{"id":3396,"job_id":7035,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3393 (job 7035)\n\nSource: accepted return #3393 (route 42, problem 1: exact compatible-phase uniform first positive Lc_6 = 330 at k = 6, slack_6 = 2.200; accepted at verified with spot verification, review #1105). Report sha256 e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | unresolved |\n| formalize | inapplicable |\n| measure | inapplicable |\n| infinitude | applicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#3393 answers the infinitude area's stated route 42 question for k = 6: Lc_6 = 330 (Lc_6(329) = 0), so slack_6 = 2.200 lies inside [1, 2.8] and below the k = 5 ratio 3.000, which kills the monotone-growth reading. #1985's 420 is reproduced as a valid cap. The adversarial area holds #1985 as an entry; #3393 confirms it and refutes a heuristic, so that entry is unresolved rather than applicable. No other area's domain is touched. The k = 7 question remains open.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T04:54:07.892Z","repo_url":null,"commit":null,"cites":{"returns":[3393]},"tokens":{"log":"summary","input":60,"models":{"claude-opus-5-5":13346},"output":13346,"source":"reported","entries":0,"cache_read":1210629,"cache_write":55452,"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_5deb00a27633d6c513556b45","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":"Mismatch. #3393 states explicitly that it makes no G2 or beta_2 claim; Lc_6 is a finite compatible-phase pair bound on #996's CRT recursion at one k, not an upper bound on G2(x#) and not an exponent. Nothing in it touches the DHR sieve exponent 4.266 or the ladder fits.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"adversarial","scope_keys":[],"evidence_md":"Partial bridge. The area carries #1985 (Lc_5(198)=1, Lc_5(197)=0, zero slack, Lc_5 not monotone) as an entry. #3393 re-derives #1985's Lc_1..Lc_5 tables with 0 mismatches, reproduces its 420 cap at k = 6 (solve_ak.py equality check, min(420) = 9), and falsifies the informal monotone-growth reading of slack_k (1.556, 2.733, 3.000, 2.200). Its independent checker check_ak.py passes and its --corrupt negative control fails with 2 detections. That is a consistency confirmation of an accepted entry plus a refuted heuristic, not a counterexample to an accepted lemma.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim. Recorded gap: whether a refuted monotone-growth reading counts as an adversarial finding is for the area to decide; no new attack is implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. #3393 is an exact finite computation over a 5760 x 30030 = 1.73e8-cell phase grid per length; the formalize area explicitly leaves finite scans unfolded unless they bear on a Lean target, and its next step (#1072/#1790, #1816, #1848) does not mention Lc_k.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Mismatch. #3393 computes one exact value rather than extending a measurement ladder or validator range. The 330 that appears in the area's L-ladder T31 support (#1473: 324 absent, 330 and 348 present) is a different object (tile support values), not Lc_6; the coincidence carries no bridge.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Direct bridge. The area's open question reads: \"Route 42: compute exact Lc_6 (chunked phase grid, m in [150, 420]) to pin slack_6 in [1, 2.8] and reproduce #1985's 420, then ask whether the gap shrinks at k = 7 (#2573).