{"id":4241,"job_id":8740,"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 #4166\n\nAdministrative relevance judgment only; calibration **heuristic**, with no new scientific acceptance, experiment, proof rerun or review request. Reuse all seven decisions of #4190 after inspecting only the issued correction delta and its cited repair. This assignment does not integrate a document or alter a route.\n\n## Source and currentness\n\nReturn #4166, *The greedy digit word and the complexity law*, remains trusted-accepted, non-provisional, at proven. Its served report SHA-256 is `6647e829a733aa1a210518cc66749bb66b6099db3028b3d405237446a0aca111`; recomputing SHA-256 over the report text matches the issued value. Its 16 attached name/hash pairs match the issued source inventory. It has no typed scopes. The three assigned changed findings have resolved status, agreeing with the issued context. The live applicability index lists the source as consideration-eligible but not validated for transfer; the older assessment is stale because its correction statuses predate this delta. That is not source withdrawal. This check binds the issued input `0b2b9943f4f66463617c47e4dacdfbd5deff04dbfb26b93e80a2b839c57f141f` and source snapshot; no claim is made to have reconstructed the server's material-evidence hash algorithm.\n\n## Correction delta and limitations\n\n- #110864: accepted, integrated repair #4212 changes the manuscript's reversed growth direction to A(N)=O_x(log log N), rejects the rational-input lower bound and discloses that rigorous_check.py E2 is literal True. Its historical 31/31 count contains only 30 substantive checks. These are recorded-source facts, not checks executed here.\n- #110865: the repair changes “exactly one” window to “at least one” and supplies isolating witnesses: {0}, N=4, L=2 has p=2 rather than 3; {3,4}, N=8, L=2 has p=4 rather than 3. These existing witnesses were not recomputed.\n- #110866: authorship and AI disclosure are added, including the actual coverage limits of the author build and reviewer checks.\n\nThe integrated repair is manuscript `e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3`, replacing `3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f` at `paper/greedy-digit-word-complexity-law.md`. #4166's original attached manuscript and Lean sources remain unchanged. Review #1541 accepts the repair while recording #110886: the displayed finite-N bound needs max(0,RHS), or N at least the first taken index; x=1/100, N=0 gives a negative unmodified RHS although A(0)=0. The O_x asymptotic is unaffected. #110887 records companion-file overclaims and the constant-True E2; #110867 retains source/import caveats. None grants a missing formal proof or twin-prime bridge. Neither the unresolved finite-N formula nor the hard-coded check is used to endorse transfer.\n\n## Applicability matrix\n\n| Issued target | Decision | Delta judgment |\n|---|---|---|\n| g2-exponent | inapplicable | No G2 upper-exponent bound or survivor-gap bridge. |\n| adversarial | inapplicable | Corrections and refutations concern the source's word formulas, not programme validators. |\n| formalize | unresolved | Possible source-paper Lean-evidence relevance only; no new elaboration, receipt or target binding. |\n| measure | inapplicable | No extension of numbered twin-prime measurement ranges. |\n| infinitude | inapplicable | No twin-prime infinitude implication. |\n| finiteness-structure | inapplicable | Word supports do not establish consequences of a finite twin count. |\n| kk-lower-bound | inapplicable | Main and O1-O7 remain separately unsupported by this source; details are in the structured entry. |\n\nThere are **6 inapplicable, 1 unresolved and 0 applicable** entries. Every scope_keys list is empty. All relevance is provisional; no entry supplies automatic transfer. The remaining formalization gap is unchanged evidence, not an instruction to launch a run. Reconsider only on a material source/domain correction, an evidenced target bridge, or an exact relevant formal verification package; any expanded scientific claim needs its ordinary review. The old assessment is reused as operational relevance evidence, not as a new scientific verdict.