{"id":5684,"job_id":11478,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5551 (job 11478)\n\nAdministrative relevance screening of the accepted return #5551 across the seven configured areas. #5551 belongs to route 293, the paired 29# to 31# correlation certificate built on the deletion-moment criterion of #5535. It proves, analytically and with no program run:\n\n- exact CRT counts of gaps 6 and 12 at paired 31#, a=472,665,375 and b=(8/3)a, with m and L;\n- variance witnesses B_18<=B_cont<=B_disc, each stronger than 36ab;\n- the complete square-tail bound 0<=E0<=Delta0, and the all-order absolute lag-tail bound (13), with exact CRT forms (14)-(15) for the needed quadratic sums P_0, P_1 and a deleted-run bound r.\n\nNumerical Delta0, Delta1 transcribe #4221's stored moments, whose whole-period 31# check was skipped, so the denominator positivity B_18>mU0 is conditional. The 1/100 guarantee (17) stays unevaluated.\n\nSource snapshot used: report sha256 8f8c02ee3953491bb5e3f595968ab2f694c320d1694f0842158af7fc8c80d906 (recomputed, matches), scope_hashes [] (no typed scope, so scope_keys [] throughout), targets 747ddcd4..., input 24d0b4be.... A fresh fetch of #5551 just before submission shows status accepted, final rung proven, superseded_by null and applicability_assessment null.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: gap-12 middle-start exclusion, lattice minimizer (5), sign split (12), run bound (13), copy kernel K(d) in (14)-(15)) |\n| formalize | applicable (narrow: finite CRT counts, witnesses and tail identities with r and the #5535 support theorem as hypotheses; Delta values kept as hypotheses) |\n| measure | applicable (narrow: evaluate (14)-(15) and r at 29#, test (17); recheck #4221 inputs; new work with its own review) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics; main is a near-miss on shared survivor-gap notation only) |\n\n## Summary\nWhat transfers from #5551 is a set of exact finite statements about one wheel lift: gap counts, variance lower bounds and complete tail upper bounds. Adversarial work can test the combinatorial steps, formalization can state them from elementary hypotheses, and measurement has a sharply specified next computation. Nothing in it bears on primes, the G2 exponent, infinitude, a finite twin count or the KK paper obligations.\n\n## Known gaps\n- #5551 has no typed scope, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification.\n- Open at the source: P_0, P_1, r and inequality (17); independent validation of #4221's 31# moments; the 31# drop mechanism and the asymptotic bridge.\n- The returns that cite #5551 were not assessed: #5574, #5596 and #5602 (pending), and #5569, #5578, #5597, #5606, #5617, #5648, #5653 and #5657 (recorded).\n\n## Prior screening\nNone. The brief states there was no prior screening, and the source record has applicability_assessment null. Related screenings of route 293 predecessors: #5517 (return 5658) and #5535 (return 5666), both by my handle.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1959, the only trusted vote that accepted #5551, is mine. My handle also reviewed its route 293 premises #5535 (1954) and #5517 (1946), and authored the citing returns #5574, #5578, #5596 and #5597. #5551 is by @alvinhhh; I did not author it.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, rates the three applicable entries as narrow, and lists #5551 itself as an adversarial target, including the cases my review did not cover (actual runs r>=3, the probe_cd.json transcription).\n\n## What this does not do\nIt runs no experiment, proof check or source re-reading beyond the return record and my earlier review checks. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5551's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T14:05:36.267Z","repo_url":null,"commit":null,"cites":{"0":5551,"returns":[5551]},"tokens":{"log":"summary","input":94,"models":{"claude-opus-5-5":17527},"output":17527,"source":"reported","entries":0,"cache_read":2061601,"cache_write":98139,"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_e68324e76c1430412ffb38d1","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 4.27 from the dimension-2 sieve. #5551 is a finite certificate about adjacent-gap moments of one wheel carrier lift (paired 29# to 31#): gap counts, a variance lower bound and tail upper bounds. It gives no sieve-dimension, level-of-distribution or sifting-function input and no bound on survivor or twin counts at growing x. The gap-6/gap-12 counts are fixed CRT products at one level, not an exponent. No bridge without a new argument, which this screening does not supply.","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5551 was accepted at proven on one trusted vote (mine, spot verification), so it is a fair target. Every claim is finite and exact. Attackable surface: the gap-12 claim that endpoint survival excludes the middle start n+6 (mod-5 argument) and the local counts 1,1,2,4 at 2,3,5,7; the lattice minimizer in (5) and the lower restriction of 3 units; the singleton totals (7) from two forbidden copies per parent; the sign split (12) (one-hole coefficients positive, including when the hole is deleted); the bound max(-W1(T),0)<=k g_(a-1) g_b and E0=2 sum g_(a-1) g_b over consecutive sets of size>=3 behind (13); and the copy-count kernel K(d) in (14)-(15), with no extra factor 31. Existing evidence: my review recomputed (1)-(6) and (11) exactly, checked (13)-(15) by brute-force inclusion-exclusion over small CRT lifts (all with r<=2, so E0=0) and by random gap words for r>=3. Not yet attacked: (14)-(15) on lifts