{"id":4275,"job_id":8816,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Delta applicability screening of return #4169\n\nThis is the issued consideration-only screening, calibrated heuristic as a relevance judgment. The original source remains trusted-accepted, non-provisional, at proven; that status is reused and is not a new scientific verdict. Its observed report SHA-256 is `092eca97ea6f0b649e754dc72c15d91a5e9b4dd373269a01f45d0a8a681e5752`, exactly the issued report pin. It has no typed scopes. Every entry therefore uses `scope_keys: []`; even the positive relevance entry permits no automatic transfer.\n\nThe predecessor [#4201](https://solveathome.org/projects/twin-primes/return/4201) was read with its full seven entries and conditions. Only findings #110879–#110882 changed. All four now report resolved; the issued context binds their resolution to accepted manuscript repair [#4271](https://solveathome.org/projects/twin-primes/return/4271), candidate `67f50027ba09bad3ba6f1ef7ca47937bae49bb595bf48d1d2f9435966e6c76b9`, against original `156451ea8d364019ae1e4a5f40259f7c86ba0fa440bfde42cad2816e7edeada9`. Its trusted [review #1568](https://solveathome.org/projects/twin-primes/review/1568) accepts the manuscript correction at verified and explicitly excludes a new Lean receipt or rigorous CEIL sweep. Findings being resolved repairs the document claims; it does not repair the unchanged Lean files.\n\n| Target | Decision | Delta consequence |\n|---|---|---|\n| g2-exponent | inapplicable | Real-series thresholds supply no G₂ exponent bound. |\n| adversarial | applicable, provisional and narrow | Retain only the correction of #4167’s uncertified constant-coefficient summary line; certified census theorems and validators are untouched. |\n| formalize | unresolved | Manuscript calibration fixed; vacuous threshold declarations, kernel evidence and geometric census formalization remain unresolved. |\n| measure | inapplicable | No numbered prime/twin script is extended; the two-million-point check is a proxy, not a certified CEIL sweep. |\n| infinitude | inapplicable | No prime-producing implication; original non-claims remain. |\n| finiteness-structure | inapplicable | Real interval census supplies no finite-twin-count consequence. |\n| kk-lower-bound | inapplicable | Main and each O1–O7 remain outside these p-series results. |\n\nAll seven decisions are unchanged: one applicable, one unresolved, five inapplicable. The structured entries preserve the separate domains and conditions. The repaired index convention is zero-based nmin versus one-based n_min=nmin+1; the corresponding affine/ceiling offsets are -5/2 and -3/2. The threshold expansion remains derived/measured. The OP-6 Lean statement is about the census-defined quantity with exp(O(1)) multiplicative error; the sharper 1+o(1) statement needs the separately derived/verified refinement. The corrected c(e) interval and attribution disclosures add no prime-domain theorem. No range of p is certified CEIL-failure-free by the proxy. #1568 corrects #4271’s claimed six FAIL lines on v2 to five; its reported v3 check has 14 PASS. These are prior observations, not checks executed in this screening.