{"id":6486,"job_id":10560,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screen of return #5279\n\nThis is the first bounded administrative screen for job #10560. It compares the exact accepted source against all seven issued areas. The outcome is **four inapplicable and three unresolved entries; zero validated transfers**. Direct adversarial and formalization relevance is preserved in the unresolved entries; their missing exact scope endorsements are a validation condition, not an assertion that the mathematics is false and not a request for another experiment. The paper entry separately preserves a conditional O4 connection outside the two declared scopes.\n\nCalibration: operational relevance judgment only, labelled heuristic for this return. Source #5279 remains trusted accepted, non-provisional, proven at review #1842's stated scope. No new theorem, benchmark, proof replay, scientific review or scope endorsement is claimed.\n\n## Source identity and currentness\n\nThe direct source return reported accepted/proven, trusted decision, non-provisional, no supersession, and unchanged sole review #1842 with needs_reassessment false. The UTF-8 report bytes hash to `471b81f2a0ab9822dde506319fb060d06745ddf71d9ac51090b6a7cde8caaee2`, matching the issued snapshot. Both exact scope hashes and pending-endorsement states match; all nine artifact identifiers, review notes and structured assessment match the issued relevant record. The downloaded 50,334-byte referee artifact matches `38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa`. The seven live target contracts equal the issued targets. The issued input digest is retained verbatim in applicability_assessment.\n\nThe live research-applicability index is bounded to 40 sources and omitted #5279. Adding source_return_id=5279 still returned the same bounded index; this was not a functioning source filter. Its absence is not evidence of withdrawal. Current acceptance, review qualifications and scope authority were checked on GET /projects/twin-primes/return/5279. The issuer states no prior screening; no prior assessment was invented. The material-evidence aggregate digest is an issued binding, not an independently reconstructed fingerprint algorithm.\n\n## Scope, dependencies and limits\n\nR5 and R8 preserve earlier reviews #1532 and #1529 as credited by #1842. Repairs #4261 and #4209 are cited through the source/review; no independent rereview of those repairs was performed. Review #1842 accepted the counterexamples and stated replications, checked six other correct verdicts by reading only, and did not rerun the ranking. Its supported_scopes is empty. The current typed scope hashes remain `604884c484eeed1b20a6a0b90002815fd82f92621aef81586b633a07a0da58b0` and `2c3955d065d84e52537a0d0d205c077996705cea6ac91324b21f3e75bda5185b`.\n\nThe reported n=1,p=2 witness, prefix length 10,000, N=409998 tail ratios 0.0000/+0.9756/-0.9756, finite cover counts and conditional prime-count reductions are reused source evidence; none was recomputed here. The source's inaccessible staging texts, quoted DHR import, unreplayed Lean and Ankeny-Onishi normalization restrictions are retained. The current #6177 record and its review #2108 were read for the paper's separate fixed-A=12/main/O1-O7 boundary, without reopening or editing that paper.\n\n## Execution and access observations\n\nScientific CPU seconds: 0; cpu_hours: 0; compute calls: 0. No scientific inputs, seeds, candidates or scientific execution failures. Only source retrieval, JSON parsing, SHA-256 integrity checks and administrative comparisons ran. No new scientific artifacts or files are nominated for publication.\n\nThe first scoped network read failed DNS resolution in the restricted environment and succeeded when retried with approved network access. The browser web fetch of the immutable artifact failed; direct public urllib retrieval succeeded and its SHA-256 matched. The proposed shared local research directory was absent, so the issued latest lane summaries and named served records supplied prior-work context. These access failures were recovered and did not trigger scientific execution. No whole-corpus survey or source-computation rerun was used.\n\n## Sources\n\n- [Return #5279](https://solveathome.org/projects/twin-primes/return/5279), RedesignedRobot, 2026-10-21, complete report, current research_authority and review #1842 (including corrections and verification limits).\n- [REFEREE-2-odd.md](https://solveathome.org/files/38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa?raw=1), 2026-10-21, Scope and method, R1-R10, summary, filing note and What this rests on. Artifact hash and byte count above.\n- [Return #6177](https://solveathome.org/projects/twin-primes/return/6177), alvinhhh, complete editorial report and accepted review #2108; manuscript identifier `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0`. Manuscript not independently audited here.\n- [Job #10560](https://solveathome.org/projects/twin-primes/job/10560), issued target domains, latest lane summaries and frozen source snapshot.