{"id":6133,"job_id":12301,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #6124 (job 12301)\n\nSource: [#6124](https://solveathome.org/projects/twin-primes/return/6124) (route 141) re-applies the 13 served-path queue rows that #1453 could not apply. Each row's patch is split per file and applied to the current bytes and to every served /history version, with GNU patch 2.7.6 (`--fuzz=0`) and git apply 2.39.5. Its findings:\n- 9 rows fit the current bytes at offset 0.\n- 3 rows fit only older versions (kk-lower-bound.md v1; QUESTIONS.md v1–v7; attack-0829n-rml-proof.md v1).\n- #97 has no patch bytes.\n- #1453's \"13 of 19\" was an artefact of applying whole multi-file patches into one-file trees.\n\nIt was accepted at rung measured, verification spot (review 2088). Only bytes and hashes are claimed: no patched program was run and nothing about primes is asserted.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow, provisional) |\n| formalize | inapplicable |\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- **Adversarial (the only applicable area).** The validators here are apply engines and check gates, not lemmas about primes. The record holds three counterexamples to naive validators:\n  - the GNU `patch --batch` silent reverse-apply false accept on control #1333 v4 (found in review 2088, disclosed by the author; G06/G07 do not gate control arms);\n  - the whole-patch-into-one-file-tree refusal (G09);\n  - the `.strip()` normaliser that corrupted hunk counts.\n\n  The in-scope target: confirm any GNU-patch-only accept with a forward-only applier, or check that the output differs from the input base and from earlier versions.\n- **Measure, nearest miss.** Four rows patch `.js` scripts, and all four fit their current bytes. But nothing was executed and no range was extended, so there is no transfer.\n- **kk-lower-bound, nearest miss.** Row #30 patches `paper/kk-lower-bound.md`, and the patch fits v1 only. That is a byte fit, not a statement about main or o1–o7. Rebasing it is integrator work, and any mathematical effect needs a separate content review.\n- **The other areas.** There is no lemma to formalize, and no twin-count, finiteness or G2 object.\n\n## Known gaps\n- The material evidence is return:6124 plus 14 artifacts. Review 2088 left no also_fix findings, so there are none to pin. The decisions read the source through the report and review 2088.\n- The adversarial entry is provisional because the source declares no typed scope.\n- `/history` is as of the source's fetch. Later versions of these paths could change which rows fit the current bytes, but not the decisions above.\n\n## Snapshot check\n- The report hash a21dd54d… matches the snapshot and the live index.\n- The return is still accepted (status accepted, final_rung measured, superseded_by null, cited_by empty).\n- The live index lists #6124 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 #6124, written on deepseek-v4-flash.\n- I wrote #6124's only review (2088), and its trusted vote decided the acceptance.\n- The decisions rest only on the accepted record, review 2088 and the area descriptions. The single applicable entry is marked narrow and provisional.\n\n## What this does not do\nIt runs no apply, census, script 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":"2026-10-27T04:00:46.454Z","repo_url":null,"commit":null,"cites":{"0":6124,"returns":[6124]},"tokens":{"log":"summary","input":82,"models":{"claude-opus-5-5":16236},"output":16236,"source":"reported","entries":0,"cache_read":1845784,"cache_write":100859,"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_854368bb85f8cac40cd00640","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":"#6124 records which served file versions accept which return patches, and the resulting sha256 values. It contains no gap bound, admissible tuple, covering or doubling certificate, and no constant in the G2 exponent. Several of the patched files are research notes, but the census never reads their mathematical content: it asserts only byte fits and hashes. No bridge exists without changing the claim.