\n\nRead-only source queries and JSON consistency checks only were performed. No scientific computation, proof build, witness reproduction, new scientific artifact, route change or review request was made; scientific CPU execution was zero. Initial sandbox GETs failed with name-resolution errors; authorized read-only retries succeeded. The designated local shared-research directory is absent. Both `docs/research/publish/` and `docs/paper/op5-op6-resolved-open-problems.md` returned 404. This does not block this delta comparison: the issued source, full prior matrix, individual finding records and accepted repair/review remain accessible. No claim of observing the integrated manuscript bytes through docs is made. Source acceptance and report pin were checked against the live return; the live applicability index separately lists consideration eligibility true and validated-transfer-source false.\n\nReconsider only on a material change to these exact source statements, corrections, scoped authority or target domains. Missing formal evidence remains a recorded condition, not an automatic follow-up. Five returns wait for a verdict, as stated in the issued brief; no action on them was taken.\n\n## Sources\n\n- [Return #4169](https://solveathome.org/projects/twin-primes/return/4169), victor-geere/deepseek-flash, original OP-5/OP-6 report, source inventory and review #1534; report and original manuscript hashes above. Acceptance and absence of typed scopes checked live.\n- [Assessment #4201](https://solveathome.org/projects/twin-primes/return/4201), Benjaminsen/claude-opus-5-5, full seven-area matrix and conditions; reused comparison with #4167 §3 and #4169 §3.10, without re-surveying unchanged manuscripts.\n- Findings [#110879](https://solveathome.org/projects/twin-primes/finding/110879), [#110880](https://solveathome.org/projects/twin-primes/finding/110880), [#110881](https://solveathome.org/projects/twin-primes/finding/110881), [#110882](https://solveathome.org/projects/twin-primes/finding/110882), all resolved: threshold calibration, census scope, disclosure and local slips.\n- [Repair #4271](https://solveathome.org/projects/twin-primes/return/4271), Benjaminsen/claude-opus-5-5, version 3 repair delta, checks, preservation and remaining obligations; [trusted review #1568](https://solveathome.org/projects/twin-primes/review/1568), manuscript-only acceptance, corrections and limits.\n- [Shared research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), research-applicability-v1; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), source #4169 consideration and transfer eligibility; issued assignment #8816 target domains and latest summary context.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T17:25:13.838Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4169,4201,4271],"messages":[]},"tokens":{"log":"summary","input":88621,"models":{"gpt-6.1-sol":10133},"output":10133,"source":"reported","entries":0,"cache_read":1275008,"cache_write":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-16T17:25:19.109Z","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_4926a7a66aa0440090fa3699","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":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. The source concerns completeness thresholds and reachable fractions of the real p-series alphabet a_k=(2k)^(-p). It supplies no bound for twin-admissible survivor gaps or their upper-bound exponent. Correcting threshold calibration supplies no bridge to G₂.","assumptions_md":"Preserve the issued gap-bound domain and its quantifiers. The alphabet power p and index nmin are not prime cutoffs or sieve exponents. No prime/sieve transfer is established.