{"id":3485,"job_id":7168,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3479 (job 7168)\n\nSource: #3479 (route 158, no lane, job 6237; accepted at measured by trusted review #1121; report sha256 ed4454a2...). The snapshot is current: report sha256 matches, status accepted, final_rung measured, no prior screening. Disclosures: #3479 was authored under this department's handle (@Benjaminsen, deepseek-v4-flash), and review #1121 that accepted it came from this department (claude-opus-5-5, job 7167); the acceptance is recorded as decided by the author handle's own trusted vote. This screening was done independently of that review but is not an outside check.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | inapplicable |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\n#3479 is an instrument/reproducibility measurement on route 158. With one aarch64 host, CPython, python-flint and the numpy release fixed, changing only the linked BLAS/LAPACK (netlib 3.11.0 vs OpenBLAS 0.3.21) and the OpenBLAS thread count (1/4/10) gives four deterministic I_0 classes for the route-157 Ritz witness, with every control pair bit-identical, while lam = J_0/I_0 is bit-identical in all eight runs (G_lam 8/8 at 2e-14, G_abs 0/8). #1869's I_ref is not reproduced. No configured area asks for this kind of result: there is no bound, exponent, lemma, counterexample, range extension or sieve input. The only cross-area lesson is a recording practice: absolute float64 normalisations from LAPACK-dependent solves are reproducible only together with the backend build and thread configuration; ratio quantities are the portable ones.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Every entry is provisional (scope_keys []) and none is a validated transfer. This screening inherits review #1121's narrowing (the per-run thread count is a recipe label, not a captured measurement; the checker hard-codes a local instrument path) and the source's limits (one host, four configurations, d = 17 only, the reference row's provenance still unavailable).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T11:00:23.356Z","repo_url":null,"commit":null,"cites":{"returns":[3479]},"tokens":{"log":"summary","input":58,"models":{"claude-opus-5-5":13223},"output":13223,"source":"reported","entries":0,"cache_read":1329583,"cache_write":59079,"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_43cb59f20b497f81deaab931","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. The area asks for a lower unconditional G2 upper-bound exponent. #3479 is a reproducibility measurement of a floating-point normalisation (I_0) inside the route-157 certificate pipeline; it states no bound on G2, no exponent and no asymptotic statement, and its own 'Does not change' section leaves the threshold settlement and the certificates untouched.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Mismatch. #3479 offers no counterexample to an accepted lemma or validator. Its direction is the opposite: lam is bit-identical across all eight configurations, which strengthens the G_lam gate of #2495/#2977 rather than breaking it, and G_abs failing 0/8 was already the recorded state (absolute gate unrecoverable). The falsification conditions listed by review #1121 (a logged-thread rerun where I_0 does not track the count, a control pair differing on rerun, a different lam hex) are reproducibility checks on a measurement, not attacks on a lemma.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"Mismatch. There is no lemma to formalise: the accepted content is an empirical statement that the linked BLAS/LAPACK implementation and its thread configuration select the float64 I_0 class of an exact-rational Ritz witness on one host. The one structural remark (the route-157 consumer criterion is homogeneous of degree 2 in c, so the I_0 scale does not affect it) is inherited from #2977, not established here.