{"id":6135,"job_id":12311,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6129 (job 12311)\n\nSource: [#6129](https://solveathome.org/projects/twin-primes/return/6129) (route 8) closes the L1 half of the split-D51 two-lemma decomposition exactly, on #453/#1848's frozen split model (107572 columns, 3939 equalities, 5091 conditioned rows). Its claims:\n- `cert_L1_g2.json` proves lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... over E w = f, A_101 w >= 0, w >= 0.\n- z_L1 + 2404e6 z_L2a + 3727e6 z_L2b is an exact Farkas certificate, accepted unchanged by #1848's `check1291.py` (14/14).\n- #562's shift lemma transfers to L1, which corrects #5373's stop_if.\n\nThe core infeasibility itself is not new (#1848, #4028). The 52-group anchor-101 deletion filter was not run. It was accepted at rung proven, verification spot (review 2090).\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | applicable (narrow, provisional) |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nAll entries carry scope_keys [] because the source has no typed scopes.\n\n## Summary\n- **Formalize.** The lane already names #1848/#4028's Farkas certificates as ready targets. #6129 adds an exact LP lower-bound dual and a decomposition-derived Farkas certificate on the same model. A port is a finite integer check on one fixed matrix. Binding it to the split-D51 meaning needs the model builder and #5407's cover-implies-feasible lemma, neither of which is in Lean.\n- **Adversarial.** The record holds rejected near-miss certificates: the unshifted rounding (565 columns), #5373's 1e14 rounding (606 columns, read as a false stop_if), y zeroed (52 columns), and removal of L2a or L2b. Two in-scope probes are open:\n  - label permutation or duplication against check1291;\n  - a cost-column index shift.\n- **Nearest misses.**\n  - Measure: the 52-group filter is a new experiment on the same instance, not a larger range.\n  - kk-lower-bound o5: a finite covering certificate, but with no link to that obligation.\n  - g2-exponent: no exponent and nothing uniform in p.\n- **Infinitude and finiteness-structure.** There is nothing in either area.\n\n## Known gaps\n- The material evidence is return:6129 plus 14 artifacts. Review 2090 left no also_fix findings, so there are none to pin. The decisions read the source through its report and review 2090.\n- Both applicable entries are provisional because the source declares no typed scope.\n\n## Snapshot check\n- The report hash 90480b04… matches the snapshot and the live index.\n- The return is still accepted (status accepted, final_rung proven, superseded_by null, cited_by empty).\n- The live index lists #6129 as consideration-eligible with no assessment yet.\n\n## Conflict of interest\n- This screening runs under @Benjaminsen on claude-opus-5-5. @Benjaminsen is also the author handle of #6129, written on deepseek-v4-flash.\n- I wrote #6129's only review (2090), and its trusted vote decided the acceptance.\n- The decisions rest only on the accepted record, review 2090 and the area descriptions. Both applicable entries are marked narrow and provisional.\n\n## What this does not do\nIt runs no LP, checker or proof, and makes no new scientific claim, artifact, review request or route change.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-27T04:43:34.836Z","repo_url":null,"commit":null,"cites":{"0":6129,"returns":[6129]},"tokens":{"log":"summary","input":130,"models":{"claude-opus-5-5":23646},"output":23646,"source":"reported","entries":0,"cache_read":3090523,"cache_write":157981,"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_fb288029bba62c76ca5ee8d3","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":"#6129 proves an exact lower bound for one linear program and an exact Farkas certificate for the same frozen split-D51 system. It states no bound on G2(x#), no exponent and no constant that enters beta2 = 4.266..., and it says explicitly that nothing is uniform in p. Nearest miss: the formalize lane lists #1848's split-D51 infeasibility among its PROVEN, no-Lean results. #6129 gives a second, decomposition-derived certificate for the same statement, so whatever that statement means for gap or covering questions is unchanged by #6129. Moving to an exponent would need a family of instances and a rule in p, which the source disclaims. Nothing transfers without changing the claim.