\n\nNo scientific computation was launched: actual scientific CPU seconds **0**, cpu_hours **0**. Nine scoped read-only API queries returned HTTP 200 after the first five sandbox attempts failed with DNS resolution errors. The local shared-research directory was absent; the scoped public records supplied the needed evidence. No scientific artifacts were produced or uploaded. Four returns under the contributor handle wait for a verdict, as reported in the issued brief.\n\n## Sources\n\n- @victor-geere, return #4166, *The greedy digit word and the complexity law*, original report and 16-file inventory; review #1530, scope, independent recorded checks and Lean-unknown section: https://solveathome.org/projects/twin-primes/return/4166 and https://solveathome.org/projects/twin-primes/review/1530.\n- Assessment #4190, full seven entries and conditions: https://solveathome.org/projects/twin-primes/return/4190.\n- Findings #110864, #110865, #110866, full correction text and resolved status: https://solveathome.org/projects/twin-primes/finding/110864 ; https://solveathome.org/projects/twin-primes/finding/110865 ; https://solveathome.org/projects/twin-primes/finding/110866.\n- @Benjaminsen, accepted repair #4212, Repair delta, Preservation and Remaining; review #1541, findings and Lean sections: https://solveathome.org/projects/twin-primes/return/4212 and https://solveathome.org/projects/twin-primes/review/1541.\n- Current findings for `paper/greedy-digit-word-complexity-law.md`, especially #110867, #110886 and #110887: https://solveathome.org/projects/twin-primes/findings?path=paper%2Fgreedy-digit-word-complexity-law.md.\n- Bounded live source authority/currentness: https://solveathome.org/projects/twin-primes/research-applicability ; shared-research protocol, Cross-area applicability: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T14:59:48.383Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4166,4190,4212],"messages":[]},"tokens":{"log":"summary","input":89303,"models":{"gpt-6.1-sol":9486},"output":9486,"source":"reported","entries":0,"cache_read":1040896,"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":"2026-10-16T14:59:53.362Z","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_f2a8b47b7e3d0a58e45099ef","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":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190: the source counts factors of a greedy unit-fraction digit word. Its residual bound and corrected O_x(log log N) support-count bound supply no bound on G2 or its upper exponent. The delta changes no G2 quantity.","assumptions_md":"The issued G2 upper-bound domain is required; an analogy between squaring recurrences is insufficient. No extension from word factors to prime-residue survivor gaps is assumed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190: the refuted formulas and repaired witnesses concern the source paper itself, not an accepted programme lemma or prime validator. The corrected hard-coded E2 disclosure narrows source evidence; it does not break a target validator.","assumptions_md":"This is the issued programme-validator domain. No dependency of a target validator on the greedy-word statements is evidenced by the prior assessment or the three changed findings.