\" #3393 is route 42 and answers the first part: Lc_6 = 330, slack_6 = 2.200 inside [1, 2.8], 420 reproduced as a valid cap. It updates the route 42 entries #2427/#2573 (which listed slack_6 <= 2.800, Lc_6 not computed). The k = 7 question stays open.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim. The value is finite and conditional on #1985/#996; it is a bound inside the route 42 programme, not a step toward infinitude by itself.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. #3393 does not assume finitely many twins or derive any consequence for the tile, E-dagger, D_y or K(x) from such an assumption; it is an unconditional finite computation on CRT residue recursions.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for main and O1-O7. main and O3: no survivor gaps or A parameter. O1, O4, O6: no prime harmonic, dyadic prime count or two-sided density statement. O2: no smooth-number content. O5: the only CRT content is a finite sieve-window pair bound at k = 6 for #996's recursion, not one of the accepted finite CRT results that O5 consolidates. O7: no eq. (28) content.","assumptions_md":"Provisional relevance only: #3393 has no typed research_evidence scopes (scope_keys []), so nothing here is a validated transfer. Source scope preserved: one exact finite value, the compatible-phase uniform first positive Lc_6 = 330 at k = 6 (W_6 = 30030, 5760 admissible tau, argmin (b,tau) = (0,2) with value 3, Lc_6(329) = 0), giving slack_6 = 330/150 = 2.200; conditional on #1985's Proposition and #996's identity (1) (both verified). No Pi(x) bound, no asymptotics, no k = 7 value, no G2/beta_2 claim.","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":true},"effective":true,"check_job_id":7035,"input_sha256":"1e56af7cd8797b3cb4211ee95604757bfbba239e34d29527745256e7aafcd165","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3393,"material_evidence":{"sha256":"ca46b53278636e2de08de3cbef17b0e044886ddeb963cd54e7549e7e917fafd2","entries":{"return:3393":"f0631c77f417f0b0aa4737bb59be6169d23412f9338adb67d5c5cb20a2091c1f","artifact:3393:0a8bfaee869f64a5a4c349dcdc342fb7d74a0545c860754468134f5485258f8e":"0a8bfaee869f64a5a4c349dcdc342fb7d74a0545c860754468134f5485258f8e","artifact:3393:0b09076b30bb80a4a59d1149516dd8d4aad477f73c646a75ecb436f187b86f88":"0b09076b30bb80a4a59d1149516dd8d4aad477f73c646a75ecb436f187b86f88","artifact:3393:183c709ab9c6e33bebb86133d7ffa081aa6e3f75bd3c47260dd91b54651a6199":"183c709ab9c6e33bebb86133d7ffa081aa6e3f75bd3c47260dd91b54651a6199","artifact:3393:34d4bae023a1192317261d76067fb1eaf0f8abe75ef165e0c0f97b8697c7806a":"34d4bae023a1192317261d76067fb1eaf0f8abe75ef165e0c0f97b8697c7806a","artifact:3393:3e2de6ec32698bb4f840c6fb2faca47a6798b91656d277cb43ec320397dd4367":"3e2de6ec32698bb4f840c6fb2faca47a6798b91656d277cb43ec320397dd4367","artifact:3393:42cb680525933f7e0ca6f7807c267748b0484c05fc0d2035935859332df4f7db":"42cb680525933f7e0ca6f7807c267748b0484c05fc0d2035935859332df4f7db","artifact:3393:47d29a703fe811730b7fe1f86c430488e16aa0a8146bb495fa230b545aecb6ea":"47d29a703fe811730b7fe1f86c430488e16aa0a8146bb495fa230b545aecb6ea","artifact:3393:482cbb04fd473d2b6c04f7425cd68bd6888effb1b3d2bab6bafbdbbfda966318":"482cbb04fd473d2b6c04f7425cd68bd6888effb1b3d2bab6bafbdbbfda966318","artifact:3393:4cabafb48ff1d74f7f6a335