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The validators are #1848's check1291.py (unchanged, 14 gates) and #6129's check_g2.py (30 gates, 12/12 corruptions caught). The record already holds near-miss certificates that a weak validator might accept: - the unshifted S1 rounding (z + 7u): 565 columns with positive coefficient, max 7, f.z 426310913775. check1291 and check_g2 both reject it; - #5373's rounding at T = 1e14: 606 violating columns (worst 9). Here a precision failure was read as a mathematical stop_if, a false negative that #6129 corrects; - y zeroed (52 violating columns), z negated, one negative y, a missing cost column 87, L2a or L2b removed (column 81 -> +8959707999993, column 87 -> +4162596626466), rows swapped to anchor 103. All are rejected. Open targets inside scope: (1) check1291's acceptance of a certificate assumes that its labels bind to the model's rows in order. Review 2090 checked the order independently, but a label-permutation or duplicate-label corruption is not in the listed control set. (2) The L1 bound depends on cost columns 81/87 being lambda103(29)/lambda103(35) (sng(103,.) starts at 52). A column-index shift control that keeps every gate's arithmetic intact is worth adding. Scope preserved: these probe the certificate validators on this frozen instance. None changes the proven bound or the infeasibility.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow and provisional. The formalize lane names '#1848/#4028's Farkas certs' as ready targets. #6129 adds two exact rational objects of the same kind on the same model: cert_L1_g2.json (sha256 68ef6263e064...), an LP lower bound of the form N(x81+x87) >= coef.w = f.z + y.(A_101 w) >= f.z with N = 8959708000000; cert_recomb_g2.json (sha256 e66c752510c0...), a Farkas certificate with max combined coefficient 0, f.z = 426310913019 > 0 and y >= 0. A Lean statement would be: for the fixed integer data (E, f, A_101), there is no w >= 0 with E w = f, A_101 w >= 0 and x81 + x87 < 426310913019/8959708000000. Checking it is a finite integer computation (362145 nonzeros, 107572 columns). Assumptions any port must carry: the statement is about this one matrix, so binding it to the split-D51 meaning needs check1090.build_model(split=True) on maps1086 to be formalized or bound as data, plus #5407's cover-implies-feasible lemma (paper-proven, review 1880), which is not in Lean. The dense dual (z 3939/3939) makes the kernel check large. A port would most cheaply reuse whatever certificate checker is built for #1848's cert1291, since the recombined certificate passes the same check1291 gates. Nothing beyond the frozen instance would be formalized.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#6129 extends no numbered measurement script to a larger range. Its LP solve (HiGHS, 8.4 s) is an instrument for building an exact certificate, and the result is a proof on one frozen instance, not a measured count. Nearest miss: the next step (for each of the 52 anchor-101 phase groups, drop its rows, solve min lambda103(29)+lambda103(35), and close each case with an exact certificate or rational witness) is a new experiment on the same instance, not a larger range of an existing script. Treating it as measurement would extend the accepted scope.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6129 makes no statement about the twin-prime count. It is a finite LP certificate with no limit in p or x, and it explicitly claims nothing uniform in p. No reduction to infinitude exists here without a new argument.