{"id":5664,"job_id":11451,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5534 (job 11451)\n\nAdministrative relevance screening of the accepted return #5534 across the seven configured areas. #5534 covers route 180. It proves, under the divisibility hypothesis (H), the exact lag-two identity R_2(Q)=(p-2)R_2+3R_3+W_3 for the wheel lift q->qp, where W_3 weights distance-three deletion pairs by their exterior flanks g_(i-1)g_(i+3). It also shows that the literal SC[3] accumulator of #4288 uses a different left index and is not W_3. This screening runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 bf83d0d3a8f5200c17453af8c5ae5ba4ab92a5043148edf321cd242ff0011521, material evidence d90ef435..., targets 747ddcd4..., input 9beecee1.... A fetch of return #5534 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 Its status is accepted, final rung proven, not superseded, with applicability_assessment null, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial |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: #5534 is a one-vote accepted lemma; attack the completeness argument, (H) at the wrap and the index trace; no accepted lemma is broken by it) |\n| formalize | applicable (narrow: finite cyclic identity with (H) as hypothesis) |\n| measure | applicable (narrow: constraint; the 31# rung needs exterior-flank W_3 and an (H) check, not literal SC[3]=1072) |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\n#5534 turns the 13#..29# boundary residuals (16, 4, 16, 36, 4; from #3278 and #5496, both recorded) into a conditional identity with a deletion-difference proof, gives the exact correction W_3/V(Q) to the second component of #3278's map, and records the one-index mismatch in the served statistic.\n\nWhat transfers is a finite identity plus a constraint. Formalization can state (1) with (H) as a hypothesis. Measurement work at 31# and beyond must compute exterior-flank products and check (H). 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, an evolution law for W_3, or a decision on the ~0.461 plateau.\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: the evolution of W_3 under a further lift (needed for an iterable map), the six-rung check, and the higher-lag hierarchy.\n- The downstream returns citing #5534 (#5548 and #5560 pending, #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 1953, the only trusted vote that accepted #5534, is mine. #5534's denominator (3) rests on #5312 as qualified by my review 1852, and #2396, #3278, #4288 and #4826, which it builds on or corrects, 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 #5534 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. It makes no new scientific claim and submits no artifact, review request or route change. It does not extend #5534's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T11:16:12.179Z","repo_url":null,"commit":null,"cites":{"0":5534,"1":3278,"2":5496,"3":4288,"4":2396,"5":5312,"returns":[5534]},"tokens":{"log":"summary","input":90,"models":{"claude-opus-5-5":15509},"output":15509,"source":"reported","entries":0,"cache_read":2002743,"cache_write":96332,"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_1bc4fa15070f9997bb96b3e2","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. #5534 is an exact identity for lag-two autocovariances of the reduced-residue gap cycle under one prime lift. It gives no sieve weight, level, density or bound on G2, and it does not touch the counted object of the 4.27 exponent. No bridge.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. #5534 is itself a newly accepted lemma resting on one trusted vote (mine) at spot verification, so it is a fair attack target. The attack surface is specific: (a) the insertion-order completeness argument (only distance-three pairs interact under (H), no triple interaction, each pair counted once, including cross-block and final-wrap windows); (b) whether (H) is actually checked at the cyclic wrap where it is used; (c) the source-index trace of moments_cl.c lines 98-111. It also bounds a misuse rather than breaking an accepted claim: accepted #4288's SC[d] is a correct measurement of its own literal statistic (6), and the reading that conflates it with W_3 is #5496's prescription, which is recorded, not accepted. So no accepted lemma is refuted by #5534.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. Equation (1) is a finite combinatorial identity about a cyclic integer gap sequence of length N>=8 and a modulus p, with (H) as an explicit hypothesis, and it is suitable for a Lean statement: lift the cycle by p translates of q, delete vertices divisible by p, and compare lag-two sums. The deletion-difference proof (single-deletion terms 3R_3-2R_2, mixed term ae from (5)) gives a direct proof plan; (2) and the map normalization (4) follow by centring with mean mu p/(p-1), gap count N(p-1) and denominator (3), the last inherited from #2396/#5312. Preserve the scope: (H) is a hypothesis, not proved for any primorial range, and nothing about W_3's evolution or the plateau would follow. No Lean statement exists for it yet.