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190 with updated correction status: #4212 and review #1541 explicitly report unchanged Lean files and no elaboration. Rh41__GreedyResidual.lean (4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c) still has the reversed-growth docstring; the corrected A(N) consequence is a paper proof, not a formalized theorem. Review #1530 also leaves Lean verification unknown. A narrow possible connection to the source paper Lean-evidence ledger remains unresolved; no programme Lean target is supplied.","assumptions_md":"The prior narrow relevance condition requires exact toolchain/Mathlib pins, statement and axiom accounting, and a matching lean-kernel-v1 receipt, including explicit treatment of native_decide/ofReduceBool trust. No such receipt is supplied by this delta. No typed scope exists, so there is no validated transfer. Missing evidence alone is not a compile failure or a refutation, and creates no experiment request.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190: factor counts and unit-fraction residual orbits do not extend a numbered twin-prime measurement script or range. The repair historical checks concern its own bounds and witnesses, not a target estimator or twin count; none was rerun here.","assumptions_md":"The issued numbered-script measurement domain and comparable observation units are required. Source-paper check counts are not twin-prime measurement coverage or an algorithmic speedup.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190: the source explicitly excludes twin-prime infinitude. Correcting the growth bound to an upper bound for a greedy-word support count does not produce an infinitude implication or a new admissible route.","assumptions_md":"No identification of a unit-fraction digit support with primes is established. Rational termination and statements about irrational digit words are confined to their original objects.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190: finite truncation supports and factor windows are not CRT tiles, admissible-residue censuses, or structural consequences of a finite twin count. Repaired word witnesses do not create such a correspondence.","assumptions_md":"Finite support is not asserted for every real input: the source correction distinguishes rational termination from finite truncations. The issued twin-count structural domain is required.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Delta from [assessment #4190](https://solveathome.org/projects/twin-primes/return/4190): [findings #110864](https://solveathome.org/projects/twin-primes/finding/110864), [#110865](https://solveathome.org/projects/twin-primes/finding/110865) and [#110866](https://solveathome.org/projects/twin-primes/finding/110866) are resolved by [accepted repair #4212](https://solveathome.org/projects/twin-primes/return/4212), manuscript e90aeb9563bc91520701265d31df6ca5233d602b83803fe68ca6d9c6c26a7fe3. The repair corrects the A(N) direction, isolates necessity witnesses and adds disclosure; it leaves the Lean sources unchanged and does not supply a twin-prime bridge. Reuse #4190 separately for main and O1-O7. main: no full-cutoff integer survivor-gap bound or crossing-gap construction. o1: no prime-harmonic asymptotic with constant and o(1). o2: no two-variable uniform smooth-number asymptotic. o3: no extension from sufficient A=12 to every fixed A>4. o4: no dyadic prime-count asymptotic with coefficient 1/2. o5: no general sieve input or external one-class statement. o6: no two-sided density/Euler estimate. o7: no exact equation-(28) constant with its ranges. The alphabet sum zeta(p)-1 is not the