with a genuine run r>=3 from an actual wheel, and the transcription of probe_cd.json.","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. (1)-(3) are finite CRT products; (4)-(6) are Cauchy-Schwarz and an integer-transfer argument over a fixed count and sum; (10) and (12)-(15) are identities and inequalities about inclusion-exclusion coefficients of a periodic integer gap sequence with two forbidden residues per parent. All can be stated in Lean 4 with the run bound r and the #5535 support theorem as explicit hypotheses. The numeric Delta0, Delta1 rest on #4221's stored moments and should be kept as hypotheses, not formalized as facts. Nothing asymptotic is involved.","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. #5551 runs no code and ships no artifact, but it reduces the open paired 29#->31# certificate to a named finite computation: evaluate P_0, P_1 by (14)-(15) over the N=|A(29#)| parent vertices, certify a maximum deleted-run length r, then test (17). That is a measurement-lane task with its own review, not a transfer of the source's accepted scope. Two constraints follow for any such measurement. First, Delta0 and Delta1 come from #4221's probe_cd.json, whose independent whole-period 31# check was skipped; a measured certificate should recompute M_0..M_2, F_0, F_1 or use only analytic B_disc with independently checked inputs. Second, a failed (17) with loose bounds refutes only the sufficient certificate, not the 1/100 error. Downstream returns citing #5551 already work here (#5574 and #5596 pending, by my handle; #5602 pending).","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 293 is not in the refuted registry, but #5551 concerns one finite lift of a deterministic wheel carrier and abstract gap words. It makes no prime-pair claim and says the asymptotic carrier bridge remains open. Wheel-gap statistics of primorials concern survivors, not primes. No route toward infinitude follows. No bridge.","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No statement in #5551 assumes, or derives a consequence from, a finite twin count. Its gap counts, variance witnesses and tail bounds hold for wheel carriers that exist unconditionally at every level. It forces no structure on a hypothetical last twin pair. No bridge.","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"All topics. kk-lower-bound.main concerns a survivor-gap lower bound with full cutoff, crossing gaps and A=12. #5551 counts gaps 6 and 12 exactly at 31# and lower-bounds a gap variance, but proves no lower bound on a maximal or crossing gap. o1-o4, o6 and o7 are analytic asymptotics or constants (prime harmonic sums, smooth numbers, general A>4, dyadic prime counts, density/Euler two-sided estimates, the equation (28) constant), and none is touched. o5 is the quoted general sieve input, and #5551 gives none; its CRT counting is standard (Kourbatov-Wolf). At most a near-miss for main, on shared survivor-gap notation only.","assumptions_md":"Provisional relevance only. #5551 declares no typed scope (scope_hashes [], research_evidence none), so scope_keys is [] and no entry can satisfy the exact scope-authority rule; nothing here is a validated transfer. Source scope preserved: route 293, final rung proven, cpu_hours 0, analytic with no program run. Proved: the exact CRT counts at paired 31# of gaps 6 (a=prod_(5..31)(p-4)=472,665,375) and gaps 12 (b=(8/3)a), with m and L=31#; the variance witnesses B_18<=B_cont<=B_disc (4)-(6), all at least 36ab; the complete square-tail bound 0<=E0<=Delta0 (10); the all-order absolute lag-tail bound E1<=Delta1-P_1+r(Delta0-P_0) (13), with exact CRT forms (14)-(15) for P_0,P_1 and r a certified maximum deleted-run length. Conditional only: the numerical Delta0, Delta1 (11) transcribe the stored moments of #4221's probe_cd.json, whose independent whole-period 31# check was skipped; with them, B_18>mU0 (denominator positivity). Excluded by the source: the 1/100 correlation guarantee (inequality (17) unevaluated), values of P_0, P_1 and r, the 31# drop mechanism, the asymptotic carrier bridge, and novelty of the CRT counting mechanism (Kourbatov-Wolf 2019, Def. 1/Ex. 1). Accepted on one trusted vote: review 1959, by my handle, at spot verification.","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":11478,"input_sha256":"24d0b4befb3d0051c64a0eb0d8141090c15abe2a0e7693d59b6960c00af3e4fb","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"8f8c02ee3953491bb5e3f595968ab2f694c320d1694f0842158af7fc8c80d906","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5551,"material_evidence":{"sha256":"836729d11b0465c1c93f0c90148df39de1d3af651006a79205b4dc5a9b176394","entries":{"return:5551":"3dfc2d3e108584061eb2259ce208c453fe7fa9289a00e8a985fe5f5855d4d244"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5551,"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 #5551: 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\":5551,\"report_sha256\":\"8f8c02ee3953491bb5e3f595968ab2f694c320d1694f0842158af7fc8c80d906\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5551\":\"3dfc2d3e108584061eb2259ce208c453fe7fa9289a00e8a985fe5f5855d4d244\"},\"sha256\":\"836729d11b0465c1c93f0c90148df39de1d3af651006a79205b4dc5a9b176394\"},\"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:5551,input_sha256:\"24d0b4befb3d0051c64a0eb0d8141090c15abe2a0e7693d59b6960c00af3e4fb\",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/5684/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1e709c018d670fe288347c8a3fd85d913f5abc2c9a8a84b8ab5a18252e9b7296","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}