e51bbbe7c62ea03628b5d957dade7cb53a17f903a":"4cabafb48ff1d74f7f6a335e51bbbe7c62ea03628b5d957dade7cb53a17f903a","artifact:3393:5f2d679f03cd011f2117fdeda235aea825b84cd967a2cea46c753b84d85068e5":"5f2d679f03cd011f2117fdeda235aea825b84cd967a2cea46c753b84d85068e5","artifact:3393:6199667ee0fb4f1e805331d4e9578444c75ecf466931570c153f15abff633370":"6199667ee0fb4f1e805331d4e9578444c75ecf466931570c153f15abff633370","artifact:3393:6aece039ee7db4672ea5ac529a7d4133ddc3b3ccdf6d003f65e745417e075b70":"6aece039ee7db4672ea5ac529a7d4133ddc3b3ccdf6d003f65e745417e075b70","artifact:3393:6d2c5e412c7a54df38d14c98b5a9d39a98e4b4967c53d18d1a45c1aac69b1d70":"6d2c5e412c7a54df38d14c98b5a9d39a98e4b4967c53d18d1a45c1aac69b1d70","artifact:3393:76ed253f98ccb07100a07235f16605038550a8feb2fa4a2d8b7282ef1d7e0882":"76ed253f98ccb07100a07235f16605038550a8feb2fa4a2d8b7282ef1d7e0882","artifact:3393:78c606cca41fdd1c20f1379db657c850af9b5dae29df71782c5f788898f6a6fb":"78c606cca41fdd1c20f1379db657c850af9b5dae29df71782c5f788898f6a6fb","artifact:3393:8dac3d917f3e29163b5c3937f2bd678dad9cef77d10eeb22451df858c05771bd":"8dac3d917f3e29163b5c3937f2bd678dad9cef77d10eeb22451df858c05771bd","artifact:3393:90db699dbd11951aa90f27e46e51197eae63fae9724dbdcdad8ec7cef427bb50":"90db699dbd11951aa90f27e46e51197eae63fae9724dbdcdad8ec7cef427bb50","artifact:3393:a97417ff74e7093cc4beb8f4761cd1d456a7afb849e4da4b9d3af70574e0560b":"a97417ff74e7093cc4beb8f4761cd1d456a7afb849e4da4b9d3af70574e0560b","artifact:3393:af60b4f72ebda692b0a36ff07ce8878fe9635eada4ebc98ca0cd8a1c8f003e83":"af60b4f72ebda692b0a36ff07ce8878fe9635eada4ebc98ca0cd8a1c8f003e83","artifact:3393:bcf64682d0cbd65a65c63ed79291154113482e55e45c6cd1b77b8f1725c02a54":"bcf64682d0cbd65a65c63ed79291154113482e55e45c6cd1b77b8f1725c02a54","artifact:3393:c7603a1e9da918df6c4c60827df242d92209ef10a4c65faac6040d930af274ad":"c7603a1e9da918df6c4c60827df242d92209ef10a4c65faac6040d930af274ad","artifact:3393:d0790737ee72a29e180d6f937090630220520a60121838dcdcea0a5c38d75eaf":"d0790737ee72a29e180d6f937090630220520a60121838dcdcea0a5c38d75eaf","artifact:3393:e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a":"e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a","artifact:3393:f88a7f5dbfdb39a755cb8402eced8bc7a953ade16b187ef96e25c23d5758e0a1":"f88a7f5dbfdb39a755cb8402eced8bc7a953ade16b187ef96e25c23d5758e0a1"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3393,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #3393: 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\":3393,\"report_sha256\":\"e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3393\":\"f0631c77f417f0b0aa4737bb59be6169d23412f9338adb67d5c5cb20a2091c1f\",\"artifact:3393:0a8bfaee869f64a5a4c349dcdc342fb7d74a0545c860754468134f5485258f8e\":\"0a8bfaee869f64a5a4c349dcdc342fb7d74a0545c860754468134f5485258f8e\",\"artifact:3393:0b09076b30bb80a4a59d1149516dd8d4aad477f73c646a75ecb436f187b86f88\":\"0b09076b30bb80a4a59d1149516dd8d4aad477f73c646a75ecb436f187b86f88\",\"artifact:3393:183c709ab9c6e33bebb86133d7ffa081aa6e3f75bd3c47260dd91b54651a6199\":\"183c709ab9c6e33bebb86133d7ffa081aa6e3f75bd3c47260dd91b54651a6199\",\"artifact:3393:34d4bae023a1192317261d76067fb1eaf0f8abe75ef165e0c0f97b8697c7806a\":\"34d4bae023a1192317261d76067fb1eaf0f8abe75ef165e0c0f97b8697c7806a\",\"artifact:3393:3e2de6ec32698bb4f840c6fb2faca47a6798b91656d277cb43ec320397dd4367\":\"3e2de6ec32698bb4f840c6fb2faca47a6798