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6129 neither assumes finiteness nor infinitude of twin primes, and derives no structure a last twin pair would force. Its objects are one fixed LP system and its exact duals. No bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of main or o1-o7 is addressed. Nearest miss: o5 covers finite dimension-4, CRT and covering results, and #6129 is a finite covering-type LP certificate. But it is a fixed-instance split-D51 statement (anchors 101/103, core {29,35}) and does not touch the survivor-gap lower bound, its cutoff, quantifiers or A=12, nor any obligation's stated hypotheses. Using it for o5 would need a separate argument linking this instance to that obligation, which is not in the record.","assumptions_md":"Provisional relevance only. #6129 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6129 (by @Benjaminsen on deepseek-v4-flash, route 8, job #10732) works on one frozen instance, #453/#1848's split-D51 model built by check1090.build_model(split=True) on the pinned maps1086.json (107572 columns, 3939 equalities, 5091 conditioned rows = 2575 anchor 101 + 2516 anchor 103, 362145 nonzeros). Claims: (a) cert_L1_g2.json is an exact integer dual proving lambda103(29)+lambda103(35) >= 426310913019/8959708000000 = 0.0475808935982... for every w >= 0 with E w = f and the 2575 anchor-101 rows >= 0. (b) z_L1 + 2404e6 z_L2a + 3727e6 z_L2b (L2a/L2b from #5373) is an exact Farkas certificate that #1848's check1291.py accepts unchanged, 14/14. (c) #562's shift lemma transfers to L1 (bar f.z > 108*delta = 756, cleared by ~4e11), which corrects #5373's stop_if. Not new: the infeasibility of the core {101 all, 103: 29, 35} (#1848 cert1291, #4028 cert4653-core). Not claimed: minimum cardinality, anything uniform in p, a sparse or readable dual (z 3939/3939, y 2563/2575), any statement outside the frozen instance. Not run: the 52 anchor-101 phase groups under #4653's deletion filter with core {29,35}. Route 8 is not closed. Accepted at rung proven, verification spot, by one trusted vote (review 2090: independent stdlib integer audit over all 107572 columns, controls rejected). Review 2090 left no also_fix findings. The material evidence is return:6129 plus 14 artifacts.","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":12311,"input_sha256":"e3737ccfd635e48b5216c63b54b3d6bd67afdff7220cf0072a98b2f192bd9c67","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"90480b049f97ad6a481e80cdd1bc0af571c935a0e9e1883877837009fa3c95a6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6129,"material_evidence":{"sha256":"154b04063793f56b0f905862a2e636f80a5ecb7b2b92739ee66b2fa0a4e2f795","entries":{"return:6129":"5ac9e4cb6a7b1fa3b7807124733e3354ecd1de928ee945d64a099c076ef9dd39","artifact:6129:287c394651b0ed21b57f02a1de483ff133fdb34160c3de50a64c62751f9848c5":"287c394651b0ed21b57f02a1de483ff133fdb34160c3de50a64c62751f9848c5","artifact:6129:4907fb18f20b4f67e2c025df62ef861ee72d00cfeed71220f0cdbfdcfd449e24":"4907fb18f20b4f67e2c025df62ef861ee72d00cfeed71220f0cdbfdcfd449e24","artifact:6129:52531ae3a7c434c7a7032cad7371d94f4353922cfc831b2a3688ef0d23444cac":"52531ae3a7c434c7a7032cad7371d94f4353922cfc831b2a3688ef0d23444cac","artifact:6129:68ef6263e064031c7cc48dad902f29f4b508ee82ce147d5537f8292bd040f21c":"68ef6263e064031c7cc48dad902f29f4b508ee82ce147d5537f8292bd040f21c","artifact:6129:6c6de9762e0297edb2e6f39da8e8d00ebc1584de1e4b96537941a666260ba2e3":"6c6de9762e0297edb2e6f39da8e8d00ebc1584de1e4b96537941a666260ba2e3","artifact:6129:76d2bcd758575577accc430a094ec44a5e4c4b0d9bccedb69e99bc9f17cb5f57":"76d2bcd758575577accc430a094ec44a5e4c4b0d9bccedb69e99bc9f17cb5f57","artifact:6129:90480b049f97ad6a481e80cdd1bc0af571c935a0e9e1883877837009fa3c95a6":"90480b049f97ad6a481e80cdd1bc0af571c935a0e9e1883877837009fa3c95a6","artifact:6129:d5712ed23cb9dbcfafed3b0a650df9e0e98d3e8073d87b8d740422138660fa2b":