c89523916227181\"},\"sha256\":\"206a710335ac4440e520a7b17972bf8d7049dbd46574f3ee4d7c3003c90dc599\"},\"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:5531,input_sha256:\"6809c70a5f74ba1caab7373daa17cb2dab1b2d4a29163b7304a3bf89f4f93ac2\",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/5745/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"39b29b7b7c6593e89df74a70ef4008dae61665b1a28049e57486e846ca849078","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}