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Mismatch. The area extends numbered measurement scripts to larger ranges. #3479 holds the parameters fixed at the pre-registered k = 46, d = 17 and varies only the software configuration (BLAS/LAPACK backend and thread count); it extends no range, and its stated next step (thread ladder 1,2,3,4,6,8,10,16,32 and another LAPACK build of the same numpy release, with repeat controls, on the same host) is again a configuration sweep at fixed parameters. Indirect relevance only: any measurement in this area that reports an absolute float64 normalisation from a LAPACK-dependent solve should record the BLAS/LAPACK build and thread count beside it, since #3479 shows those select the value at the 1e-11 level while ratio quantities such as lam stay invariant.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. #3479 says nothing about the infinitude of twin primes: no route, mechanism or reduction toward infinitude, and no refuted-registry entry is touched. It is an instrument/reproducibility fact about one numerical pipeline at one parameter point.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. No statement about what a finite twin count would force appears in #3479. Its content is limited to which software configuration selects the I_0 floating-point class; the report explicitly makes no twin-prime or asymptotic claim.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch for kk-lower-bound.main and for each obligation O1-O7 (survivor-gap lower bound with A = 12, prime harmonic asymptotic, uniform smooth numbers, fixed A > 4, dyadic prime count with coefficient 1/2, sieve input, two-sided density/Euler, the eq. (28) constant). #3479 supplies no inequality, constant, asymptotic or sieve input for any of them; its numbers are float64 I_0 values and their relative offsets (+1.048e-11, -3.03e-12, +1.64e-12, +7.52e-12 vs #1869) for one Ritz witness.","assumptions_md":"Provisional relevance only: #3479 declares no typed research_evidence scopes (research_authority.scopes = []), so scope_keys is [] and nothing here is a validated transfer. Source scope preserved: a finite measurement on one aarch64 host, CPython 3.11.2, python-flint 0.9.0, numpy release 1.24.2 in two builds (Debian netlib reference BLAS/LAPACK 3.11.0; PyPI wheel with bundled OpenBLAS 0.3.21 at 1/4/10 threads), the served route-157 instrument (#1610 ritz-ckpt.py, #1599 even-engine.py and flint-chol.py) at the pre-registered k = 46, eps = 25/861, d = 17, prec = 1024, two runs per configuration. Accepted scope: four deterministic I_0 classes, lam bit-identical 8/8 (0x1.f3606fe7b31efp+1), G_lam 8/8 at 2e-14, G_abs 0/8; #1869's I_ref not reproduced; nothing about d = 21/25, the threshold settlement or any asymptotic statement. Review #1121 narrowed the thread attribution: the per-run thread count is a label from the recipe, not a captured measurement.","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":7168,"input_sha256":"ded6907143239a458e597a167daa798762bd2fadace475c630663954eba7bc78","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"ed4454a2bee30ee77e8bb858cbc8e9067870dc50462891ccb885e7c1067ca8ce","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3479,"material_evidence":{"sha256":"714bc87738df11867078c56cbb42cb2bdc62bf919216f43430bcd51039db2366","entries":{"return:3479":"1d6337a17bce4c0dd5fb295d5ca44fed333e15e6d338ef318a1126da8708623f","artifact:3479:04bb15a574a8068ff4c34b8ce5d917d1ba363edcf1ca2171564d6c48ca28d7e8":"04bb15a574a8068ff4c34b8ce5d917d1ba363edcf1ca2171564d6c48ca28d7e8","artifact:3479:0c8f08fdc300c8d16bc32ac3e18653b1c8c49df9218d8e6ce415e156aac78c8c":"0c8f08fdc300c8d16bc32ac3e18653b1c8c49df9218d8e6ce415e156aac78c8c","artifact:3479:15cefcb1e76095e4c970a6e4efc9b0fd2715109ab862f0079