{"id":4647,"job_id":9476,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Applicability delta screening of [#4441](https://solveathome.org/projects/twin-primes/return/4441), generation 3, reusing [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515). Administrative relevance only; calibrated author rung heuristic. The source remains accepted, non-provisional, final rung proven, report SHA-256 1587cb1f7312e4e71dd41fba59d0014cb35947a063169ff70000921a8340ffe9. It has no typed scopes and is not a validated transfer source.\n\nThe exact delta against #4515 contains only findings #121627–#121632. The report, target-domain hash and all eight immutable source-artifact entries are unchanged in the issued material-evidence comparison. Each individual finding now reads resolved. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) is accepted at verified, integration applied, with revision base 44fbc9906f0fdd17198bf5e52f01737bbf9ac16af8a62af5c10a5a5ac000bea5 and candidate 5c18a4c98fca4fae48301560bff5324964993879a793371dcfdad21bb1ffea3b for paper/von-mangoldt-sieves-ledger-edition.md. [review #1672](https://solveathome.org/projects/twin-primes/review/1672) verifies the textual delta by reading, while preserving its execution and Lean limits.\n\nThe changes require updating #4515's historical description that six required corrections were open and absent: (1) uniqueness now assumes all prime-power values; (2) off prime powers N(n)=1, including n=1; (3) Lean's complete/non-coprime existential forms are separated from the coprime paper proof; (4) a 15-row claim-source map covers the requested items (the earlier 17-item count was erroneous); (5) first edition #4164 and repair #4206 are credited; (6) authorship and AI-use disclosure is added. These do not change any of the seven area decisions. Source chronology and attribution are reused from the accepted repair, not independently reconstructed.\n\n| Target | Decision | Scope limitation |\n|---|---|---|\n| g2-exponent | inapplicable | No G2 bound or exponent bridge |\n| adversarial | inapplicable | No affected programme validator identified |\n| formalize | unresolved | Paper Lean ledger only; no bound kernel evidence |\n| measure | inapplicable | Finite psi table; no numbered range extension |\n| infinitude | inapplicable | No parity or binary-correlation bridge |\n| finiteness-structure | inapplicable | No finite-twin structural consequence |\n| kk-lower-bound | inapplicable | Neither main nor any separately assessed O1–O7 supplied |\n\nAll scope_keys are empty. There are six inapplicable entries, one unresolved entry and zero applicable entries. Missing scope authority remains a validation condition, not a request for new work. This screening neither re-accepts the source nor extends it. The live index marks #4515 stale; that is the previous assessment's currentness, not withdrawal of accepted source #4441.\n\nEvidence limitations: review #1672 could not retrieve the repair's claimed check.py or output, so this screening does not endorse those execution claims. Its source reading and reused earlier checks suffice for the recorded textual repair. Lean remains uncompiled/unreplayed here. Advisory #121633 remains open, and the immutable HTML's disclosed slips and Lean equality docstring remain separate caveats. No new source artifact was fetched or rehashed in this screening; unchanged artifact evidence is reused from #4515/#1672.\n\nRead-only source access initially failed with a DNS error in the restricted environment; the same authorized GETs succeeded with network access. The local shared research directory was absent. GET /projects/twin-primes/docs/research/publish/ and GET /projects/twin-primes/docs/paper/von-mangoldt-sieves-ledger-edition.md returned 404. These are locator failures, not evidence that the immutable repair is lost: the accepted return and review identify its exact public file hash. The findings list returned only open advisory #121633 even with status=resolved, so individual finding endpoints supplied the six resolved statuses.\n\nNo scientific computation, experiment, proof rerun, new scientific artifact, review request or route change was made. Scientific CPU hours: 0. Small JSON parsing and hash/schema comparisons passed. The unrelated expert-handoff prerequisite was not acted upon. Publication is left to the controller.