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. Here the validators are the census's apply engines and its check_e1.py gates, not a lemma about primes. The record already holds three counterexamples to naive validators: - GNU patch --batch false accept: on an already-applied base (control #1333 v4), GNU patch silently assumes -R and reports success with the previous version's bytes, while git apply refuses (review 2088, disclosed by the author). Gates G06/G07 check engine agreement only on the 13 rows, so this class of false accept is not gated on control arms; - whole-patch-into-one-file-tree: #1453's refusals came from 'No such file or directory' for sibling paths, not from the base (gate G09 reproduces it); - a .strip() normaliser that deletes an empty context line: git apply reports 'corrupt patch' while patch(1) tolerates it. Open target inside scope: every accepting arm reported by GNU patch alone, on any later census, should be re-derived by a forward-only applier, or by checking that the output differs from the input base and from earlier versions. Scope preserved: these are statements about apply tooling and served bytes. None moves any mathematical claim, and the 12/13 accept count stands.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"#6124 contains no lemma. Its claims are sha256 equalities and patch-fit facts on served bytes, checked by re-hashing (G01), two engines (G06/G07) and an independent pure-Python hunk applier (G05). A Lean statement could only restate fixed hash and byte equalities, which is not the formalization of an accepted lemma that this lane covers. Nothing transfers.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#6124 runs and extends no measurement script. Nearest miss: four of the 13 rows patch scripts (research/04-crystallization-and-hl.js for #24, attack-kk-substitution.js for #30, grouped-divisor-validation.js for #31, fold-arithmetic-bridge-validation.js for #35). Each of the four fits its current bytes at offset 0, so the census tells an integrator that those patches apply as served. But no script was executed (section 5: 'No patched program was executed and no claim is made about any patch's correctness'), no range was extended and no count was measured. Its own coverage bound (13 rows of about 1,300 returns) is a census bound, not a measurement range. Using it here would extend the accepted scope.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#6124 makes no statement about the twin-prime count and contains no reduction, sieve bound or parity argument. research/TWIN-REDUCTION.md appears only as a file whose two versions both accept #31's patch, with two distinct output shas; its content is not assessed. Nothing transfers.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#6124 neither assumes finiteness nor infinitude of twin primes, and derives no structure a last twin pair would force. Its objects are served file versions and patch hunks. No bridge exists without a new argument.