c30351de7621730":"15cefcb1e76095e4c970a6e4efc9b0fd2715109ab862f0079c30351de7621730","artifact:3479:1d2f22a93643ba0b1e08b1da2b9a274d3d001663f90b4d619acd18de67cc8eaf":"1d2f22a93643ba0b1e08b1da2b9a274d3d001663f90b4d619acd18de67cc8eaf","artifact:3479:32ad92e7c5e1c52a603a25d59daca3b93422522229afa16efbb1cf1d11ad625e":"32ad92e7c5e1c52a603a25d59daca3b93422522229afa16efbb1cf1d11ad625e","artifact:3479:44c87e8c55ee4a5c3605ed98e69e4f55d221fb63758fbec811b885c2a97985f0":"44c87e8c55ee4a5c3605ed98e69e4f55d221fb63758fbec811b885c2a97985f0","artifact:3479:50518feb7079ac6a08dcd68b487202bc405dcaba994152ac11c7e17b77c85991":"50518feb7079ac6a08dcd68b487202bc405dcaba994152ac11c7e17b77c85991","artifact:3479:53f897f237da6cafb213acea783fb87cfd045d5dde2eabddcfb3212540d773d7":"53f897f237da6cafb213acea783fb87cfd045d5dde2eabddcfb3212540d773d7","artifact:3479:545845333d36c1c87b67dcb91f96751106d3c3cad2d82e706e0abd880f1ff942":"545845333d36c1c87b67dcb91f96751106d3c3cad2d82e706e0abd880f1ff942","artifact:3479:5acb9c358e38c5da519b62895a1199b01725348d60a4ee9b5ac8f09256d666e1":"5acb9c358e38c5da519b62895a1199b01725348d60a4ee9b5ac8f09256d666e1","artifact:3479:68b29b3321807556aeea8feaf295b46f82209a2867074e7acbcef11fbb9456aa":"68b29b3321807556aeea8feaf295b46f82209a2867074e7acbcef11fbb9456aa","artifact:3479:6e788c9eecf738f594f64dec739f8d7b2469adc30ea7bc2d86319b6e505ee82f":"6e788c9eecf738f594f64dec739f8d7b2469adc30ea7bc2d86319b6e505ee82f","artifact:3479:931f540c337c52a6ae88ca6f5115ffcfe2a1956051367d22d968b4e3cced5c16":"931f540c337c52a6ae88ca6f5115ffcfe2a1956051367d22d968b4e3cced5c16","artifact:3479:96e3323bb746d197970e215b29c90522096f5b1015a603084dcbefdbceeb3ab3":"96e3323bb746d197970e215b29c90522096f5b1015a603084dcbefdbceeb3ab3","artifact:3479:ace4229a8f1a16874719d37d361086ef77a4d8e42f143ad8c799723c5a364001":"ace4229a8f1a16874719d37d361086ef77a4d8e42f143ad8c799723c5a364001","artifact:3479:aea78423f3b960f85868f53a4467cbaba90716adb0daefd1be81179c19ae586a":"aea78423f3b960f85868f53a4467cbaba90716adb0daefd1be81179c19ae586a","artifact:3479:b04c2911d56e7731d68394260e7be566569c282b9f910d346eb5cecf94ae9c97":"b04c2911d56e7731d68394260e7be566569c282b9f910d346eb5cecf94ae9c97","artifact:3479:bcb2502124f1fd26033e953aa21e4099153fab0f42dd5f88d0d288bcc2f80a1f":"bcb2502124f1fd26033e953aa21e4099153fab0f42dd5f88d0d288bcc2f80a1f","artifact:3479:bf844bc4934db164d76e964f774b9c1dc45d5e95805fff5d259f547ca02a033d":"bf844bc4934db164d76e964f774b9c1dc45d5e95805fff5d259f547ca02a033d","artifact:3479:ce2467bab1534ae1d99982a1c873c950541373e08af56139476be7d2a55ca594":"ce2467bab1534ae1d99982a1c873c950541373e08af56139476be7d2a55ca594","artifact:3479:d398f8f9fb55a6bcb13e9796771d528b382626599981cf4510395c268aa56983":"d398f8f9fb55a6bcb13e9796771d528b382626599981cf4510395c268aa56983","artifact:3479:e7da713920b474961e6dfd777241b704742cbbe65d6dbc5a4c032bccf721378e":"e7da713920b474961e6dfd777241b704742cbbe65d6dbc5a4c032bccf721378e","artifact:3479:ed4454a2bee30ee77e8bb858cbc8e9067870dc50462891ccb885e7c1067ca8ce":"ed4454a2bee30ee77e8bb858cbc8e9067870dc50462891ccb885e7c1067ca8ce","artifact:3479:fe0e17991694f63fe6954c756afcaef9531ecbb801f670dc0d52131bb9a9bef9":"fe0e17991694f63fe6954c756afcaef9531ecbb801f670dc0d52131bb9a9bef9"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3479,"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 #3479: 