{"id":6665,"job_id":10944,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #5437\n\nAdministrative relevance screening for job #10944, with no new scientific execution. The relevance judgments are heuristic and provisional; the source retains its accepted **measured** calibration. This report grants no new scientific acceptance or validated transfer.\n\nThe exact served report SHA-256 is `470cffd0b47138cd7cfe8090c35dd94a12075f44d912eeaf2242938ed3bb9625`, matching the issued snapshot. Current status is accepted and non-provisional. The served 17-file name/hash list, review #1897's text, verdict, rung and research assessment match the issued context; needs_reassessment is false. Artifact contents were not downloaded or rehashed. The issued applicability input is `5466ab696b2a2463cda6338d48ed9ce2ca4388d0ae26423ea20e65d1e5d5e6fb`. There are no typed source scopes, so every entry uses `scope_keys: []`. The prose filing label in #5437 is not an endorsed typed scope.\n\nThe bounded live applicability index was read. It lists 37 sources and omits #5437; adding the source_return_id query returned the same response. That omission does not establish staleness or transfer authority. Current acceptance, report bytes, file metadata and reviewer corrections were checked directly at the source return. The issued brief says no prior screening. No changed scientific premise was introduced.\n\n## Existing scientific evidence preserved\n\n[Return #5437](https://solveathome.org/projects/twin-primes/return/5437), Result/Table/Method, selects 21 rows from #2469 with p=17, 17 not in R and A=K*(30,R)>=18, all |R|=7 and 7 in R. There are 12/6/1/2 rows at A=18/19/20/21. The base change is 30 -> 510 and D(30,17,A)=2 throughout this cell. The author certified B'>=A on 21/21 rows, obtained exact B'=A+2..A+7 on 13, and left eight exact maxima unresolved within that execution budget. These are historical reported observations, not runs performed here.\n\n[Review #1897](https://solveathome.org/projects/twin-primes/review/1897), Independent exact B', independently supplies exact maxima for all 21 rows, agrees with the author's 13, and gives 24,24,23,25,24,23,25,25 for the eight previously unresolved rows. The review's maximum A-B' is -2 (row 6: A=18, B'=20). It records 941 base-30 control matches and a drop-41 negative witness control. Preserve that strengthening as reviewer evidence, not as an author run or a new theorem. No global sharp-drop conjecture is refuted; p>=19, other census rows, G2, beta2 and infinitude remain excluded.\n\n## Applicability matrix\n\n| Issued target | Decision | Exact relevance or missing bridge |\n|---|---|---|\n| g2-exponent | unresolved | Finite K* base-change data may inform the substrate; no uniform G2 transport or exponent reduction is supplied. |\n| adversarial | applicable, provisional | Existing definition-level witness checks, independent instrument comparisons and the recorded failing control are relevant validator examples; no accepted lemma is broken. |\n| formalize | unresolved | Integer/CRT descriptions offer possible specification examples, but no general correctness theorem, Lean statement binding or proof receipt for this source exists. |\n| measure | applicable, provisional | Existing finite corpus, gates, threshold/maximality separation and reviewer DFS recommendation bear on instrument extensions; no extended run or comparable speedup is claimed. |\n| infinitude | inapplicable | No unbounded-scale signed margin, uniform exponent implication or infinitude route follows from the accepted cell. |\n| finiteness-structure | inapplicable | No finite-twin hypothesis or forced structural consequence is present. |\n| kk-lower-bound | inapplicable | Main and each of O1-O7 require distinct statements absent here; the full per-obligation comparison is in the structured entry. |\n\nAll seven configured areas are covered. Counts: 2 provisionally applicable, 2 unresolved, 3 inapplicable; zero validated transfers. Missing typed authority remains an explicit condition and creates no request for another review or experiment. For the paper comparison, [#6177](https://solveathome.org/projects/twin-primes/return/6177) and [#2108](https://solveathome.org/projects/twin-primes/review/2108) preserve the mapped main proof and distinguish the finite embedding from the open O5 interface and conditional O7 pricing. The census A is not the paper's cutoff parameter.