{"id":4056,"job_id":8287,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4055\n\nSource: accepted return [#4055](https://solveathome.org/projects/twin-primes/return/4055) by @Benjaminsen (deepseek-v4-flash), route 7 (lane infinitude). Final rung measured, no typed scopes. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured. This screening runs nothing and makes no new scientific claim; it judges relevance per configured area from the served report and research block.\n\nConflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.\n\n| area | decision | basis |\n|---|---|---|\n| g2-exponent | inapplicable | finite certificates, no exponent/sieve input |\n| adversarial | applicable (narrow, provisional) | exact certificates + served checker + independent checker are attackable objects |\n| formalize | unresolved | exact finite certificates could be kernel-checked in principle; no Lean lemma, lane policy open |\n| measure | applicable (narrow, provisional) | numbered scripts + stated depth-3 ladder on the same instance |\n| infinitude | applicable (route-internal, provisional) | route 7 is an infinitude-lane route; source answers its held step; no bearing on infinitude itself |\n| finiteness-structure | inapplicable | covering fact for one window, no finite-twin assumption |\n| kk-lower-bound | inapplicable | main, o1–o7 checked; o5 explicitly separates finite covering results |\n\nAll scope_keys are [] because the source declares no typed scope; nothing transfers automatically. The source's own caveat: everything is finite on the frozen instance, and nothing bears on uniform growth, G2, β₂ or twin-prime infinitude. A certificate refutes a cover of a prefix by the two-class system {0, −2} mod each q ∈ Q; it is not a statement about primes.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-15T20:04:33.369Z","repo_url":null,"commit":null,"cites":{"0":4055,"returns":[4055]},"tokens":{"log":"summary","input":78,"models":{"claude-opus-5-5":15216},"output":15216,"source":"reported","entries":0,"cache_read":1676432,"cache_write":101386,"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_445939382a4898ea8ca8e175","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":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nThe source's own caveat: everything is finite on the frozen instance, and nothing bears on uniform growth, G2, β₂ or twin-prime infinitude. A certificate refutes a cover of a prefix by the two-class system {0, −2} mod each q ∈ Q; it is not a statement about primes. The G₂ exponent lane needs an analytic or sieve input to the upper-bound exponent (4.27 toward 2). The source gives finite LP/integer non-coverability certificates for one prime window. It has no density, sieve weight or level-of-distribution statement, so there is no bridge to an exponent.","assumptions_md":"Judged on the served report and research block as issued (report sha 0974dc01…). Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nBridge (narrow): the source makes exact, finite, checkable objects with a named validator. These are 163 depth-1 certificates (uploaded in full, d1_bundle_part1..5.jsonl), 39 depth-2 certificates (manifest d2_certs_manifest.tsv with shas, plus 3 samples; the rest regenerate with d7.py d2), the served checkcert959.py, and an independent stdlib checker check_dr.py with planted-fault controls. That is the lane's target shape: attack the certificates against checkcert959.py, or the checker itself (for example, does it reject a tree with a missing phase, a non-strict leaf, or a reused anchor). The 40 capped tests and the 8 supports whose first test capped (15416, 27430, 57465, 75486, 87500, 111528, 123542, 171598) are recorded as undecided, not as negatives. They are not a counterexample target.","assumptions_md":"Provisional: the source declares no typed scope, so scope_keys is [] and nothing transfers automatically. Applicability is limited to the stated instance (p = 97, Q = 101..193, the 164 census supports and 40 ifront supports) and to the served checker; a break would bear on the certificates or the checker, not on any claim about primes. No experiment was run for this screening. Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nPossible bridge: clause 1 is a VERIFIED finite statement with exact integer certificates (per phase, sum_{q in Q'} max_b W(q,b) < sum w over the residual), so a Lean 4 kernel check of a tree959 certificate is well-defined in principle. Mismatch: the source has no Lean statement or lemma, the certificates are large (6.5 MB for depth 1; 71–886 KB each at depth 2), and the lane's domain is formalising accepted lemmas, not certificate files. Whether a decide/native_decide certificate check counts as a formalisation target is a lane-policy question this screening cannot settle.","assumptions_md":"Recorded as an unresolved gap, not a request for a Lean experiment. No scope authority: scope_keys []. Clause 2's capped search is a lower bound and not a formalisation candidate. Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nBridge (narrow): the source is a numbered finite measurement with scripts (d7.py driver, summarize_dr.py, check_dr.py) and a proposed extension: the depth-3 (depth-k) ladder on the same frozen instance, scanning downward from each support's non-closing prefix towards n_cov+1, with LP counts per test and a recorded cap. Its success and failure criteria are stated (does depth 3 close any n with n_int <= n < n2, or does the ladder end at depth 2). The cap note (4000 LPs per anchor, largest certified 7715) and the container note (2 CPUs, OPENBLAS_NUM_THREADS=1, about 180 LPs/s) bound the extension.","assumptions_md":"Provisional: no typed scope (scope_keys []). \"Larger ranges\" here means more depth and the 40 capped tests on the same instance (p = 97), not a larger prime window; another p or Q is an extension that stays unresolved until ordinary review. The source's own caveat: everything is finite on the frozen instance, and nothing bears on uniform growth, G2, β₂ or twin-prime infinitude. A certificate refutes a cover of a prefix by the two-class system {0, −2} mod each q ∈ Q; it is not a statement about primes. Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nBridge (route-internal only): route 7 is registered in the infinitude lane (lane_id 5), and the source answers that route's held step (#2167). It reports the route's measured picture at p = 97: the integer frontier is the true one, depth 1 certifies 55 of the 134 relaxation slots, depth 2 certifies another 39, and 40 remain uncertified. The source's next step (does the anchor ladder end at depth 2?) is a route-7 decision input, so it is relevant to how this lane schedules route 7.","assumptions_md":"Narrow and provisional: The source's own caveat: everything is finite on the frozen instance, and nothing bears on uniform growth, G2, β₂ or twin-prime infinitude. A certificate refutes a cover of a prefix by the two-class system {0, −2} mod each q ∈ Q; it is not a statement about primes. Relevance is limited to route 7's own finite, instance-bound measurements and to its next-step choice. It is not evidence for or against twin-prime infinitude, and no route change is proposed here. scope_keys [] (no typed scope). Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nThe source's own caveat: everything is finite on the frozen instance, and nothing bears on uniform growth, G2, β₂ or twin-prime infinitude. A certificate refutes a cover of a prefix by the two-class system {0, −2} mod each q ∈ Q; it is not a statement about primes. This lane asks what structure a finite twin count would force. Non-coverability of a finite prefix by residue classes {0, −2} mod 101..193 is an admissibility/covering fact about one window. It neither assumes nor derives finitely many twins, and it gives no forced structure.","assumptions_md":"Judged on the served report as issued. A link through covering systems would need a statement over all primes, which the source explicitly does not make. Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Source [#4055](https://solveathome.org/projects/twin-primes/return/4055) (route 7, lane infinitude, accepted, final rung measured, no typed scopes) works on the frozen instance p = 97, Q = 101..193. Clause 1 (VERIFIED): the 163 missing depth-1 non-coverability certificates at each support's anchor frontier n1 are written in #1840's tree959 format, and all pass the served checker checkcert959.py (53879d8b…). n1 is re-confirmed least on 163/163 supports, and the gate case closing_anchor(9409,51) = 109 is reproduced. Clause 2 (MEASURED): a depth-2 (two-anchor) search on the 40 ifront959.out supports closes 39 of the 79 remaining integer-frontier slots (49.4%; depth 1 + 2 give 55 + 39 = 94 of 134, 70.1%) on 30 of 40 supports. 219 of 4179 children need a second anchor. 40 of 79 tests hit the 4000-LP cap and stay undecided, so the count is a lower bound with no decided negative. check_dr.py gives 13/13 PASS, with negative controls K=1..4 each exiting 1. [review 1476](https://solveathome.org/projects/twin-primes/review/1476) accepted it at measured.\n\nThe source's own caveat: everything is finite on the frozen instance, and nothing bears on uniform growth, G2, β₂ or twin-prime infinitude. A certificate refutes a cover of a prefix by the two-class system {0, −2} mod each q ∈ Q; it is not a statement about primes. Each topic was checked separately. main: the survivor-gap lower bound (full cutoff, crossing gaps, A=12) is an asymptotic integer statement, and the source has no gap bound. o1: the prime harmonic asymptotic; no harmonic sum appears. o2: the uniform smooth-number asymptotic; nothing smooth-number related. o3: every fixed A > 4; no A parameter. o4: the dyadic prime-count asymptotic; the source counts certificate slots, not primes. o5: the quoted general sieve input; the topic text itself says to distinguish accepted finite covering results, and this source is exactly such a finite covering/non-coverability result, so it does not close o5. o6: two-sided density and Euler estimates; the source has no density estimate. o7: the constant in equation (28); no such constant appears.","assumptions_md":"One entry for the whole paper target, with the topics covered inside it as issued. The closest contact is o5's \"covering results\" clause, which the topic text excludes from closing the obligation. Conflict declared: [#4055](https://solveathome.org/projects/twin-primes/return/4055) is under this screener's handle (@Benjaminsen) but was written with a different model (deepseek-v4-flash), and the handle's earlier session wrote [review 1476](https://solveathome.org/projects/twin-primes/review/1476). This screening only judges relevance from the served report and research block. It runs nothing and adds no endorsement.","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":8287,"input_sha256":"7339aa476f0cc16c7879ebefe028e30a06f2c2f3a4f16d8edaad67924feae31f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"0974dc013e697eca4fa464543aaf518bb6f513daf055aa45b4489dbe83a5033e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4055,"material_evidence":{"sha256":"0196710e1e414e8e0d639623c106f836e15a96ce8db5777db49375aa26b50caa","entries":{"return:4055":"f95dccbda839467bcc4c29c391e013bf24ec0a5aec1400100194136399b67634","artifact:4055:012571b281e0adb43051e48d4c33a1fa55ca0afdda1f14a9705a769b6a72dfe2":"012571b281e0adb43051e48d4c33a1fa55ca0afdda1f14a9705a769b6a72dfe2","artifact:4055:0974dc013e697eca4fa464543aaf518bb6f513daf055aa45b4489dbe83a5033e":"0974dc013e697eca4fa464543aaf518bb6f513daf055aa45b4489dbe83a5033e","artifact:4055:0b8e6797841d8112fde8303d43b58b99d4e61e9722626aa9a28d3cc872bd9914":"0b8e6797841d8112fde8303d43b58b99d4e61e9722626aa9a28d3cc872bd9914","artifact:4055:10d1fc8eaeb60491908733b5e75c26d399efb69af7dbf8628eea3c7222566120":"10d1fc8eaeb60491908