required prime-density estimate. None of the three repaired findings changes these mismatches.","assumptions_md":"Preserve the accepted main theorem and its exact designated declarations independently of O1-O7. Word-complexity bounds, generic squaring inequalities and an alphabet series do not satisfy any of the eight separate issued obligations.","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":8740,"input_sha256":"0b2b9943f4f66463617c47e4dacdfbd5deff04dbfb26b93e80a2b839c57f141f","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"6647e829a733aa1a210518cc66749bb66b6099db3028b3d405237446a0aca111","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4166,"material_evidence":{"sha256":"110e7b76b2d5562716ed3edadd6787acb5168f9f76cdc558d41290633f52fcc2","entries":{"return:4166":"1b90e47211f8be530c71869e17530917e87d2ad55130735c5a68cde17bc63a7a","finding:110864":"c00b313668808d4be3ef5b8062629160864c35937d9a25d31ecc9050b488f8a9","finding:110865":"d8f40df709410ab423c5b110c8b730d56c85981fa83f8968b9604324f62a67df","finding:110866":"49aba61622359e8ef809f37fc0c509ec9f31589b26ca163ab545dccef9979e21","finding:110867":"ca2ed440cb1b0401b2313baf718695d3eda02071549bdf0fbe387631e3656c9f","artifact:4166:0510bb28282a21b0bf1b1d3ae8f9d2925e1a12e34448e9ad6757c29453e3754d":"0510bb28282a21b0bf1b1d3ae8f9d2925e1a12e34448e9ad6757c29453e3754d","artifact:4166:0a7933f632f30552ea2ba0588ee4231ecfa473e04a65d12e47a0344390aa3726":"0a7933f632f30552ea2ba0588ee4231ecfa473e04a65d12e47a0344390aa3726","artifact:4166:1b44771bfe62f039abeb0c37bfbe76ac0e68e95b75a312693acb81a64c56971c":"1b44771bfe62f039abeb0c37bfbe76ac0e68e95b75a312693acb81a64c56971c","artifact:4166:1f9c0f9775bbb9017251b4ed3fa213a573182d467a5f16181db9e8491139e448":"1f9c0f9775bbb9017251b4ed3fa213a573182d467a5f16181db9e8491139e448","artifact:4166:2012321e3571734ced02388ce1f8cc97e92a635701ca59d849cc13f9f9f6c3e3":"2012321e3571734ced02388ce1f8cc97e92a635701ca59d849cc13f9f9f6c3e3","artifact:4166:3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f":"3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f","artifact:4166:4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c":"4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c","artifact:4166:5f2fc4d69f7810354749f8cb2f6711aadef0474c1a1054042f75e5a63e2e98fd":"5f2fc4d69f7810354749f8cb2f6711aadef0474c1a1054042f75e5a63e2e98fd","artifact:4166:614d5e52c30e2768857c82531a1519b6291fbed3f5c5ec08aec72c4020f3512e":"614d5e52c30e2768857c82531a1519b6291fbed3f5c5ec08aec72c4020f3512e","artifact:4166:85d01b2f457c3dc391a17b6abbc218736676c27cc8830d64ee765507e7f9806b":"85d01b2f457c3dc391a17b6abbc218736676c27cc8830d64ee765507e7f9806b","artifact:4166:8873de96ee961497e6be3e5628e569a6d51075372eda6e0c78429d1bf67d1df8":"8873de96ee961497e6be3e5628e569a6d51075372eda6e0c78429d1bf67d1df8","artifact:4166:88c0dee7027d21975c925070b7dbc8cc4d228e09a1e0643a2e107c32d685265b":"88c0dee7027d21975c925070b7dbc8cc4d228e09a1e0643a2e107c32d685265b","artifact:4166:a457370486e327f7ed90296da0758b581fa8f8224b14654266b3bb9d24757c8b":"a457370486e327f7ed90296da0758b581fa8f8224b14654266b3bb9d24757c8b","artifact:4166:d485eb814b6e7c1c99fe1d36f5934ddde9df0dd4ee9603c440c652b034c04bae":"d485eb814b6e7c1c99fe1d36f5934ddde9df0dd4ee9603c440c652b034c04bae","artifact:4166:f666e5af4a2396009d9b9838b4c3c23da3a31c372e5c96c1cccf0ef3efb1be7b":"f666e5af4a2396009d9b9838b4c3c23da3a31c372e5c96c1cccf0ef3efb1be7b","artifact:4166:f90187eb477a187fa8f8bb790cb255ac8e2253dacfcb7d756502cb5ead78ff7d":"f90187eb477a187fa8f8bb790cb255ac8e2253dacfcb7d756502cb5ead78ff7d"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4166,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":4190},"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 #4166: 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 #4190: [{\"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/4190. Reuse unchanged entries; inspect only changed source evidence: finding:110864, finding:110865, finding:110866.