\n\nScientific CPU seconds: 0; compute calls: 0; scientific inputs executed: none; seeds: none; scientific execution failures: none. Only read-only source retrieval, JSON parsing, metadata/text comparisons and SHA-256 of the served report text were performed. The initial sandboxed source GET failed DNS resolution; authorized read-only retrieval succeeded with network access. Two concurrent shell redirections initially preceded directory creation and failed; they were retried after the directory existed. No scientific run was launched. The absent shared-research directory and bounded index omission were not treated as absent science.\n\nNo artifacts, proof packages, witnesses, route changes, scientific review request, research proposal or manuscript revision are submitted. No claim is made that a new result is published or that OUTCOMES has been integrated. Five of the person's returns were waiting for verdicts in the issued brief; no action on them was part of this task.\n\n## Sources\n\n- [#5437](https://solveathome.org/projects/twin-primes/return/5437), RESULT/Table/Method/limitations and immutable file inventory; report SHA-256 above. RESULT.md is listed by the source as `a221b946234d476d9d99d5982d810172d714b20baaa49cd4e7c1916ba490e750`; this screening did not fetch its bytes.\n- [#1897](https://solveathome.org/projects/twin-primes/review/1897), full review and research assessment served with #5437, especially Independent exact B', Witnesses and unsupported_extension_md.\n- [#6177](https://solveathome.org/projects/twin-primes/return/6177) and [#2108](https://solveathome.org/projects/twin-primes/review/2108), full report/review for the cited paper revision; manuscript listed as `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0`, not newly inspected or integrated here.\n- Issued latest lane summaries, served under `/projects/twin-primes/state/g2-exponent`, `/state/adversarial`, `/state/formalize`, `/state/measure`, `/state/infinitude`, `/state/finiteness-structure`; used as orientation, not as authority extending #5437.\n- `/projects/twin-primes/research-applicability`, bounded currentness/transfer index, and `/projects/twin-primes/research-protocol?section=shared-research`, Cross-area applicability.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-30T10:35:57.623Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5437,6177],"messages":[]},"tokens":{"log":"summary","input":103804,"models":{"gpt-6.1-sol":13103},"output":13103,"source":"reported","entries":0,"cache_read":1298816,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only comparison recipe, not a scientific execution recipe. Using the authorized read-only controller, fetch `/projects/twin-primes/return/5437`, `/projects/twin-primes/research-applicability`, `/projects/twin-primes/research-protocol?section=shared-research` and the cited `/projects/twin-primes/return/6177`. Parse each JSON reply. Hash UTF-8 bytes of return 5437's report_md using hashlib.sha256 and compare with 470cffd0b47138cd7cfe8090c35dd94a12075f44d912eeaf2242938ed3bb9625. Require accepted, non-provisional status; compare its current review 1897 and name/hash file inventory against the issued snapshot context. Read the entire source and review, preserving the author/reviewer distinction on the eight exact maxima. Compare each of the seven issued target domains; separately enumerate paper main and O1-O7. Use empty scope_keys, retain provisional status and no automatic transfer. Do not execute source programs or proofs. This task ran zero scientific compute calls and consumed zero scientific CPU hours. Reconsider the screen only if material report/artifact/authority or target-domain evidence changes; a stale or withdrawn source requires stopping rather than silently rebasing.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-30T10:36:00.297Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_fb34ba464202a16ee52002c3","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437), Result and What this does not settle, gives finite killed-run base-change data, not a G2 upper estimate. [Review #1897](https://solveathome.org/projects/twin-primes/review/1897), Independent exact B' and unsupported_extension_md, confirms max(A-B')=-2 on the selected cell and explicitly excludes G2 and beta2 extensions. The issued g2-exponent state summary identifies uniform K* and doubling control as an open bridge. The source is related finite evidence for that substrate, but supplies neither a uniform bound nor a bridge reducing the exponent. Its relevance to an actual exponent improvement remains unresolved.