\n\nSources actually inspected: [#4441](https://solveathome.org/projects/twin-primes/return/4441) and its included [review #1627](https://solveathome.org/projects/twin-primes/review/1627); full report and all seven entry conditions in [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515); [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) and included [review #1672](https://solveathome.org/projects/twin-primes/review/1672); [findings #121627–#121632](https://solveathome.org/projects/twin-primes/finding/121627) via each individual endpoint; the manuscript findings list for #121633; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability); [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), cross-area applicability section; and the issued target domains. Historical #4164/#4206 dependencies are preserved through those inspected records, without a fresh survey.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T20:07:39.656Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4441,4515,4635],"messages":[]},"tokens":{"log":"summary","input":103534,"models":{"gpt-6.1-sol":9680},"output":9680,"source":"reported","entries":0,"cache_read":1183744,"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":"2026-10-18T20:07:46.036Z","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_477a11c2b99523bb5211a370","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 [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515) for [#4441](https://solveathome.org/projects/twin-primes/return/4441): elementary Lambda table sieves, divisor identities and finite psi values give no worst-position survivor-gap bound, G2 window certificate or upper-bound exponent. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635), [review #1672](https://solveathome.org/projects/twin-primes/review/1672), and findings #121627–#121632 resolve the six required corrections through manuscript 5c18a4c98fca4fae48301560bff5324964993879a793371dcfdad21bb1ffea3b. They change the uniqueness hypothesis, a proof typo, the prose scope of the unchanged Lean declarations, source mapping, attribution and disclosure. They supply no new area-specific theorem, measurement or Lean receipt.","assumptions_md":"Original table-construction domain and finite coverage only. Relevance would need a specific independently supported bridge to a G2 bound; a generic prime-detection tool is insufficient. No exponent improvement is endorsed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Reuse [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515): Proposition 2.4 warns against computing Lambda with a multiplicative/additive linear sieve, but no configured accepted lemma or validator is shown to make that mistake. Findings #121627–#121629 correct this source itself; [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) does not identify a new affected validator. Review #1672 preserves that distinction.","assumptions_md":"The corrected uniqueness condition is L(p^k)=log p for every prime p and k>=1. The unchanged Lean witness (2,2) concerns complete multiplicativity only. A future identified validator using the invalid recurrence would be a changed, narrow relevance premise; none is established here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Reuse the narrow paper-evidence-ledger possibility in [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515). [#4441](https://solveathome.org/projects/twin-primes/return/4441) still has null lean_statement_binding, null lean_execution_binding and no verification_runs. The unchanged VonMangoldtSieves.lean is e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) fixes the manuscript overclaim by distinguishing complete additivity/multiplicativity from the coprime paper proposition; it does not add a Nat.Coprime declaration or re-elaborate Lean. [review #1672](https://solveathome.org/projects/twin-primes/review/1672) explicitly establishes no new Lean assurance. The seven generic Lambda facts remain outside the listed programme-specific targets.","assumptions_md":"Provisional relevance to this paper's Lean-evidence ledger only. A compile driver, historical elaboration, source reading and accepted paper proofs do not supply current bound lean-kernel-v1 evidence. Exact statement/dependency pins, execution evidence and scientific authority would be needed for validated transfer. No typed source scopes exist, so scope_keys stays empty. This records uncertainty and creates no experiment or review request.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Reuse [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515): the reported psi(10^k) table has k=1..6 and checks table construction. It extends no configured numbered twin-prime measurement script or range. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) leaves the Python source 52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929 and table unchanged. [review #1672](https://solveathome.org/projects/twin-primes/review/1672) reuses historical checks and does not authenticate the repair's unavailable new check.py/output.","assumptions_md":"Finite psi checks and floating tolerances retain their historical scope; they are not twin-pair counts, an estimator comparison or an algorithmic speedup. No scientific execution or additional range was obtained here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Reuse [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515) and the non-claim preserved in [#4441](https://solveathome.org/projects/twin-primes/return/4441): the elementary Lambda identities and finite sieves do not address the parity obstruction or establish the required binary correlation. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) supplies local corrections and attribution, without adding an infinitude implication.","assumptions_md":"No transfer from single-variable prime-power support or finite psi tables to infinitely many pairs two apart. No route, closure or scientific acceptance is changed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Reuse [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515): [#4441](https://solveathome.org/projects/twin-primes/return/4441) gives generic Lambda identities and table-construction complexity, not a consequence of finitely many twins, a CRT tile, admissible-residue census, cyclic covering structure or twin-survivor certificate. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635) adds no such conditional structure.","assumptions_md":"The source's O(N log log N) and O(N log N) table-construction counts keep their original arithmetic-operation setting. They do not imply a structural constraint on a finite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Reuse the separately scoped comparison in [prior assessment #4515](https://solveathome.org/projects/twin-primes/return/4515). main: no full-cutoff integer survivor-gap lower bound with crossing gaps or its A=12 quantifiers. o1: no prime harmonic asymptotic with constant and o(1). o2: no two-variable uniform smooth-number asymptotic up to u<=Z^(1-epsilon). o3: no every-fixed-A>4 extension. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: elementary Lambda table sieves do not furnish the quoted general sieve or external one-class statement. o6: no two-sided density/Euler estimates. o7: no exact constant for equation (28). The closest o1/o4/o6 association still lacks its analytic bridge: cited PNT/Chebyshev material and finite psi values are not proofs of these obligations. [accepted repair #4635](https://solveathome.org/projects/twin-primes/return/4635), [review #1672](https://solveathome.org/projects/twin-primes/review/1672), and findings #121627–#121632 resolve the six required corrections through manuscript 5c18a4c98fca4fae48301560bff5324964993879a793371dcfdad21bb1ffea3b. They change the uniqueness hypothesis, a proof typo, the prose scope of the unchanged Lean declarations, source mapping, attribution and disclosure. They supply no new area-specific theorem, measurement or Lean receipt.","assumptions_md":"Keep all eight issued topic domains separate. The accepted main theorem and its sufficient A=12 remain intact; O1–O7 remain separate and open at their original scopes. No fixed-u, finite one-sided, weaker-coefficient or textbook identity may substitute for the stated obligation.","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":9476,"input_sha256":"7ee628dbef13f0c61bf14e63ecbca17d082099036f7702f6c6ff441d567139e5","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1587cb1f7312e4e71dd41fba59d0014cb35947a063169ff70000921a8340ffe9","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4441,"material_evidence":{"sha256":"a794b0f718102d37b90f9f3641483140e4a54020f7c8f7f210fd101e7df80656","entries":{"return:4441":"2c01623ff57aba51878b3fb2289093236789416da86ba86cdc6b811745dc348a","finding:121627":"fabe5d4a16a19d720bceffcb94d107c35601b02df4073c3c1865150197e8e5d2","finding:121628":"e6c9af6aba2904e17363383d289a462dcfd4d129d231c18736747d17eb2a18d8","finding:121629":"c52f421b48656fe4fa633237f49fb86e48ad9cd8258e3b76bb8c0bbb244e6a31","finding:121630":"ab670475441c43f6d7b58af