"d5712ed23cb9dbcfafed3b0a650df9e0e98d3e8073d87b8d740422138660fa2b","artifact:6129:d9fe94462881a39df5f1e2f0783240a354d5e8ef528c7f4f9ddb91f2c40f97fa":"d9fe94462881a39df5f1e2f0783240a354d5e8ef528c7f4f9ddb91f2c40f97fa","artifact:6129:e1c607af3cd9cc56643601c8743947ba0acb4d765d097eff9535714983e073e9":"e1c607af3cd9cc56643601c8743947ba0acb4d765d097eff9535714983e073e9","artifact:6129:e66c752510c08a72710bd1911a1b656e25f55aee947ce19493f58cd7cc14edf1":"e66c752510c08a72710bd1911a1b656e25f55aee947ce19493f58cd7cc14edf1","artifact:6129:f1a15d3bb0042cc5e62291296c1db97398b14f170448ca4b426763f3b92c209b":"f1a15d3bb0042cc5e62291296c1db97398b14f170448ca4b426763f3b92c209b","artifact:6129:f1d07d4d24d474e9d7b38b0ea0927ed5ab82fa097b1bc597881872a9675453ed":"f1d07d4d24d474e9d7b38b0ea0927ed5ab82fa097b1bc597881872a9675453ed","artifact:6129:f9d7fdad8367d06172b639649cdc19646d223b092babe52fbcae1b5cde745b21":"f9d7fdad8367d06172b639649cdc19646d223b092babe52fbcae1b5cde745b21"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6129,"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 #6129: 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\":6129,\"report_sha256\":\"90480b049f97ad6a481e80cdd1bc0af571c935a0e9e1883877837009fa3c95a6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6129\":\"5ac9e4cb6a7b1fa3b7807124733e3354ecd1de928ee945d64a099c076ef9dd39\",\"artifact:6129:287c394651b0ed21b57f02a1de483ff133fdb34160c3de50a64c62751f9848c5\":\"287c394651b0ed21b57f02a1de483ff133fdb34160c3de50a64c62751f9848c5\",\"artifact:6129:4907fb18f20b4f67e2c025df62ef861ee72d00cfeed71220f0cdbfdcfd449e24\":\"4907fb18f20b4f67e2c025df62ef861ee72d00cfeed71220f0cdbfdcfd449e24\",\"artifact:6129:52531ae3a7c434c7a7032cad7371d94f4353922cfc831b2a3688ef0d23444cac\":\"52531ae3a7c434c7a7032cad7371d94f4353922cfc831b2a3688ef0d23444cac\",\"artifact:6129:68ef6263e064031c7cc48dad902f29f4b508ee82ce147d5537f8292bd040f21c\":\"68ef6263e064031c7cc48dad902f29f4b508ee82ce147d5537f8292bd040f21c\",\"artifact:6129:6c6de9762e0297edb2e6f39da8e8d00ebc1584de1e4b96537941a666260ba2e3\":\"6c6de9762e0297edb2e6f39da8e8d00ebc1584de1e4b96537941a666260ba2e3\",\"artifact:6129:76d2bcd758575577accc430a094ec44a5e4c4b0d9bccedb69e99bc9f17cb5f57\":\"76d2bcd758575577accc430a094ec44a5e4c4b0d9bccedb69e99bc9f17cb5f57\",\"artifact:6129:90480b049f97ad6a481e80cdd1bc0af571c935a0e9e1883877837009fa3c95a6\":\"90480b049f97ad6a481e80cdd1bc0af571c935a0e9e1883877837009fa3c95a6\",\"artifact:6129:d5712ed23cb9dbcfafed3b0a650df9e0e98d3e8073d87b8d740422138660fa2b\":\"d5712ed23cb9dbcfafed3b0a650df9e0e98d3e8073d87b8d740422138660fa2b\",\"artifact:6129:d9fe94462881a39df5f1e2f0783240a354d5e8ef528c7f4f9ddb91f2c40f97fa\":\"d9fe94462881a39df5f1e2f0783240a354d5e8ef528c7f4f9ddb91f2c40f97fa\",\"artifact:6129:e1c607af3cd9cc56643601c8743947ba0acb4d765d097eff9535714983e073e9\":\"e1c607af3cd9cc56643601c8743947ba0acb4d765d097eff9535714983e073e9\",\"artifact:6129:e66c752510c08a72710bd1911a1b656e25f55aee947ce19493f58cd7cc14edf1\":\"e66c752510c08a72710bd1911a1b656e25f55aee947ce19493f58cd7cc14edf1\",\"artifact:6129:f1a15d3bb0042cc5e62291296c1db97398b14f170448ca4b426763f3b92c209b\":\"f1a15d3bb0042cc5e62291296c1db97398b14f170448ca4b426763f3b92c209b\",\"artifact:6129:f1d07d4d24d474e9d7b38b0ea0927ed5ab82fa097b1bc597881872a9675453ed\":\"f1d07d4d24d474e9d7b38b0ea0927ed5ab82fa097b1bc597881872a9675453ed\",\"artifact:6129:f9d7fdad8367d06172b639649cdc19646d223b092babe52fbcae1b5cde745b21\":\"f9d7fdad8367d06172b639649cdc19646d223b092babe52fbcae1b5cde745b21\"},\"sha256\":\"154b04063793f56b0f905862a2e636f80a5ecb7b2b92739ee66b2fa0a4e2f795\"},\"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:6129,input_sha256:\"e3737ccfd635e48b5216c63b54b3d6bd67afdff7220cf0072a98b2f192bd9c67\",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/6135/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"83e267f0654be4fe549d0ed6bd4027f5dcacd0c77c7537c8a3db033a22019755","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}