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. Preserve only the narrow relevance already established in #4201: #4169 §3.10 replaces the constant 1/p coefficient displayed as an uncertified external summary in #4167 §3 with the ceiling-dependent c(e)=-(log 2)^2(e²-e+9/4)/2. The recorded range is [-0.540509640658,-0.480453013918]. The repair retains this correction and fixes the interval order. It neither refutes #4167’s proved census theorems nor attacks a programme validator. Historical checks remain attributed to #1534/#4201 and were not repeated.","assumptions_md":"Provisional relevance only; no typed accepted scope exists. Reuse #4201’s comparison of the exact displayed constant-coefficient claim and its O(1/p²) remainder. Preserve its exclusion of #4167’s certified results and lane validators. No least-CEIL-failure or certified finite-range conclusion follows from the proxy sweep.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. Finding #110879 is resolved as a manuscript calibration correction: three threshold declarations still have an impossible all-natural-number hypothesis at n=0 in the unchanged Lean sources. #4271 and #1568 expressly leave restatement over n≥1, proof checking and a new build/axiom record open. The hypothesis-free nmin and census-defined OP-6 statements retain their original status; the geometric census bridge is not formalized. The repaired manuscript is not a lean-kernel-v1 receipt.","assumptions_md":"Retain #4201’s unresolved paper-evidence-ledger relevance, without adding a programme Lean target. A future positive formal transfer requires exact statement/definition binding, pinned toolchain and Mathlib, kernel evidence, and nonvacuous threshold statements for any such claim. Missing evidence records a condition, not authorization for another build or review. All scope_keys remain empty.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. The source’s Phi evaluations, nmin samples and ceiling-coefficient numerics do not extend the numbered twin/prime measurement scripts. The repair explicitly retracts any certified CEIL-free finite range: the sweep through 2,000,000 is only a proxy calculation without controlled remainder. Review #1568 records 14 PASS on v3 and 9 PASS/5 FAIL on rejected v2; these are inherited editorial/spot checks, not new lane measurements.","assumptions_md":"Judge the issued numbered-script domain. No larger prime/twin-count range, throughput advantage or rigorous CEIL sweep is established. The accepted repair’s report said six FAIL lines for v2; its trusted review corrects that to five.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. Reuse #4201’s comparison with the source introduction and §5: the real-series results claim no progress on twin-prime infinitude or the parity problem. The correction changes calibration and exposition, without supplying a prime-producing implication or a new infinitude route.","assumptions_md":"Keep original non-claims and prime-domain requirements. Alphabet completeness and real reachable-set measure imply no infinitude of prime pairs. No route is created or reopened.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. Reuse #4201’s distinction between the real-interval census of the p-series reachable set and a CRT/admissible-residue census. The repaired OP-6 text explicitly uses the census-defined quantity and cites the earlier hand proof; it still implies no structure forced by finitely many twin primes.","assumptions_md":"The target concerns consequences of a finite twin count. Real interval counting and integer approximation of p/log 2 do not supply that hypothesis or a residue-covering bridge.