b91656d277cb43ec320397dd4367\",\"artifact:3393:42cb680525933f7e0ca6f7807c267748b0484c05fc0d2035935859332df4f7db\":\"42cb680525933f7e0ca6f7807c267748b0484c05fc0d2035935859332df4f7db\",\"artifact:3393:47d29a703fe811730b7fe1f86c430488e16aa0a8146bb495fa230b545aecb6ea\":\"47d29a703fe811730b7fe1f86c430488e16aa0a8146bb495fa230b545aecb6ea\",\"artifact:3393:482cbb04fd473d2b6c04f7425cd68bd6888effb1b3d2bab6bafbdbbfda966318\":\"482cbb04fd473d2b6c04f7425cd68bd6888effb1b3d2bab6bafbdbbfda966318\",\"artifact:3393:4cabafb48ff1d74f7f6a335e51bbbe7c62ea03628b5d957dade7cb53a17f903a\":\"4cabafb48ff1d74f7f6a335e51bbbe7c62ea03628b5d957dade7cb53a17f903a\",\"artifact:3393:5f2d679f03cd011f2117fdeda235aea825b84cd967a2cea46c753b84d85068e5\":\"5f2d679f03cd011f2117fdeda235aea825b84cd967a2cea46c753b84d85068e5\",\"artifact:3393:6199667ee0fb4f1e805331d4e9578444c75ecf466931570c153f15abff633370\":\"6199667ee0fb4f1e805331d4e9578444c75ecf466931570c153f15abff633370\",\"artifact:3393:6aece039ee7db4672ea5ac529a7d4133ddc3b3ccdf6d003f65e745417e075b70\":\"6aece039ee7db4672ea5ac529a7d4133ddc3b3ccdf6d003f65e745417e075b70\",\"artifact:3393:6d2c5e412c7a54df38d14c98b5a9d39a98e4b4967c53d18d1a45c1aac69b1d70\":\"6d2c5e412c7a54df38d14c98b5a9d39a98e4b4967c53d18d1a45c1aac69b1d70\",\"artifact:3393:76ed253f98ccb07100a07235f16605038550a8feb2fa4a2d8b7282ef1d7e0882\":\"76ed253f98ccb07100a07235f16605038550a8feb2fa4a2d8b7282ef1d7e0882\",\"artifact:3393:78c606cca41fdd1c20f1379db657c850af9b5dae29df71782c5f788898f6a6fb\":\"78c606cca41fdd1c20f1379db657c850af9b5dae29df71782c5f788898f6a6fb\",\"artifact:3393:8dac3d917f3e29163b5c3937f2bd678dad9cef77d10eeb22451df858c05771bd\":\"8dac3d917f3e29163b5c3937f2bd678dad9cef77d10eeb22451df858c05771bd\",\"artifact:3393:90db699dbd11951aa90f27e46e51197eae63fae9724dbdcdad8ec7cef427bb50\":\"90db699dbd11951aa90f27e46e51197eae63fae9724dbdcdad8ec7cef427bb50\",\"artifact:3393:a97417ff74e7093cc4beb8f4761cd1d456a7afb849e4da4b9d3af70574e0560b\":\"a97417ff74e7093cc4beb8f4761cd1d456a7afb849e4da4b9d3af70574e0560b\",\"artifact:3393:af60b4f72ebda692b0a36ff07ce8878fe9635eada4ebc98ca0cd8a1c8f003e83\":\"af60b4f72ebda692b0a36ff07ce8878fe9635eada4ebc98ca0cd8a1c8f003e83\",\"artifact:3393:bcf64682d0cbd65a65c63ed79291154113482e55e45c6cd1b77b8f1725c02a54\":\"bcf64682d0cbd65a65c63ed79291154113482e55e45c6cd1b77b8f1725c02a54\",\"artifact:3393:c7603a1e9da918df6c4c60827df242d92209ef10a4c65faac6040d930af274ad\":\"c7603a1e9da918df6c4c60827df242d92209ef10a4c65faac6040d930af274ad\",\"artifact:3393:d0790737ee72a29e180d6f937090630220520a60121838dcdcea0a5c38d75eaf\":\"d0790737ee72a29e180d6f937090630220520a60121838dcdcea0a5c38d75eaf\",\"artifact:3393:e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a\":\"e67331e659e013237b1174ab2ef4f75b07653ddf8a3cf977a4a55935c9da9b5a\",\"artifact:3393:f88a7f5dbfdb39a755cb8402eced8bc7a953ade16b187ef96e25c23d5758e0a1\":\"f88a7f5dbfdb39a755cb8402eced8bc7a953ade16b187ef96e25c23d5758e0a1\"},\"sha256\":\"ca46b53278636e2de08de3cbef17b0e044886ddeb963cd54e7549e7e917fafd2\"},\"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:3393,input_sha256:\"1e56af7cd8797b3cb4211ee95604757bfbba239e34d29527745256e7aafcd165\",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/3396/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"90cae8124da2ba01ebddf5aaa4e30472a3207b0e79e440ef0eaf665757a2c949","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}