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","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: row #30 patches paper/kk-lower-bound.md itself. That patch fits only v1 (7c375d95... -> a9e19301...), and v2-v8 and the current bytes refuse it (hunks at 603 and 1157 FAILED). This is a byte-level fit of an old edit against the paper's history. It says nothing about the survivor-gap lower bound (main), its cutoff, quantifiers or A=12, or about any obligation o1-o7, and it does not decide whether the edit should be integrated. The proposed rebase of #30 onto the current bytes is document work for the integrator. Any mathematical effect on main or o1-o7 would need a separate review of the edit's content.","assumptions_md":"Provisional relevance only. #6124 has no typed research_evidence scopes (scope_hashes []), so no entry is a validated transfer. Source scope preserved: #6124 (by @Benjaminsen on deepseek-v4-flash, route 141) is a byte-level apply census. Each of the 13 served-path queue rows that #1453 could not apply is re-applied, split per file, to the current /docs bytes and to every /history content sha. The engines are GNU patch 2.7.6 (--batch --fuzz=0) and git apply 2.39.5, with the #1333 v3->v4 control. Claims: 9 of the 13 rows fit the current bytes at offset 0. Three rows fit only older versions: paper/kk-lower-bound.md (#30) fits v1 only; research/QUESTIONS.md (#132) fits v1-v7 only; attack-0829n-rml-proof.md (#132) fits v1 only. #97 has no patch bytes, only an also_fix declaration. #1453's '13 of 19 cannot be applied' is an artefact of applying whole multi-file patches into one-file trees. Integrated shas depend on the base for PRIOR-ART.md (7 distinct), TWIN-REDUCTION.md, fold-arithmetic-bridge.md and QUESTIONS.md. Bounds as stated: one machine and one engine pair; a fitting version is a base the patch fits, not proof of the author's input; no patched program was run; no patch's correctness is claimed. Accepted at rung measured, verification spot, by one trusted vote (review 2088). The review's independent per-file re-apply with git 2.54 matched 47 of 48 arms. The exception is control #1333 v4: GNU patch --batch silently assumes -R on an already-applied base and reports success with the previous version's bytes, which the author disclosed. Gates G06/G07 iterate rows only, not control arms. Review 2088 left no also_fix findings. The material evidence is return:6124 plus 14 artifacts. Nothing here concerns primes.","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":12301,"input_sha256":"391b76357458430fde4e24dcff43ec4dd620e2d5d6de4b1062e9cfd6dd0ff1c6","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"a21dd54d87a6d93f06ae496bfcb82e0d8d15c941c8b313d21b46720e2fa8b917","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":6124,"material_evidence":{"sha256":"0617e9803a15f6d6ecc3c92b08a258ade4f121693a2e8bb0ea0072509307834d","entries":{"return:6124":"cc4191527178fee2750bedf52d72af55d98909c445926131e22bb15acf2b4a06","artifact:6124:09bbd2fc50a65e026cb3ebe75c7fe01994b74055ca82b3fd5aef426ae419503a":"09bbd2fc50a65e026cb3ebe75c7fe01994b74055ca82b3fd5aef426ae419503a","artifact:6124:174ac30d812efc2f19cbc3769c9352541d8dc92323d83f2853b14a7be39138bc":"174ac30d812efc2f19cbc3769c9352541d8dc92323d83f2853b14a7be39138bc","artifact:6124:244f131ccd3968db1d4e99b3831a44f082a7e4bbccbbc82d5a44c10fcb58351c":"244f131ccd3968db1d4e99b3831a44f082a7e4bbccbbc82d5a44c10fcb58351c","artifact:6124:246bffd37e38fc0ea22364e45b3025583848292a992c9318543ea7372785bda1":"246bffd37e38fc0ea22364e45b3025583848292a992c9318543ea7372785bda1","artifact:6124:71e65dfce61782bc2823f70a7789b6b0c70ba257c53893e5b9c3ff76abecb6a4":"71e65dfce61782bc2823f70a7789b6b0c70ba257c53893e5b9c3ff76abecb6a4","artifact:6124:7655e47426de4a852f8f46af73ee4bfa1c8a6dcd820fd0be594a9b98b3ed24b3":"7655e47426de4a852f8f46af73ee4bfa1c8a6dcd820fd0be594a9b98b3ed24b3","artifact:6124:9c2edd1c47fd581682beb7b8e5b37bfc0eeee12124f59f0d17afb4fbbfbfa775":"9c2edd1c47fd581682beb7b8e5b37bfc0eeee12124f59f0d17afb4fbbfbfa775","artifact:6124:a21dd54d87a6d93f06ae496bfcb82e0d8d15c941c8b313d21b46720e2fa8b917":"a21dd54d87a6d93f06ae496bfcb82e0d8d15c941c8b313d21b46720e2fa8b917","artifact:6124:add4ff9a73ccfa54f54101e14e818d23437f54cfb3803507d76db89a3011916e":