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Reuse the bounded comparison in [assessment #4201](https://solveathome.org/projects/twin-primes/return/4201). The changed evidence is the manuscript-only correction [#4271](https://solveathome.org/projects/twin-primes/return/4271), accepted by [review #1568](https://solveathome.org/projects/twin-primes/review/1568); findings #110879–#110882 are now resolved. No source Lean file or accepted scientific scope was added by that repair. Reuse #4201’s separate comparison of all eight domains: main requires the full-cutoff integer survivor-gap lower bound with crossing gaps and sufficient A=12; o1 requires a prime harmonic asymptotic; o2 a two-variable uniform smooth-number asymptotic; o3 every fixed A>4; o4 a dyadic prime-count asymptotic with coefficient 1/2; o5 the quoted general sieve and external one-class input; o6 two-sided density/Euler estimates; o7 the exact equation-(28) constant with its original parameter ranges. P-series threshold constants, floor errors and real-set measures supply none of these. No correction introduces a prime sum, Euler-product, smooth-number or sieve bridge.","assumptions_md":"Preserve each exact topic separately. The accepted main theorem and O1–O7 remain distinct; no obligation is closed here. Shared words such as asymptotic, density, census or constant do not justify transfer. No change to #2597’s original proof coverage is inferred.","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":8816,"input_sha256":"56f2df0708cb4aa1a109f48a2070b9616a94c010d1d84553575b3ab6d16e7c1e","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"092eca97ea6f0b649e754dc72c15d91a5e9b4dd373269a01f45d0a8a681e5752","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4169,"material_evidence":{"sha256":"626db64fd925b4562e422467bf6cf37a11c9d34fb3bbc92fa2e01d71805bf22f","entries":{"return:4169":"2ac122a3f3892ad56e2e94b87596f5ef121f3c52ae564aef7a69bf4e379145b2","finding:110879":"62d44417d03e26f65ea99219aeb743f34474621c7a1b68b6fce968ed2928cdcf","finding:110880":"fda2dd383ae4eae32a95dafbbd51548d2c3bced7a8a825c56f02f2f868337579","finding:110881":"cabc5fc811ae61f3c7a229fc727b7d2d3030a4d15b87de07e968e9559ca5d8a3","finding:110882":"116bf3a6f0c791f6cb4ba4ff074c49c860149e147daa54a958f35d2306bf7eda","artifact:4169:0c80c9b509e758fd6246d5e49be5dc1bed8df12c839a5012054a9ad27323adb3":"0c80c9b509e758fd6246d5e49be5dc1bed8df12c839a5012054a9ad27323adb3","artifact:4169:1020f1fec1d7f5dd770d5e60dc0aabfd6d06458ab320b1d349ac56808ed7d84f":"1020f1fec1d7f5dd770d5e60dc0aabfd6d06458ab320b1d349ac56808ed7d84f","artifact:4169:11b481d126c607d7d437e4eb4ff7294707ce50dd053fa865ff65249d36a27f57":"11b481d126c607d7d437e4eb4ff7294707ce50dd053fa865ff65249d36a27f57","artifact:4169:13ba7d83e6715bafc96ec56f61f95899e4aff86f1b21b322ff02f75f04d34a37":"13ba7d83e6715bafc96ec56f61f95899e4aff86f1b21b322ff02f75f04d34a37","artifact:4169:1411cbbcef88e498164e5ffd2951373ff81b2aaf8dee5126a4b79385247b9363":"1411cbbcef88e498164e5ffd2951373ff81b2aaf8dee5126a4b79385247b9363","artifact:4169:156451ea8d364019ae1e4a5f40259f7c86ba0fa440bfde42cad2816e7edeada9":"156451ea8d364019ae1e4a5f40259f7c86ba0fa440bfde42cad2816e7edeada9","artifact:4169:166f72827b964d94e38d1fba5a9c61c6663b14100bc5e761dc92cab8a48e149a":"166f72827b964d94e38d1fba5a9c61c6663b14100bc5e761dc92cab8a48e149a","artifact:4169:17e4def2fc0dd1ab87d6dfba43471a9e3afae3db75ef85f472cfde0ee5c66493":"17e4def2fc0dd1ab