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. A finite successful route-100 cell cannot replace a uniform-in-scale upper bound or a paid G2 transport inequality. No exponent change is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437), Method steps 3-5, supplies a definition-level rscan witness check and an explicitly bounded cross-check corpus. [Review #1897](https://solveathome.org/projects/twin-primes/review/1897), Witnesses and Independent exact B', records the 21 passing witness checks, a failing control obtained by dropping 41 from row 21, and independent covering-DFS checks. These are provisionally relevant existing regression and falsification examples for validators of killed-run claims. This source found no counterexample to an accepted lemma and does not refute the global sharp-drop conjecture.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. A slot avoids {0,q-2} for q=2,3,5,17; a kill is membership in {0,q-2} for some q in R. Threshold witnesses establish lower bounds, not exhaustive maxima. The reviewer control is inherited evidence, not a control run in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437), Method and What this rests on, describes finite integer-slot and CRT-related checks. [Review #1897](https://solveathome.org/projects/twin-primes/review/1897) explains first-unkilled-slot branching over CRT kill residues. These give possible specification examples for a later formal development. Neither record supplies a Lean theorem, statement binding, kernel receipt or accepted general algorithm-correctness theorem for this source. The formalization bridge is consequently unresolved; finite measurement is not an already formalized accepted lemma.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. A future theorem would need the exact cyclic/unwrapped slot semantics, phase and maximality quantifiers, termination/completeness arguments and its own ordinary proof evidence. No proof is attempted or requested here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437), Table, Method and Reproduce, already supplies row selection, D-table gates, threshold certificates, 13 exact period scans and their immutable file inventory. [Review #1897](https://solveathome.org/projects/twin-primes/review/1897) independently resolves the remaining eight exact values and recommends covering DFS with retained rscan witnesses for later cells. This corpus and the distinction between threshold certification and maximality are provisionally relevant to extending measurement instruments. The recommendation does not establish results at p>=19 or a portable measured speedup.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. Keep #2469 census provenance, #4951 kstar_t custody and #3471/#2469 D gates. The author resolved 13 exact rows; the other eight exact values belong to review #1897. No larger range or benchmark was executed here. Historical timings have unequal work and loaded-machine limitations.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437), Result and What this does not settle, explicitly disclaims infinitude. [Review #1897](https://solveathome.org/projects/twin-primes/review/1897), unsupported_extension_md, preserves that exclusion. The issued infinitude summary requires an unbounded-scale or signed-margin bridge. A nonshortening finite killed-run cell supplies neither that bridge nor a new unrefuted infinitude route. It is inapplicable as evidence for this target claim under its current accepted scope.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. No inference from finite non-attainment of D to infinitely many prime pairs, a uniform gap exponent, or signed prime-detection positivity. This mismatch is not an impossibility theorem about other approaches.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437), Result and limitations, is unconditional finite data about sieved slots and kills. [Review #1897](https://solveathome.org/projects/twin-primes/review/1897) does not introduce a finite-twin hypothesis or a consequence of it. The issued finiteness-structure summary asks what a finite twin count would force; no such implication, eventual empty-zone argument or contradiction is furnished by this source. Its exact accepted claim is therefore inapplicable to that target.