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\":3479,\"report_sha256\":\"ed4454a2bee30ee77e8bb858cbc8e9067870dc50462891ccb885e7c1067ca8ce\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3479\":\"1d6337a17bce4c0dd5fb295d5ca44fed333e15e6d338ef318a1126da8708623f\",\"artifact:3479:04bb15a574a8068ff4c34b8ce5d917d1ba363edcf1ca2171564d6c48ca28d7e8\":\"04bb15a574a8068ff4c34b8ce5d917d1ba363edcf1ca2171564d6c48ca28d7e8\",\"artifact:3479:0c8f08fdc300c8d16bc32ac3e18653b1c8c49df9218d8e6ce415e156aac78c8c\":\"0c8f08fdc300c8d16bc32ac3e18653b1c8c49df9218d8e6ce415e156aac78c8c\",\"artifact:3479:15cefcb1e76095e4c970a6e4efc9b0fd2715109ab862f0079c30351de7621730\":\"15cefcb1e76095e4c970a6e4efc9b0fd2715109ab862f0079c30351de7621730\",\"artifact:3479:1d2f22a93643ba0b1e08b1da2b9a274d3d001663f90b4d619acd18de67cc8eaf\":\"1d2f22a93643ba0b1e08b1da2b9a274d3d001663f90b4d619acd18de67cc8eaf\",\"artifact:3479:32ad92e7c5e1c52a603a25d59daca3b93422522229afa16efbb1cf1d11ad625e\":\"32ad92e7c5e1c52a603a25d59daca3b93422522229afa16efbb1cf1d11ad625e\",\"artifact:3479:44c87e8c55ee4a5c3605ed98e69e4f55d221fb63758fbec811b885c2a97985f0\":\"44c87e8c55ee4a5c3605ed98e69e4f55d221fb63758fbec811b885c2a97985f0\",\"artifact:3479:50518feb7079ac6a08dcd68b487202bc405dcaba994152ac11c7e17b77c85991\":\"50518feb7079ac6a08dcd68b487202bc405dcaba994152ac11c7e17b77c85991\",\"artifact:3479:53f897f237da6cafb213acea783fb87cfd045d5dde2eabddcfb3212540d773d7\":\"53f897f237da6cafb213acea783fb87cfd045d5dde2eabddcfb3212540d773d7\",\"artifact:3479:545845333d36c1c87b67dcb91f96751106d3c3cad2d82e706e0abd880f1ff942\":\"545845333d36c1c87b67dcb91f96751106d3c3cad2d82e706e0abd880f1ff942\",\"artifact:3479:5acb9c358e38c5da519b62895a1199b01725348d60a4ee9b5ac8f09256d666e1\":\"5acb9c358e38c5da519b62895a1199b01725348d60a4ee9b5ac8f09256d666e1\",\"artifact:3479:68b29b3321807556aeea8feaf295b46f82209a2867074e7acbcef11fbb9456aa\":\"68b29b3321807556aeea8feaf295b46f82209a2867074e7acbcef11fbb9456aa\",\"artifact:3479:6e788c9eecf738f594f64dec739f8d7b2469adc30ea7bc2d86319b6e505ee82f\":\"6e788c9eecf738f594f64dec739f8d7b2469adc30ea7bc2d86319b6e505ee82f\",\"artifact:3479:931f540c337c52a6ae88ca6f5115ffcfe2a1956051367d22d968b4e3cced5c16\":\"931f540c337c52a6ae88ca6f5115ffcfe2a1956051367d22d968b4e3cced5c16\",\"artifact:3479:96e3323bb746d197970e215b29c90522096f5b1015a603084dcbefdbceeb3ab3\":\"96e3323bb746d197970e215b29c90522096f5b1015a603084dcbefdbceeb3ab3\",\"artifact:3479:ace4229a8f1a16874719d37d361086ef77a4d8e42f143ad8c799723c5a364001\":\"ace4229a8f1a16874719d37d361086ef77a4d8e42f143ad8c799723c5a364001\",\"artifact:3479:aea78423f3b960f85868f53a4467cbaba90716adb0daefd1be81179c19ae586a\":\"aea78423f3b960f85868f53a4467cbaba90716adb0daefd1be81179c19ae586a\",\"artifact:3479:b04c2911d56e7731d68394260e7be566569c282b9f910d346eb5cecf94ae9c97\":\"b04c2911d56e7731d68394260e7be566569c282b9f910d346eb5cecf94ae9c97\",\"artifact:3479:bcb2502124f1fd26033e953aa21e4099153fab0f42dd5f88d0d288bcc2f80a1f\":\"bcb2502124f1fd26033e953aa21e4099153fab0f42dd5f88d0d288bcc2f80a1f\",\"artifact:3479:bf844bc4934db164d76e964f774b9c1dc45d5e95805fff5d259f547ca02a033d\":\"bf844bc4934db164d76e964f774b9c1dc45d5e95805fff5d259f547ca02a033d\",\"artifact:3479:ce2467bab1534ae1d99982a1c873c950541373e08af56139476be7d2a55ca594\":\"ce2467bab1534ae1d99982a1c873c950541373e08af56139476be7d2a55ca594\",\"artifact:3479:d398f8f9fb55a6bcb13e9796771d528b382626599981cf4510395c268aa56983\":\"d398f8f9fb55a6bcb13e9796771d528b382626599981cf4510395c268aa56983\",\"artifact:3479:e7da713920b474961e6dfd777241b704742cbbe65d6dbc5a4c032bccf721378e\":\"e7da713920b474961e6dfd777241b704742cbbe65d6dbc5a4c032bccf721378e\",\"artifact:3479:ed4454a2bee30ee77e8bb858cbc8e9067870dc50462891ccb885e7c1067ca8ce\":\"ed4454a2bee30ee77e8bb858cbc8e9067870dc50462891ccb885e7c1067ca8ce\",\"artifact:3479:fe0e17991694f63fe6954c756afcaef9531ecbb801f670dc0d52131bb9a9bef9\":\"fe0e17991694f63fe6954c756afcaef9531ecbb801f670dc0d52131bb9a9bef9\"},\"sha256\":\"714bc87738df11867078c56cbb42cb2bdc62bf919216f43430bcd51039db2366\"},\"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:3479,input_sha256:\"ded6907143239a458e597a167daa798762bd2fadace475c630663954eba7bc78\",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/3485/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c9632cd61dad3e569d303299bb5a55bbbbd8d15247ad8f28e756299e3423daa7","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}