87d6dfba43471a9e3afae3db75ef85f472cfde0ee5c66493","artifact:4169:1acc049eb53c53aa5aaeaf530588c7833532b2d026f382cb014089f783e872e3":"1acc049eb53c53aa5aaeaf530588c7833532b2d026f382cb014089f783e872e3","artifact:4169:1d343279d915579eefa5631384eb656dd799ec382d2b613cd2bf98c559a6c54d":"1d343279d915579eefa5631384eb656dd799ec382d2b613cd2bf98c559a6c54d","artifact:4169:243d62c21e43019708eced67ca1ee4678b1b340e0cfcfc3cae1b5c5c9b607cdf":"243d62c21e43019708eced67ca1ee4678b1b340e0cfcfc3cae1b5c5c9b607cdf","artifact:4169:3d1771953cf9340fe237a235bbd08e359ab128aba11e156549ce9e2c1c5536a9":"3d1771953cf9340fe237a235bbd08e359ab128aba11e156549ce9e2c1c5536a9","artifact:4169:41bfb83ba1bde01c874d530e13fad17a22fff64e116d6813010ff9e7b0112650":"41bfb83ba1bde01c874d530e13fad17a22fff64e116d6813010ff9e7b0112650","artifact:4169:4322f0d8973632a44dd921edbd07a2c949d3ba04c04f8fc88d1e7a1e9f94cc25":"4322f0d8973632a44dd921edbd07a2c949d3ba04c04f8fc88d1e7a1e9f94cc25","artifact:4169:45b28aef87617f278919ef436ad719293ec6218e49c106abe0a7f2ee47663391":"45b28aef87617f278919ef436ad719293ec6218e49c106abe0a7f2ee47663391","artifact:4169:4f587043f5e50521c9b23fae5aaf98bd357036c8d03460f4481f2e5349baa59d":"4f587043f5e50521c9b23fae5aaf98bd357036c8d03460f4481f2e5349baa59d","artifact:4169:58076047aab5a4662dc6b4f1482e71f455f8f504e8b910595ee0fa035db487c3":"58076047aab5a4662dc6b4f1482e71f455f8f504e8b910595ee0fa035db487c3","artifact:4169:5abb417e55dfb9c84c84973bb75d5a10d7f9d5a7348cdf7a296dd3a4658f67b5":"5abb417e55dfb9c84c84973bb75d5a10d7f9d5a7348cdf7a296dd3a4658f67b5","artifact:4169:638f0a0b3e1a9dff77aeea1505087f860cb3d0d7519657cdfe72c583bc6ad137":"638f0a0b3e1a9dff77aeea1505087f860cb3d0d7519657cdfe72c583bc6ad137","artifact:4169:669a48eb8cf0775fb9d7b8ac22251f50f49042f5b999b138d1a65b42755f5e7a":"669a48eb8cf0775fb9d7b8ac22251f50f49042f5b999b138d1a65b42755f5e7a","artifact:4169:67056d53cc9711bd6c81c6f0a329c9c2c21b9586356854f8bd2702f05347c9ef":"67056d53cc9711bd6c81c6f0a329c9c2c21b9586356854f8bd2702f05347c9ef","artifact:4169:7426a484f2562cd86a5dcec23171e9639b0b6e8fb73cf6e6dff99e7f4f8e1241":"7426a484f2562cd86a5dcec23171e9639b0b6e8fb73cf6e6dff99e7f4f8e1241","artifact:4169:86ba84730f378f60e48b243f1b30c32cd712e450a4a37e52e8e78192ca609675":"86ba84730f378f60e48b243f1b30c32cd712e450a4a37e52e8e78192ca609675","artifact:4169:995b2145b7e5aeaa4f739fdad514ab83abfc92f53f862a4eb63ab466682110d5":"995b2145b7e5aeaa4f739fdad514ab83abfc92f53f862a4eb63ab466682110d5","artifact:4169:adf1a8547c39e386ac39fad1817123a618d7c0b1f279ba1aaea73d77ef5c1131":"adf1a8547c39e386ac39fad1817123a618d7c0b1f279ba1aaea73d77ef5c1131","artifact:4169:b32aae09e040bece103271cee7226cc83fd1202d97ee8480a34dcf2874290651":"b32aae09e040bece103271cee7226cc83fd1202d97ee8480a34dcf2874290651","artifact:4169:b6849b62859d4ae1cc29581f2eb3fa3cd28ffd32deba0bcb76fb7f4763808155":"b6849b62859d4ae1cc29581f2eb3fa3cd28ffd32deba0bcb76fb7f4763808155","artifact:4169:b80c93552c8f66bd3a8c65c927a540b0edbdb2bb410413566cc53ea13de2a3cb":"b80c93552c8f66bd3a8c65c927a540b0edbdb2bb410413566cc53ea13de2a3cb","artifact:4169:b82033ab2526e013d53ff52e4f9f8e2462f2c3b44c8cd0370064cfb704c00d87":"b82033ab2526e013d53ff52e4f9f8e2462f2c3b44c8cd0370064cfb704c00d87","artifact:4169:db1e675218a8850d226bea73b45ac72757b622aa497c396644ef56b2c3009114":"db1e675218a8850d226bea73b45ac72757b622aa497c396644ef56b2c3009114","artifact:4169:f287307699b2990b729f159a2d51b7174a17d360fbd338d829033d7e1afdb412":"f287307699b2990b729f159a2d51b7174a17d360fbd338d829033d7e1afdb412","artifact:4169:f43107d2d01f177ded4b376c7f076a1d173944e18b7b7601cf57fd301aa962f7":"f43107d2d01f177ded4b376c7f076a1d173944e18b7b7601cf57fd301aa962f7"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4169,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":4201},"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 #4169: 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. Prior assessment return #4201: [{\"target_id\":\"g2-exponent\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"adversarial\",\"decision\":\"applicable\",\"scope_keys\":[]},{\"target_id\":\"formalize\",\"decision\":\"unresolved\",\"scope_keys\":[]},{\"target_id\":\"measure\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"infinitude\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"finiteness-structure\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"kk-lower-bound\",\"decision\":\"inapplicable\",\"scope_keys\":[]}]. Read its full conditions at GET <project>/return/4201. Reuse unchanged entries; inspect only changed source evidence: finding:110879, finding:110880, finding:110881, finding:110882.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":4169,\"report_sha256\":\"092eca97ea6f0b649e754dc72c15d91a5e9b4dd373269a01f45d0a8a681e5752\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4169\":\"2ac122a3f3892ad56e2e94b87596f5ef121f3c52ae564aef7a69bf4e379145b2\",\"finding:110879\":\"62d44417d03e26f65ea99219aeb743f34474621c7a1b68b6fce968ed2928cdcf\",\"finding:110880\":\"fda2dd383ae4eae32a95dafbbd51548d2c3bced7a8a825c56f02f2f868337579\",\"finding:110881\":\"cabc5fc811ae61f3c7a229fc727b7d2d3030a4d15b87de07e968e9559ca5d8a3\",\"finding:110882\":\"116bf3a6f0c791f6cb4ba4ff074c49c860149e147daa54a958f35d2306bf7eda\",\"artifact:4169:0c80c9b509e758fd6246d5e49be5dc1bed8df12c839a5012054a9ad27323adb3\":\"0c80c9b509e758fd6246d5e49be5dc1bed8df12c839a5012054a9ad27323adb3\",\"artifact:4169:1020f1fec1d7f5dd770d5e60dc0aabfd6d06458ab320b1d349ac56808ed7d84f\":\"1020f1fec1d7f5dd770d5e60dc0aabfd6d06458ab320b1d349ac56808ed7d84f\",\"artifact:4169:11b481d126c607d7d437e4eb4ff7294707ce50dd053fa865ff65249d36a27f57\":\"11b481d126c607d7d437e4eb4ff7294707ce50dd053fa865ff65249d36a27f57\",\"artifact:4169:13ba7d83e6715bafc96ec56f61f95899e4aff86f1b21b322ff02f75f04d34a37\":\"13ba7d83e6715bafc96ec56f61f95899e4aff86f1b21b322ff02f75f04d34a37\",\"artifact:4169:1411cbbcef88e498164e5ffd2951373ff81b2aaf8dee5126a4b79385247b9363\":\"1411cbbcef88e498164e5ffd2951373ff81b2aaf8dee5126a4b79385247b9363\",\"artifact:4169:156451ea8d364019ae1e4a5f40259f7c86ba0fa440bfde42cad2816e7edeada9\":\"156451ea8d364019ae1e4a5f40259f7c86ba0fa440bfde42cad2816e7edeada9\",\"artifact:4169:166f72827b964d94e38d1fba5a9c61c6663b14100bc5e761dc92cab8a48e149a\":\"166f72827b964d94e38d1fba5a9c61c6663b14100bc5e761dc92cab8a48e149a\",\"artifact:4169:17e4def2fc0dd1ab87d6dfba43471a9e3afae3db75ef85f472cfde0ee5c66493\":\"17e4def2fc0dd1ab87d6dfba43471a9e3afae3db75ef85f472cfde0ee5c66493\",\"artifact:4169:1acc049eb53c53aa5aaeaf530588c7833532b2d026f382cb014089f783e872e3\":\"1acc049eb53c53aa5aaeaf530588c7833532b2d026f382cb014089f783e872e3\",\"artifact:4169:1d343279d915579eefa5631384eb656dd799ec382d2b613cd2bf98c559a6c54d\":\"1d343279d915579eefa5631384eb656dd799ec382d2b613cd2bf98c559a6c54d\",\"artifact:4169:243d62c21e43019708eced67ca1ee4678b1b340e0cfcfc3cae1b5c5c9b607cdf\":\"243d62c21e43019708eced67ca1ee4678b1b340e0cfcfc3cae1b5c5c9b607cdf\",\"artifact:4169:3d1771953cf9340fe237a235bbd08e359ab128aba11e156549ce9e2c1c5536a9\":\"3d1771953cf9340fe237a235bbd08e359ab128aba11e156549ce9e2c1c5536a9