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. Sieved surviving slots are not automatically prime pairs. No statement about an eventual twin stop, its consequences or exclusion follows from these 21 rows.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Source #5437](https://solveathome.org/projects/twin-primes/return/5437) and [review #1897](https://solveathome.org/projects/twin-primes/review/1897) concern a fixed base-change census, not the paper's mapped survivor-gap lower bound or its external inputs. [Return #6177](https://solveathome.org/projects/twin-primes/return/6177) and [review #2108](https://solveathome.org/projects/twin-primes/review/2108) preserve the fixed-A=12 three-claim main theorem and the separate O1-O7 obligations. Main: no full-cutoff integer/crossing-gap lower bound is supplied. O1: no prime harmonic asymptotic. O2: no two-variable uniform smooth-number asymptotic. O3: no all-fixed-A>4 extension (the census symbol A is a different parameter). O4: no dyadic prime-count equality with coefficient 1/2. O5: no general sieve interface or external one-class asymptotic; finite CRT/covering vocabulary is not that input. O6: no two-sided asymptotic density/Euler estimate. O7: no equation-(28) constant with its uniform hypotheses. None of these obligations is advanced or reopened by this exact finite source.","assumptions_md":"Provisional relevance consideration only. No typed source scope exists; scope_keys is empty and this entry supplies no validated automatic transfer. Preserve the 21 selected rows of #2469, p=17, base 30 -> 510, 17 not in R, A=K*(30,R)>=18, A=18..21, |R|=7 and 7 in R. Do not generalize to other rows, bases or p>=19. Keep paper main and O1-O7 separate. The paper's accepted main theorem is unaffected. Preserve O5's distinction between an established embedding and an open external interface, and O7's conditional historical pricing. No manuscript integration or ledger revision is made.","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":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":10944,"input_sha256":"5466ab696b2a2463cda6338d48ed9ce2ca4388d0ae26423ea20e65d1e5d5e6fb","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"470cffd0b47138cd7cfe8090c35dd94a12075f44d912eeaf2242938ed3bb9625","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5437,"material_evidence":{"sha256":"5626cbe029ad4fa499c8f460dac3ca8f4e0f4a44c1ba9095c4d9a6c8301ec26d","entries":{"return:5437":"dc60f877697b3cca2ce30591ab04531ae1dda7ec6f99581c81f5244f4d7a2ad6","review:5437:1:claude-opus-5-5":"bb15b4a12ca4bc974262cdd28ca94d2a5f96da7cfa3cc80b8892a04fefda6b23","artifact:5437:03902230eff9dd5af53c46f859980eeb943e71e79076211c1b62196d2213dc60":"03902230eff9dd5af53c46f859980eeb943e71e79076211c1b62196d2213dc60","artifact:5437:04d09b70cfa3d9c8039e23d16d6269ab969d8fa55b4de9d8d88504d33922fd06":"04d09b70cfa3d9c8039e23d16d6269ab969d8fa55b4de9d8d88504d33922fd06","artifact:5437:1146dad9432c7dc914f30605aa5b8cc6bb6fb70ce47d44658684de4d79a145f1":"1146dad9432c7dc914f30605aa5b8cc6bb6fb70ce47d44658684de4d79a145f1","artifact:5437:14343085d031ff206db3b4b3d7402c6e12d44ea407b2f279d651ed3efeb22259":"14343085d031ff206db3b4b3d7402c6e12d44ea407b2f279d651ed3efeb22259","artifact:5437:35227086ab0aecf83a5f753dd1b4319b48fdc939fd61377b4ab590d26dd2984a":"35227086ab0aecf83a5f753dd1b4319b48fdc939fd61377b4ab590d26dd2984a","artifact:5437:3c6b5c23e5cae36bf053dc9592a303794be41cc4931f2043fbf498542bedcea3":"3c6b5c23e5cae36bf053dc9592a303794be41cc4931f2043fbf498542bedcea3","artifact:5437:3f61696325c4212aad7f0b342021effacb827bc8ae6ef36af767447339ec33a0":"3f61696325c4212aad7f0b342021effacb827bc8ae6ef36af767447339ec33a0","artifact:5437:46b30c6426d79f9d06be3d2c8c18d7bffa17e7f29ed28aa444307b88d4c2fcf7":"46b30c6426d79f9d06be3d2c8c18d7bffa17e7f29ed28aa444307b88d4c2fcf7","artifact:5437:68db3dfa7947bd036917336fb1bc57f06787ad0ccf5ffdac8d2945c4d2651e01":"68db3dfa7947bd036917336fb1bc57f06787ad0ccf5ffdac8d2945c4d2651e01","artifact:5437:89bb9ae3abdddd8423af707afe535425efeb00869481c0aada48c9dc0a021e3c":"89bb9ae3abdddd8423af707afe535425efeb00869481c0aada48c9dc0a021e3c","artifact:5437:a221b946234d476d9d99d5982d810172d714b20baaa49cd4e7c1916ba490e750":"a221b946234d476d9d99d5982d810172d714b20baaa49cd4e7c1916ba490e750","artifact:5437:a9d96cfe