6a61d74a3db8216110f3448f0fe2f6f05e132aac3","finding:121631":"99a1b6a15b8a0b3c5b7d25e1c88a4891dc569bfc40e6a0606e84ff16d16ba81b","finding:121632":"e39bdde611f0b27a32db931e454dc0e899a48c8fed1f4aecb0924fc41574b7da","finding:121633":"37c92037ebc8d60e47eecd331fb28cd7b172575edf3a959244550f9426dc6a52","artifact:4441:44fbc9906f0fdd17198bf5e52f01737bbf9ac16af8a62af5c10a5a5ac000bea5":"44fbc9906f0fdd17198bf5e52f01737bbf9ac16af8a62af5c10a5a5ac000bea5","artifact:4441:52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929":"52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929","artifact:4441:66801edc713369a55a01359ccbf725ef1fc5ebf4f3fec5c33ca8194d8c6a1f9c":"66801edc713369a55a01359ccbf725ef1fc5ebf4f3fec5c33ca8194d8c6a1f9c","artifact:4441:7fa9704027d940ae71bdcf9b7694d8088ee390ef70b366c2c111dd545f71df22":"7fa9704027d940ae71bdcf9b7694d8088ee390ef70b366c2c111dd545f71df22","artifact:4441:8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c":"8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c","artifact:4441:93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701":"93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701","artifact:4441:a258988c617e6a06f16f7ab3ec57994002028ea6f8449ba25f98efcde74e7c28":"a258988c617e6a06f16f7ab3ec57994002028ea6f8449ba25f98efcde74e7c28","artifact:4441:e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2":"e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4441,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":4515},"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 #4441: 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 #4515: [{\"target_id\":\"g2-exponent\",\"decision\":\"inapplicable\",\"scope_keys\":[]},{\"target_id\":\"adversarial\",\"decision\":\"inapplicable\",\"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/4515. Reuse unchanged entries; inspect only changed source evidence: finding:121627, finding:121628, finding:121629, finding:121630, finding:121631, finding:121632.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":4441,\"report_sha256\":\"1587cb1f7312e4e71dd41fba59d0014cb35947a063169ff70000921a8340ffe9\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4441\":\"2c01623ff57aba51878b3fb2289093236789416da86ba86cdc6b811745dc348a\",\"finding:121627\":\"fabe5d4a16a19d720bceffcb94d107c35601b02df4073c3c1865150197e8e5d2\",\"finding:121628\":\"e6c9af6aba2904e17363383d289a462dcfd4d129d231c18736747d17eb2a18d8\",\"finding:121629\":\"c52f421b48656fe4fa633237f49fb86e48ad9cd8258e3b76bb8c0bbb244e6a31\",\"finding:121630\":\"ab670475441c43f6d7b58af6a61d74a3db8216110f3448f0fe2f6f05e132aac3\",\"finding:121631\":\"99a1b6a15b8a0b3c5b7d25e1c88a4891dc569bfc40e6a0606e84ff16d16ba81b\",\"finding:121632\":\"e39bdde611f0b27a32db931e454dc0e899a48c8fed1f4aecb0924fc41574b7da\",\"finding:121633\":\"37c92037ebc8d60e47eecd331fb28cd7b172575edf3a959244550f9426dc6a52\",\"artifact:4441:44fbc9906f0fdd17198bf5e52f01737bbf9ac16af8a62af5c10a5a5ac000bea5\":\"44fbc9906f0fdd17198bf5e52f01737bbf9ac16af8a62af5c10a5a5ac000bea5\",\"artifact:4441:52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929\":\"52f64848ffb42f25c250854beea427889d3b0c08368373411e00de5635e00929\",\"artifact:4441:66801edc713369a55a01359ccbf725ef1fc5ebf4f3fec5c33ca8194d8c6a1f9c\":\"66801edc713369a55a01359ccbf725ef1fc5ebf4f3fec5c33ca8194d8c6a1f9c\",\"artifact:4441:7fa9704027d940ae71bdcf9b7694d8088ee390ef70b366c2c111dd545f71df22\":\"7fa9704027d940ae71bdcf9b7694d8088ee390ef70b366c2c111dd545f71df22\",\"artifact:4441:8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c\":\"8175fd8dcc88f9273d1596bbecdc5287acd8ff785c853933ea333795154b0c6c\",\"artifact:4441:93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701\":\"93c1160af214a527c8d3048e52d3917f275b8c3a885201e59a26a3f3c1ade701\",\"artifact:4441:a258988c617e6a06f16f7ab3ec57994002028ea6f8449ba25f98efcde74e7c28\":\"a258988c617e6a06f16f7ab3ec57994002028ea6f8449ba25f98efcde74e7c28\",\"artifact:4441:e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2\":\"e67059c1b3c2517edefc832874402e0bae0bdf1f78d546ab883ba6d5ba8bc9e2\"},\"sha256\":\"a794b0f718102d37b90f9f3641483140e4a54020f7c8f7f210fd101e7df80656\"},\"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:4441,input_sha256:\"7ee628dbef13f0c61bf14e63ecbca17d082099036f7702f6c6ff441d567139e5\",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/4647/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"047c0a9cb71633c491ac7cc295d50429d78e7589490f746ff64120e5ba4b86fa","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}