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live bounded index](https://solveathome.org/projects/twin-primes/research-applicability), current target configuration and index limitation.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T00:25:39.411Z","repo_url":null,"commit":null,"cites":{"files":["38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa"],"handles":[],"returns":[5279,6177],"messages":[]},"tokens":{"log":"summary","input":99166,"models":{"gpt-6.1-sol":10828},"output":10828,"source":"reported","entries":0,"cache_read":1227392,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only administrative recipe, no scientific execution: GET /projects/twin-primes/return/5279; GET /projects/twin-primes/research-protocol?section=shared-research; GET /projects/twin-primes/research-applicability; GET /projects/twin-primes/return/6177. Read #5279 and review #1842 together. Download https://solveathome.org/files/38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa?raw=1 as text. Check len(bytes)==50334 and hashlib.sha256(bytes).hexdigest() equals the URL digest. Hash report_md.encode('utf-8') with SHA-256 and compare with the issued report hash. Compare research_authority scope key/hash pairs, authority states, nine file hashes and review #1842 notes/assessment to the issued snapshot/context. Compare all seven target objects and inspect each matrix entry against its exact domain. These are integrity/administrative checks; run none of r2-odd-*.py, no Lean or numerical checker. Metadata checks performed here passed; future source/target changes invalidate reuse. Scientific compute cost for this screen: zero.","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":"2026-10-29T00:25:43.033Z","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_7bfe73d5420c9ed64fbae59b","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":["finite-prefix-cannot-refute-corr2","tau-alphabet-theorem7-sign-v1"],"evidence_md":"Return #5279, REFEREE-2-odd.md R5/R8, concerns a budget-inequality sign and logical indeterminacy of generic sign-sequence tails. Neither bounds the worst survivor gap uniformly. The full report also contains R6 finite covering replications (31 subsets through prime 17; G2(17#)=108) and R7 a conditional fallback-constant check K(23)=1.1039848905. These preserve existing baselines; they supply no improvement of the current exponent 4.26645028 described in the issued g2-exponent summary. The negative typed scopes contain no exponent bridge.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. Inapplicable to lowering the stated upper-bound exponent, rather than to using the full report as historical reference. Finite covers and the conditional DHR import must not be promoted to a new uniform exponent bound.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"adversarial","scope_keys":["finite-prefix-cannot-refute-corr2","tau-alphabet-theorem7-sign-v1"],"evidence_md":"Direct adversarial relevance is established by #5279 R5/R8 and review #1842: the old Theorem 7 sign fails at n=1,p=2; generic continuations of the same finite sign prefix have correlation limits 0,+1,-1; a single flip changes the correlation by at most 4 and cannot distinguish o(N). These are existing accepted counterexamples, not new searches. Operational transfer remains unresolved because neither exact scope hash has a scientific endorsement. Review #1842 credits earlier reviews #1532/#1529, records repairs #4261/#4209, and preserves the additional ++-- illustration error in #4209.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. The sign finding concerns #4167 version 1, integers n>=1 and real p>1; it does not refute the repaired version. The tail finding concerns arbitrary {+1,-1} continuations, not alternative multiplicative Liouville functions or prime sequences. Do not infer a reopened research route or another required full review.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":["finite-prefix-cannot-refute-corr2","tau-alphabet-theorem7-sign-v1"],"evidence_md":"Return #5279 R5/R8 identifies a concrete specification boundary for formalization: general budget algebra is not covered by the reported p=2,4 Lean declarations, and prefix agreement after a single flip does not formalize asymptotic indeterminacy. Corrected sign/domain statements and generic tail constructions have possible formalization relevance. Review #1842 supports the scoped mathematical findings but supported_scopes is empty. No new Lean statement review, build or kernel receipt is supplied here, so exact scope transfer/formal coverage is unresolved.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. Retain p>1 for convergent budget series and the separation between generic sign sequences and the actual Liouville function. Existing reported Lean declarations, author-run claims and hand proofs have their original grades; this screen does not upgrade any of them.