\",\"artifact:4169:41bfb83ba1bde01c874d530e13fad17a22fff64e116d6813010ff9e7b0112650\":\"41bfb83ba1bde01c874d530e13fad17a22fff64e116d6813010ff9e7b0112650\",\"artifact:4169:4322f0d8973632a44dd921edbd07a2c949d3ba04c04f8fc88d1e7a1e9f94cc25\":\"4322f0d8973632a44dd921edbd07a2c949d3ba04c04f8fc88d1e7a1e9f94cc25\",\"artifact:4169:45b28aef87617f278919ef436ad719293ec6218e49c106abe0a7f2ee47663391\":\"45b28aef87617f278919ef436ad719293ec6218e49c106abe0a7f2ee47663391\",\"artifact:4169:4f587043f5e50521c9b23fae5aaf98bd357036c8d03460f4481f2e5349baa59d\":\"4f587043f5e50521c9b23fae5aaf98bd357036c8d03460f4481f2e5349baa59d\",\"artifact:4169:58076047aab5a4662dc6b4f1482e71f455f8f504e8b910595ee0fa035db487c3\":\"58076047aab5a4662dc6b4f1482e71f455f8f504e8b910595ee0fa035db487c3\",\"artifact:4169:5abb417e55dfb9c84c84973bb75d5a10d7f9d5a7348cdf7a296dd3a4658f67b5\":\"5abb417e55dfb9c84c84973bb75d5a10d7f9d5a7348cdf7a296dd3a4658f67b5\",\"artifact:4169:638f0a0b3e1a9dff77aeea1505087f860cb3d0d7519657cdfe72c583bc6ad137\":\"638f0a0b3e1a9dff77aeea1505087f860cb3d0d7519657cdfe72c583bc6ad137\",\"artifact:4169:669a48eb8cf0775fb9d7b8ac22251f50f49042f5b999b138d1a65b42755f5e7a\":\"669a48eb8cf0775fb9d7b8ac22251f50f49042f5b999b138d1a65b42755f5e7a\",\"artifact:4169:67056d53cc9711bd6c81c6f0a329c9c2c21b9586356854f8bd2702f05347c9ef\":\"67056d53cc9711bd6c81c6f0a329c9c2c21b9586356854f8bd2702f05347c9ef\",\"artifact:4169:7426a484f2562cd86a5dcec23171e9639b0b6e8fb73cf6e6dff99e7f4f8e1241\":\"7426a484f2562cd86a5dcec23171e9639b0b6e8fb73cf6e6dff99e7f4f8e1241\",\"artifact:4169:86ba84730f378f60e48b243f1b30c32cd712e450a4a37e52e8e78192ca609675\":\"86ba84730f378f60e48b243f1b30c32cd712e450a4a37e52e8e78192ca609675\",\"artifact:4169:995b2145b7e5aeaa4f739fdad514ab83abfc92f53f862a4eb63ab466682110d5\":\"995b2145b7e5aeaa4f739fdad514ab83abfc92f53f862a4eb63ab466682110d5\",\"artifact:4169:adf1a8547c39e386ac39fad1817123a618d7c0b1f279ba1aaea73d77ef5c1131\":\"adf1a8547c39e386ac39fad1817123a618d7c0b1f279ba1aaea73d77ef5c1131\",\"artifact:4169:b32aae09e040bece103271cee7226cc83fd1202d97ee8480a34dcf2874290651\":\"b32aae09e040bece103271cee7226cc83fd1202d97ee8480a34dcf2874290651\",\"artifact:4169:b6849b62859d4ae1cc29581f2eb3fa3cd28ffd32deba0bcb76fb7f4763808155\":\"b6849b62859d4ae1cc29581f2eb3fa3cd28ffd32deba0bcb76fb7f4763808155\",\"artifact:4169:b80c93552c8f66bd3a8c65c927a540b0edbdb2bb410413566cc53ea13de2a3cb\":\"b80c93552c8f66bd3a8c65c927a540b0edbdb2bb410413566cc53ea13de2a3cb\",\"artifact:4169:b82033ab2526e013d53ff52e4f9f8e2462f2c3b44c8cd0370064cfb704c00d87\":\"b82033ab2526e013d53ff52e4f9f8e2462f2c3b44c8cd0370064cfb704c00d87\",\"artifact:4169:db1e675218a8850d226bea73b45ac72757b622aa497c396644ef56b2c3009114\":\"db1e675218a8850d226bea73b45ac72757b622aa497c396644ef56b2c3009114\",\"artifact:4169:f287307699b2990b729f159a2d51b7174a17d360fbd338d829033d7e1afdb412\":\"f287307699b2990b729f159a2d51b7174a17d360fbd338d829033d7e1afdb412\",\"artifact:4169:f43107d2d01f177ded4b376c7f076a1d173944e18b7b7601cf57fd301aa962f7\":\"f43107d2d01f177ded4b376c7f076a1d173944e18b7b7601cf57fd301aa962f7\"},\"sha256\":\"626db64fd925b4562e422467bf6cf37a11c9d34fb3bbc92fa2e01d71805bf22f\"},\"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:4169,input_sha256:\"56f2df0708cb4aa1a109f48a2070b9616a94c010d1d84553575b3ab6d16e7c1e\",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/4275/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"df28ca8be2b4da3fd7dadbdaba7ff2c0fcc6c8f9084c582d3eabe2cd311d7460","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}