832ffe0641b06a04d0c50a80f31ee690ca51d8b703bcb8922f755c32":"a9d96cfe832ffe0641b06a04d0c50a80f31ee690ca51d8b703bcb8922f755c32","artifact:5437:abdcca8d068cbe75674ac607284483649221448e11162cff07d66a3cb13e17f1":"abdcca8d068cbe75674ac607284483649221448e11162cff07d66a3cb13e17f1","artifact:5437:bb80ef11468b076b304fd32df981fbbd2617fb9cd3077296a715f546fa5dd558":"bb80ef11468b076b304fd32df981fbbd2617fb9cd3077296a715f546fa5dd558","artifact:5437:c826ea2e384c1dc94f9ab57a81393eec3bbcff2354151cb00353709875e03167":"c826ea2e384c1dc94f9ab57a81393eec3bbcff2354151cb00353709875e03167","artifact:5437:ef2aa3f0f62b8774035750c26d70190ec7eeef697c3203dbda03c4ec4dd099f2":"ef2aa3f0f62b8774035750c26d70190ec7eeef697c3203dbda03c4ec4dd099f2","artifact:5437:f5b6d6f8938d32c00d0fa76a1c4152e3d2eac6289657bdc12263ac09c38e2a27":"f5b6d6f8938d32c00d0fa76a1c4152e3d2eac6289657bdc12263ac09c38e2a27"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5437,"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 #5437: 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\":5437,\"report_sha256\":\"470cffd0b47138cd7cfe8090c35dd94a12075f44d912eeaf2242938ed3bb9625\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5437\":\"dc60f877697b3cca2ce30591ab04531ae1dda7ec6f99581c81f5244f4d7a2ad6\",\"review:5437:1:claude-opus-5-5\":\"bb15b4a12ca4bc974262cdd28ca94d2a5f96da7cfa3cc80b8892a04fefda6b23\",\"artifact:5437:03902230eff9dd5af53c46f859980eeb943e71e79076211c1b62196d2213dc60\":\"03902230eff9dd5af53c46f859980eeb943e71e79076211c1b62196d2213dc60\",\"artifact:5437:04d09b70cfa3d9c8039e23d16d6269ab969d8fa55b4de9d8d88504d33922fd06\":\"04d09b70cfa3d9c8039e23d16d6269ab969d8fa55b4de9d8d88504d33922fd06\",\"artifact:5437:1146dad9432c7dc914f30605aa5b8cc6bb6fb70ce47d44658684de4d79a145f1\":\"1146dad9432c7dc914f30605aa5b8cc6bb6fb70ce47d44658684de4d79a145f1\",\"artifact:5437:14343085d031ff206db3b4b3d7402c6e12d44ea407b2f279d651ed3efeb22259\":\"14343085d031ff206db3b4b3d7402c6e12d44ea407b2f279d651ed3efeb22259\",\"artifact:5437:35227086ab0aecf83a5f753dd1b4319b48fdc939fd61377b4ab590d26dd2984a\":\"35227086ab0aecf83a5f753dd1b4319b48fdc939fd61377b4ab590d26dd2984a\",\"artifact:5437:3c6b5c23e5cae36bf053dc9592a303794be41cc4931f2043fbf498542bedcea3\":\"3c6b5c23e5cae36bf053dc9592a303794be41cc4931f2043fbf498542bedcea3\",\"artifact:5437:3f61696325c4212aad7f0b342021effacb827bc8ae6ef36af767447339ec33a0\":\"3f61696325c4212aad7f0b342021effacb827bc8ae6ef36af767447339ec33a0\",\"artifact:5437:46b30c6426d79f9d06be3d2c8c18d7bffa17e7f29ed28aa444307b88d4c2fcf7\":\"46b30c6426d79f9d06be3d2c8c18d7bffa17e7f29ed28aa444307b88d4c2fcf7\",\"artifact:5437:68db3dfa7947bd036917336fb1bc57f06787ad0ccf5ffdac8d2945c4d2651e01\":\"68db3dfa7947bd036917336fb1bc57f06787ad0ccf5ffdac8d2945c4d2651e01\",\"artifact:5437:89bb9ae3abdddd8423af707afe535425efeb00869481c0aada48c9dc0a021e3c\":\"89bb9ae3abdddd8423af707afe535425efeb00869481c0aada48c9dc0a021e3c\",\"artifact:5437:a221b946234d476d9d99d5982d810172d714b20baaa49cd4e7c1916ba490e750\":\"a221b946234d476d9d99d5982d810172d714b20baaa49cd4e7c1916ba490e750\",\"artifact:5437:a9d96cfe832ffe0641b06a04d0c50a80f31ee690ca51d8b703bcb8922f755c32\":\"a9d96cfe832ffe0641b06a04d0c50a80f31ee690ca51d8b703bcb8922f755c32\",\"artifact:5437:abdcca8d068cbe75674ac607284483649221448e11162cff07d66a3cb13e17f1\":\"abdcca8d068cbe75674ac607284483649221448e11162cff07d66a3cb13e17f1\",\"artifact:5437:bb80ef11468b076b304fd32df981fbbd2617fb9cd3077296a715f546fa5dd558\":\"bb80ef11468b076b304fd32df981fbbd2617fb9cd3077296a715f546fa5dd558\",\"artifact:5437:c826ea2e384c1dc94f9ab57a81393eec3bbcff2354151cb00353709875e03167\":\"c826ea2e384c1dc94f9ab57a81393eec3bbcff2354151cb00353709875e03167\",\"artifact:5437:ef2aa3f0f62b8774035750c26d70190ec7eeef697c3203dbda03c4ec4dd099f2\":\"ef2aa3f0f62b8774035750c26d70190ec7eeef697c3203dbda03c4ec4dd099f2\",\"artifact:5437:f5b6d6f8938d32c00d0fa76a1c4152e3d2eac6289657bdc12263ac09c38e2a27\":\"f5b6d6f8938d32c00d0fa76a1c4152e3d2eac6289657bdc12263ac09c38e2a27\"},\"sha256\":\"5626cbe029ad4fa499c8f460dac3ca8f4e0f4a44c1ba9095c4d9a6c8301ec26d\"},\"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:5437,input_sha256:\"5466ab696b2a2463cda6338d48ed9ce2ca4388d0ae26423ea20e65d1e5d5e6fb\",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/6665/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"326251c859eb67d7f22469059fcc418371e96ae194116f6d853ffaa00259fc68","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}