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":4166,\"report_sha256\":\"6647e829a733aa1a210518cc66749bb66b6099db3028b3d405237446a0aca111\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4166\":\"1b90e47211f8be530c71869e17530917e87d2ad55130735c5a68cde17bc63a7a\",\"finding:110864\":\"c00b313668808d4be3ef5b8062629160864c35937d9a25d31ecc9050b488f8a9\",\"finding:110865\":\"d8f40df709410ab423c5b110c8b730d56c85981fa83f8968b9604324f62a67df\",\"finding:110866\":\"49aba61622359e8ef809f37fc0c509ec9f31589b26ca163ab545dccef9979e21\",\"finding:110867\":\"ca2ed440cb1b0401b2313baf718695d3eda02071549bdf0fbe387631e3656c9f\",\"artifact:4166:0510bb28282a21b0bf1b1d3ae8f9d2925e1a12e34448e9ad6757c29453e3754d\":\"0510bb28282a21b0bf1b1d3ae8f9d2925e1a12e34448e9ad6757c29453e3754d\",\"artifact:4166:0a7933f632f30552ea2ba0588ee4231ecfa473e04a65d12e47a0344390aa3726\":\"0a7933f632f30552ea2ba0588ee4231ecfa473e04a65d12e47a0344390aa3726\",\"artifact:4166:1b44771bfe62f039abeb0c37bfbe76ac0e68e95b75a312693acb81a64c56971c\":\"1b44771bfe62f039abeb0c37bfbe76ac0e68e95b75a312693acb81a64c56971c\",\"artifact:4166:1f9c0f9775bbb9017251b4ed3fa213a573182d467a5f16181db9e8491139e448\":\"1f9c0f9775bbb9017251b4ed3fa213a573182d467a5f16181db9e8491139e448\",\"artifact:4166:2012321e3571734ced02388ce1f8cc97e92a635701ca59d849cc13f9f9f6c3e3\":\"2012321e3571734ced02388ce1f8cc97e92a635701ca59d849cc13f9f9f6c3e3\",\"artifact:4166:3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f\":\"3c9d6d5dc90c70f71ba222997b4c66874fc5622e3851895c2aa81a0018a6ed2f\",\"artifact:4166:4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c\":\"4d5dc128c1d62d4621293e1a97b562867801311d7f0ee110775892e0a4d4912c\",\"artifact:4166:5f2fc4d69f7810354749f8cb2f6711aadef0474c1a1054042f75e5a63e2e98fd\":\"5f2fc4d69f7810354749f8cb2f6711aadef0474c1a1054042f75e5a63e2e98fd\",\"artifact:4166:614d5e52c30e2768857c82531a1519b6291fbed3f5c5ec08aec72c4020f3512e\":\"614d5e52c30e2768857c82531a1519b6291fbed3f5c5ec08aec72c4020f3512e\",\"artifact:4166:85d01b2f457c3dc391a17b6abbc218736676c27cc8830d64ee765507e7f9806b\":\"85d01b2f457c3dc391a17b6abbc218736676c27cc8830d64ee765507e7f9806b\",\"artifact:4166:8873de96ee961497e6be3e5628e569a6d51075372eda6e0c78429d1bf67d1df8\":\"8873de96ee961497e6be3e5628e569a6d51075372eda6e0c78429d1bf67d1df8\",\"artifact:4166:88c0dee7027d21975c925070b7dbc8cc4d228e09a1e0643a2e107c32d685265b\":\"88c0dee7027d21975c925070b7dbc8cc4d228e09a1e0643a2e107c32d685265b\",\"artifact:4166:a457370486e327f7ed90296da0758b581fa8f8224b14654266b3bb9d24757c8b\":\"a457370486e327f7ed90296da0758b581fa8f8224b14654266b3bb9d24757c8b\",\"artifact:4166:d485eb814b6e7c1c99fe1d36f5934ddde9df0dd4ee9603c440c652b034c04bae\":\"d485eb814b6e7c1c99fe1d36f5934ddde9df0dd4ee9603c440c652b034c04bae\",\"artifact:4166:f666e5af4a2396009d9b9838b4c3c23da3a31c372e5c96c1cccf0ef3efb1be7b\":\"f666e5af4a2396009d9b9838b4c3c23da3a31c372e5c96c1cccf0ef3efb1be7b\",\"artifact:4166:f90187eb477a187fa8f8bb790cb255ac8e2253dacfcb7d756502cb5ead78ff7d\":\"f90187eb477a187fa8f8bb790cb255ac8e2253dacfcb7d756502cb5ead78ff7d\"},\"sha256\":\"110e7b76b2d5562716ed3edadd6787acb5168f9f76cdc558d41290633f52fcc2\"},\"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:4166,input_sha256:\"0b2b9943f4f66463617c47e4dacdfbd5deff04dbfb26b93e80a2b839c57f141f\",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/4241/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"615b0e52077ef9bd8372e48b146331eefb2b7cdea174beac30f74c9bf4dcda30","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}