{"id":5666,"job_id":11456,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5535 (job 11456)\n\nAdministrative relevance screening of the accepted return #5535 across the seven configured areas. #5535 covers route 293. It gives the exact interaction coefficients W_0, W_1 of cyclic deletion moments, an if-and-only-if criterion (8) for exactness of the singleton-plus-pair truncation, tail and witness certificates for an epsilon=1/100 correlation error, and an abstract counterexample to an unconditional guarantee. Its arithmetic sufficient condition (10) is conditional and certifies no named rung. This screening runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 fde8d9203611b843d602511ed5006b87ecc0a486c3e1fd671d815fb094006b00, material evidence 22ec1c43..., targets 747ddcd4..., input cfebef4d.... A fetch of return #5535 during this job matched the report hash. Its status is accepted, final rung proven, not superseded, with applicability_assessment null, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: one-vote accepted lemma; attack the paired-carrier window argument, the witness rule and large-n use) |\n| formalize | applicable (narrow: finite cyclic identities and the iff criterion, with (10) only as a hypothesis) |\n| measure | applicable (narrow: constraint; rung claims need (8) or (14)/(15) checked directly, since (10) fails for H={0,2} from 210 on) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\n#5535 answers the support question from #5517 (accepted, proven) exactly: W_0 lives on intervals, W_1 on intervals and one-hole intervals, and the two-interaction truncation is exact iff (8). It adds certificates (13)-(15) that bound the correlation error from low-order moments and survivor-gap witnesses, and example (16) shows that no unconditional 1/100 guarantee holds over all gap words.\n\nWhat transfers is a finite identity package plus a constraint. Formalization can state (1)-(3) and (8) directly. Measurement work on q-lifts must check (8) or the certificates at each rung rather than rely on (10). Adversarial work has a focused target in the lemma itself. The other areas have no matching statement, and no area receives a prime-pair result or an eventual-behaviour claim.\n\n## Known gaps\n- There are no typed scopes, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification.\n- Still open: whether (8) or the certificates hold at named large rungs, which is the subject of pending #5551, #5574, #5596 and #5602.\n- The downstream returns citing #5535 (#5551, #5574, #5596 and #5602 pending; #5542, #5578, #5597 and #5606 recorded) were not assessed.\n\n## Prior screening\nNone. The brief states there was no prior screening, and the source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1954, the only trusted vote that accepted #5535, is mine. I also reviewed #5517 (review 1946), on which #5535 builds, and #5574, #5596, #5578 and #5597, which cite it, are by my handle.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the three applicable entries as narrow, and lists #5535 itself as an adversarial target.\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return records and my earlier review checks. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5535's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T11:38:56.624Z","repo_url":null,"commit":null,"cites":{"0":5535,"1":5517,"returns":[5535]},"tokens":{"log":"summary","input":88,"models":{"claude-opus-5-5":14681},"output":14681,"source":"reported","entries":0,"cache_read":1930910,"cache_write":94550,"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_5228f633bd81bc31a7226603","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"This lane's G2 is the project's G2(x#) quantity with proven exponent beta2=4.26645... from the Diamond-Halberstam-Richert dimension-2 sieve. #5535 is exact combinatorics of cyclic deletion moments (sums of squares and adjacent products of merged gaps) and a correlation-error certificate. It gives no sieve weight, level, density or bound on G2, and the counted object of the 4.27 exponent is not touched. No bridge.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5535 is a newly accepted symbolic lemma resting on one trusted vote (mine) at spot verification, so it is a fair attack target. The attack surface is specific: (a) the support claims for W_0 and W_1 (intervals, one-hole intervals) including cyclic wrap and the m>=3 boundary; (b) the iff direction of (8); (c) the paired-carrier argument in section 4 that a four-vertex window holds at most two deletions; (d) the witness rule in (12), which requires gaps between consecutive permanent survivors, not partial blocks. My review's exhaustive check (n<=10, 618,032 cases) found no failure of (1)-(3) or (8), so the remaining surface is mainly (c), (d) and use at large n. Example (16) refutes only an unconditional guarantee over all gap words; it is not a wheel and refutes no accepted claim.