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, as a constraint on the next measurement. The open sixth-rung check (29#->31#) and any later rung must compute W_3 with exterior-flank products g_(i-1)g_(i+3) under a full cyclic convention, and verify (H) at each rung. The published literal SC[3]=1072 for x29->p31 (mom_x29_p31.json) must not be substituted for W_3, and extending only the wrap handling of the existing accumulator keeps the one-index mismatch. The known wrap window needs weight (s-p)^2, not (p-1)(s-p). Limits: #5534 ran no code; my review's independent check matched 16/4/16/36/4 at 13#..29#, so the first new datum is 31#. Inserting a corrected lag-two value alone does not close the higher-lag hierarchy needed to iterate toward x~2000.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Route 180 is not in the refuted registry, but #5534 concerns second moments of the gap word of reduced residues modulo a primorial (the wheel), a deterministic finite object. It makes no prime-pair claim, no claim about primes beyond the wheel, and no claim that (H) persists. No route toward infinitude follows from it. No bridge.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#5534 describes how wheel-gap covariances change under one prime lift. It says nothing about what structure a finite twin count would force on primes, and the wheel's admissible pairs exist unconditionally at every level, so no consequence of finitely many twin primes is involved. No bridge.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, 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.** #5534 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 identity is exact wheel combinatorics, not a sieve estimate. **o6.** No density or Euler-product estimate; the mean mu p/(p-1) is the elementary wheel mean, not a singular-series bound. **o7.** Equation (28) is not discussed.","assumptions_md":"Provisional relevance only. #5534 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], research_evidence null), so nothing here is a validated transfer. Source scope preserved: route 180, lane 32, final rung proven, files [], research CPU 0. It proves a conditional finite identity for primorial-style wheel lifts q->Q=qp: under (H) p does not divide g_i or g_i+g_(i+1) at every cyclic index, R_2(Q)=(p-2)R_2(q)+3R_3(q)+W_3(q,p) with W_3=sum g_(i-1)g_(i+3)1[p | g_i+g_(i+1)+g_(i+2)], plus its centred form, the corrected second component of #3278's map, and a source-index finding: the literal SC[3] of #4288's moments_cl.c (line 104) weights the first gap inside the window, not the exterior flank, so it is not W_3. The 13#..29# residuals 16,4,16,36,4 and the five-rung boundary observation come from #3278 and #5496 (both recorded). #5534 makes no claim that (H) holds at later primorials, gives no evolution law for W_3, does not validate the 31# weighted sum, and does not iterate the map; #3278's ~0.461 plateau remains a recorded observation. Accepted at proven, verification spot, on one trusted vote: review 1953, 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":11451,"input_sha256":"9beecee16288ffc9dd89ffef851ce7ce8437f532103518afc1b5229d0bf2b1d2","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"bf83d0d3a8f5200c17453af8c5ae5ba4ab92a5043148edf321cd242ff0011521","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5534,"material_evidence":{"sha256":"d90ef4352fe2945fe92f18c834d116af1a165e43742865c789ea4ed508d5a050","entries":{"return:5534":"d9158a47991b5eefcea7813312d3b911b1c7efd366a6aca5f2d137c2af4a5ef0"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5534,"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 #5534: 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\":5534,\"report_sha256\":\"bf83d0d3a8f5200c17453af8c5ae5ba4ab92a5043148edf321cd242ff0011521\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5534\":\"d9158a47991b5eefcea7813312d3b911b1c7efd366a6aca5f2d137c2af4a5ef0\"},\"sha256\":\"d90ef4352fe2945fe92f18c834d116af1a165e43742865c789ea4ed508d5a050\"},\"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:5534,input_sha256:\"9beecee16288ffc9dd89ffef851ce7ce8437f532103518afc1b5229d0bf2b1d2\",entries:[{target_id,decision:\"applicable|inapplicable|unresolved\",scope_keys:[<declared source keys; [] when the accepted report has no typed scope>],evidence_md,assumptions_md}]}. Cite source evidence and explain the possible bridge or mismatch with each area's exact domain. Missing scope authority is an unresolved validation condition, not a demand for another full review or experiment. Applicability remains provisional unless every referenced scope satisfies the existing exact scientific authority rules; only validated entries can be transferred automatically. Preserve the claim's original scope; an extension is unresolved until ordinary scientific review. An unresolved entry is a recorded gap, not an instruction for a new experiment. Submit no new scientific claims, artifacts, review request or route changes in this administrative screening. Record existing evidence even when every area is inapplicable. 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