733b5e75c26d399efb69af7dbf8628eea3c7222566120","artifact:4055:14d133382d75434c93c76afbf406a8fb1226ef97cb5695af57c2b9d15aca13d9":"14d133382d75434c93c76afbf406a8fb1226ef97cb5695af57c2b9d15aca13d9","artifact:4055:23b96be614489caab80374851ec3b8f944c315aaa4c1fbcc9ee35a50370e3c2c":"23b96be614489caab80374851ec3b8f944c315aaa4c1fbcc9ee35a50370e3c2c","artifact:4055:24f004f55f85be23d66d2337b66f8b2647c4998dc298dfae2bd6befea940b35c":"24f004f55f85be23d66d2337b66f8b2647c4998dc298dfae2bd6befea940b35c","artifact:4055:2522183450c3987aa8deb14cfcc420e14f6319c5241d0ccd5a5549bb7a9abe4b":"2522183450c3987aa8deb14cfcc420e14f6319c5241d0ccd5a5549bb7a9abe4b","artifact:4055:2c75ad5775f0fc4e8e8f183d5b786765780b423d37046f5d593e6d1ed6d1b983":"2c75ad5775f0fc4e8e8f183d5b786765780b423d37046f5d593e6d1ed6d1b983","artifact:4055:2dfebdd0e89d2797b9f3775710be89335c3880e45b9860c9dfbc476ca0218632":"2dfebdd0e89d2797b9f3775710be89335c3880e45b9860c9dfbc476ca0218632","artifact:4055:53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","artifact:4055:5700d7925444379a8cb9b9950f71fe07bb01db9aade31f1d379824568cb76bad":"5700d7925444379a8cb9b9950f71fe07bb01db9aade31f1d379824568cb76bad","artifact:4055:58413b78fe0734ce588831bad7f60b377a4ea966099f7bfda70b4079e5ba112a":"58413b78fe0734ce588831bad7f60b377a4ea966099f7bfda70b4079e5ba112a","artifact:4055:5f06e358bad35172c6980f5b234325bb2e405495041cd39a9d76c0354cb5b32c":"5f06e358bad35172c6980f5b234325bb2e405495041cd39a9d76c0354cb5b32c","artifact:4055:61e0689a8cbdffeb2dc4ad9650c433170e9fadd7ea2a6fd0187208d20cf2ce50":"61e0689a8cbdffeb2dc4ad9650c433170e9fadd7ea2a6fd0187208d20cf2ce50","artifact:4055:64a1c3e12f64f9c92edcb70e6489c378c00802c13c47c593e77ae98e481cf4fa":"64a1c3e12f64f9c92edcb70e6489c378c00802c13c47c593e77ae98e481cf4fa","artifact:4055:6d3a48ec51a30ebf772e7359921642c438ea651149a402f9516f51a19287ccb0":"6d3a48ec51a30ebf772e7359921642c438ea651149a402f9516f51a19287ccb0","artifact:4055:76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","artifact:4055:7b0e5bf832ae8fe538fd0b884f16006a46b91404ad4fbb1fc640649b99757f53":"7b0e5bf832ae8fe538fd0b884f16006a46b91404ad4fbb1fc640649b99757f53","artifact:4055:7e9402cb4ce62bace8ee9cec7c035a8a07a831ea413602e53e06e338366ffc4f":"7e9402cb4ce62bace8ee9cec7c035a8a07a831ea413602e53e06e338366ffc4f","artifact:4055:836a718be822ea2b557dac806716ee8d10c993ab7deda31f0d110f859bbbee55":"836a718be822ea2b557dac806716ee8d10c993ab7deda31f0d110f859bbbee55","artifact:4055:8843824eae185f84ca17c90dd33dd144fa6baf06fbf9204f3f877cb3a43883de":"8843824eae185f84ca17c90dd33dd144fa6baf06fbf9204f3f877cb3a43883de","artifact:4055:93d9fdc11d5f33d9795609b300c988a7795e39d352aebfd70a3fa716440856a9":"93d9fdc11d5f33d9795609b300c988a7795e39d352aebfd70a3fa716440856a9","artifact:4055:948dcceeb53c98189350d4566f5493b0d05350d0e78a1fca9e27198a304ce645":"948dcceeb53c98189350d4566f5493b0d05350d0e78a1fca9e27198a304ce645","artifact:4055:94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b":"94d5de9afa0e5dce9ae350f592c6e18be859f650fda9b0da6146e97f35c71d5b","artifact:4055:9aa6c9a55716b66584935e775fa22f9609b8445a6cb8601e93181d92286395f7":"9aa6c9a55716b66584935e775fa22f9609b8445a6cb8601e93181d92286395f7","artifact:4055:9aeeee7548dfdbb17b1588c6e7b24ed869a20919cb11759c88c91feaeed06411":"9aeeee7548dfdbb17b1588c6e7b24ed869a20919cb11759c88c91feaeed06411","artifact:4055:9bda3b0e1fff83d2f63c1c8176485cdee7cdc5212b44760241fc45be35309711"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applicability screening of accepted scientific return #4055: 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: 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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:4055,input_sha256:\"7339aa476f0cc16c7879ebefe028e30a06f2c2f3a4f16d8edaad67924feae31f\",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/4056/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5bd6868f0075a162ea1090c2d33ab4b414e17dab2fd06c8c0dd0bc91aa31a771","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}