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Formulas (1)-(3), criterion (8) and the inequalities (11)-(15) are finite statements about a positive cyclic integer word and a deletion set, with m>=3 and hat B>0 as explicit hypotheses, and are suitable for Lean: define merged-gap F_0, F_1 over subsets, the Mobius transform W_j, and prove support and the iff by inclusion-exclusion. (11) is the standard variance identity and (13) is direct quotient subtraction. Preserve the scope: section 4's arithmetic sufficient condition (10) is a hypothesis, not verified at any primorial rung, and nothing about eventual behaviour follows. No Lean statement exists for it yet.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, as a constraint on lift measurements. Any rung-level claim that the two-interaction truncation is exact must check (8) directly on the carrier, or certify (14)/(15) with actual survivor-gap witnesses; (10) cannot be assumed. My review's independent q-lift check through 30030->17 found (10) true for H={0} but false for H={0,2} from 210 on, while (8) still held at every lift checked, so the paired carrier needs the direct criterion or the three-gap condition. Downstream evaluations at paired 29#->31# and 31#->37# (#5574, #5596, both pending and by my handle) and the variance-witness work #5551 (pending) are where this applies. #5535 itself ran no code and supplies no measured value.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 293 is not in the refuted registry, but #5535 concerns deletion moments of gap words of a wheel carrier (a deterministic finite object) and abstract gap words. It makes no prime-pair claim, no claim about primes beyond the wheel, and no claim that (10) or (8) persists along primorials. No route toward infinitude follows from it. No bridge.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#5535 describes how adjacent-gap moments of a cyclic word change when vertices are deleted. It says nothing about what structure a finite twin count would force on primes; the wheel carriers exist unconditionally at every level, so no consequence of finitely many twin primes is involved. No bridge.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable for every topic. **main.** #5535 does not mention the survivor-gap manuscript or its designated declarations; nothing changes the A=12 main claims. **o1, o4.** No prime harmonic or dyadic prime-count asymptotic. **o2.** No smooth-number estimate. **o3.** No general-A argument. **o5.** No sieve input or one-class statement; the identities are exact finite combinatorics, not a sieve estimate. **o6.** No density or Euler-product estimate. **o7.** Equation (28) is not discussed.","assumptions_md":"Provisional relevance only. #5535 has no typed research_evidence scopes (research_authority.scopes []), so nothing here is a validated transfer. Source scope preserved: route 293, lane 32, final rung proven, files [], research CPU 0, symbolic only. For a positive finite cyclic gap word with deletion set D leaving m>=3 survivors it proves exact Mobius interaction coefficients W_0, W_1 of the deletion moments F_0, F_1 (W_0(T)=0 unless T is an interval, W_1(T)=0 unless T is an interval or a one-hole interval), the iff criterion (8) for exactness of the singleton-plus-pair truncation, run-length tails and the coarse bound (9), the quotient identity behind (13), witness bounds (12) and the epsilon=1/100 certificates (14)-(15), and the abstract counterexample (16) (rho=-1/3, hat rho=-5/19, gap 4/57) showing no unconditional 1/100 guarantee over all gap words. Section 4 is conditional: G<2q (10), or every three-gap sum <6q for H={0,2}, is sufficient for exactness on a carrier; #5535 certifies no named primorial rung and does not claim (10) holds eventually. Accepted at proven, verification spot, on one trusted vote: review 1954, by my handle.","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":11456,"input_sha256":"cfebef4d57ef455512be8233e6f507c0e5efe88941753390528f7aa9dad1ecde","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"fde8d9203611b843d602511ed5006b87ecc0a486c3e1fd671d815fb094006b00","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5535,"material_evidence":{"sha256":"22ec1c439a0dde370ee15a64653a951716ec8bf25d8370e0144316afc2c465c8","entries":{"return:5535":"c3720fc88b8e6fe18690d58ca5a17eb3f9207335c6fc3e90959659c382d7e1dd"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5535,"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 #5535: 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\":5535,\"report_sha256\":\"fde8d9203611b843d602511ed5006b87ecc0a486c3e1fd671d815fb094006b00\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5535\":\"c3720fc88b8e6fe18690d58ca5a17eb3f9207335c6fc3e90959659c382d7e1dd\"},\"sha256\":\"22ec1c439a0dde370ee15a64653a951716ec8bf25d8370e0144316afc2c465c8\"},\"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:5535,input_sha256:\"cfebef4d57ef455512be8233e6f507c0e5efe88941753390528f7aa9dad1ecde\",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/5666/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"63752384636001a256ed06416c88a024e0f91aa96a589f1fb4c98ba965fd04a0","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}