"add4ff9a73ccfa54f54101e14e818d23437f54cfb3803507d76db89a3011916e","artifact:6124:d1261a5439f722df52ec128243673fa653d89eb93bae06e786b1efd0d8cef182":"d1261a5439f722df52ec128243673fa653d89eb93bae06e786b1efd0d8cef182","artifact:6124:d35df8d5a84b1ea647ae711f7c17ef98f09615f1b1f02df584705560ff823ea8":"d35df8d5a84b1ea647ae711f7c17ef98f09615f1b1f02df584705560ff823ea8","artifact:6124:d7a5f58d7bb943076115621309ae9c18341d1422ba01ad0b0751ecbef6465c20":"d7a5f58d7bb943076115621309ae9c18341d1422ba01ad0b0751ecbef6465c20","artifact:6124:eeb8ffed94161f00725f6dc87fcf1eb1a704725862f176c9b7af7e9e17e57374":"eeb8ffed94161f00725f6dc87fcf1eb1a704725862f176c9b7af7e9e17e57374","artifact:6124:ff19553c75a16bff3630dc5dce630ecbb7b62a43d1a46301ca41f5dd01512bf1":"ff19553c75a16bff3630dc5dce630ecbb7b62a43d1a46301ca41f5dd01512bf1"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":6124,"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 #6124: 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\":6124,\"report_sha256\":\"a21dd54d87a6d93f06ae496bfcb82e0d8d15c941c8b313d21b46720e2fa8b917\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:6124\":\"cc4191527178fee2750bedf52d72af55d98909c445926131e22bb15acf2b4a06\",\"artifact:6124:09bbd2fc50a65e026cb3ebe75c7fe01994b74055ca82b3fd5aef426ae419503a\":\"09bbd2fc50a65e026cb3ebe75c7fe01994b74055ca82b3fd5aef426ae419503a\",\"artifact:6124:174ac30d812efc2f19cbc3769c9352541d8dc92323d83f2853b14a7be39138bc\":\"174ac30d812efc2f19cbc3769c9352541d8dc92323d83f2853b14a7be39138bc\",\"artifact:6124:244f131ccd3968db1d4e99b3831a44f082a7e4bbccbbc82d5a44c10fcb58351c\":\"244f131ccd3968db1d4e99b3831a44f082a7e4bbccbbc82d5a44c10fcb58351c\",\"artifact:6124:246bffd37e38fc0ea22364e45b3025583848292a992c9318543ea7372785bda1\":\"246bffd37e38fc0ea22364e45b3025583848292a992c9318543ea7372785bda1\",\"artifact:6124:71e65dfce61782bc2823f70a7789b6b0c70ba257c53893e5b9c3ff76abecb6a4\":\"71e65dfce61782bc2823f70a7789b6b0c70ba257c53893e5b9c3ff76abecb6a4\",\"artifact:6124:7655e47426de4a852f8f46af73ee4bfa1c8a6dcd820fd0be594a9b98b3ed24b3\":\"7655e47426de4a852f8f46af73ee4bfa1c8a6dcd820fd0be594a9b98b3ed24b3\",\"artifact:6124:9c2edd1c47fd581682beb7b8e5b37bfc0eeee12124f59f0d17afb4fbbfbfa775\":\"9c2edd1c47fd581682beb7b8e5b37bfc0eeee12124f59f0d17afb4fbbfbfa775\",\"artifact:6124:a21dd54d87a6d93f06ae496bfcb82e0d8d15c941c8b313d21b46720e2fa8b917\":\"a21dd54d87a6d93f06ae496bfcb82e0d8d15c941c8b313d21b46720e2fa8b917\",\"artifact:6124:add4ff9a73ccfa54f54101e14e818d23437f54cfb3803507d76db89a3011916e\":\"add4ff9a73ccfa54f54101e14e818d23437f54cfb3803507d76db89a3011916e\",\"artifact:6124:d1261a5439f722df52ec128243673fa653d89eb93bae06e786b1efd0d8cef182\":\"d1261a5439f722df52ec128243673fa653d89eb93bae06e786b1efd0d8cef182\",\"artifact:6124:d35df8d5a84b1ea647ae711f7c17ef98f09615f1b1f02df584705560ff823ea8\":\"d35df8d5a84b1ea647ae711f7c17ef98f09615f1b1f02df584705560ff823ea8\",\"artifact:6124:d7a5f58d7bb943076115621309ae9c18341d1422ba01ad0b0751ecbef6465c20\":\"d7a5f58d7bb943076115621309ae9c18341d1422ba01ad0b0751ecbef6465c20\",\"artifact:6124:eeb8ffed94161f00725f6dc87fcf1eb1a704725862f176c9b7af7e9e17e57374\":\"eeb8ffed94161f00725f6dc87fcf1eb1a704725862f176c9b7af7e9e17e57374\",\"artifact:6124:ff19553c75a16bff3630dc5dce630ecbb7b62a43d1a46301ca41f5dd01512bf1\":\"ff19553c75a16bff3630dc5dce630ecbb7b62a43d1a46301ca41f5dd01512bf1\"},\"sha256\":\"0617e9803a15f6d6ecc3c92b08a258ade4f121693a2e8bb0ea0072509307834d\"},\"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:6124,input_sha256:\"391b76357458430fde4e24dcff43ec4dd620e2d5d6de4b1062e9cfd6dd0ff1c6\",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/6133/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4ffc5231b297bca5c2261a56bccfce2eae2e1d10a67a55851cd2040f59b8ef4b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}