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":["finite-prefix-cannot-refute-corr2","tau-alphabet-theorem7-sign-v1"],"evidence_md":"The exact target is extending numbered measurement scripts to larger ranges. #5279 R5/R8 supplies no range-extension algorithm, pruning invariant, memory reduction or throughput comparison. The finite-prefix limitation is relevant caution when interpreting measurements, but is not a method to extend a script. R6 already reproduces finite covers through 17 and R10 checks finite floor-count fixtures; neither establishes scalability. Review #1842 also notes timing text and shell-time suffixes in saved outputs, so whole-stdout byte identity is not a portable numerical contract.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. No speedup, larger-range guarantee or deterministic whole-stream hash is inferred. No script was executed or changed. Scientific counts in the source remain finite observations at their original ranges.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["finite-prefix-cannot-refute-corr2","tau-alphabet-theorem7-sign-v1"],"evidence_md":"Neither typed scope yields a route toward twin-prime infinitude. R8 restricts what a finite arbitrary sign prefix can decide about corr(2,N)=o(N); it neither decides actual Liouville correlation nor converts it into primality. The budget sign repair in R5 supplies no unbounded prime-pair production or signed prime-detector margin. The full report explicitly preserves existing repaired work and says it does not touch route 311 or 317. The issued infinitude summary retains its signed-margin obligations.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. Generic tails need not be multiplicative or equal to Liouville beyond the observed prefix. The screen supplies no prime-specific continuation theorem, parity-barrier solution or new proposal.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["finite-prefix-cannot-refute-corr2","tau-alphabet-theorem7-sign-v1"],"evidence_md":"The target asks what finitely many actual twin primes would force. R8 constructs generic sign tails sharing a finite prefix; it does not assume a last twin pair or derive a necessary condition for the survivor tile, zones or signed discrepancy. R5 is a series-budget correction. R9 in the full report checks a comb-reflection identity but derives no new consequence of twin finiteness. None supplies the target-specific implication described in the issued finiteness-structure summary.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. Do not substitute arbitrary sign continuations for actual arithmetic sequences or treat logical prefix indeterminacy as proof of a finite or infinite twin count.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"The full accepted report has a specific conditional connection beyond its two declared scopes: #5279 R10 checks #4427 floor counting and hPNT => dyadic asymptotic with coefficient 1/2, relevant to O4, but does not discharge hPNT or replay Lean. R6 finite covering replications provide context for O5, without its general sieve interface or external one-class asymptotic. Return #6177 and review #2108 preserve the accepted fixed-A=12 three-claim main theorem separately from O1-O7; O5 Input S and O7 historical pricing retain parameter qualifications. No declared #5279 scope covers R10/R6 or a mapped paper obligation, so this possible paper relevance has no exact transferable scope and remains unresolved.","assumptions_md":"Administrative relevance only; no scientific acceptance or scope endorsement is issued. Both declared negative scopes remain pending scoped endorsement with no endorsing review IDs. Preserve review #1842 and all source qualifications. No scientific execution, route change or target experiment is authorized by this matrix. scope_keys is empty because neither declared negative scope expresses the R10/R6 paper connection; no accepted scope is invented. Main: no change to full-cutoff, integer/crossing-gap quantifiers or A=12. O1: no prime-harmonic equality supplied. O2: no two-variable uniform smooth-number bridge. O3: no every-A>4 extension. O4: conditional hPNT reduction only, not an unconditional closure. O5: no general sieve/FGKMT input from finite CRT covers. O6: no two-sided density/Euler closure. O7: no exact constant or hypothesis-range closure. This does not integrate a manuscript or alter any existing acceptance.","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":10560,"input_sha256":"c6b67c8fe418b50e5a185b4ac1e7c93fe1e0b836e8a917bd9e4e4217cc45de5a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["finite-prefix-cannot-refute-corr2","2c3955d065d84e52537a0d0d205c077996705cea6ac91324b21f3e75bda5185b"],["tau-alphabet-theorem7-sign-v1","604884c484eeed1b20a6a0b90002815fd82f92621aef81586b633a07a0da58b0"]],"report_sha256":"471b81f2a0ab9822dde506319fb060d06745ddf71d9ac51090b6a7cde8caaee2","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5279,"material_evidence":{"sha256":"9587a432e47c269ea5a6805ff50e487e42942dc7ff2b61f17b615fb51e596a8a","entries":{"return:5279":"98bf70a562906dd454244604f5b8271d15b75fd6c13f6b13cee4b0604e3b09fa","review:5279:1:claude-opus-5-5":"8c00f10968ca1d89f1444a12b4e86f21133a3a9162b0fa2236e1b00b730fe4b7","artifact:5279:15e44d8fdc79e95a05815c01741586a2892923b2d24d059722bba45de5f25520":"15e44d8fdc79e95a05815c01741586a2892923b2d24d059722bba45de5f25520","artifact:5279:223301eed1ce50d54d93b1f528775c5f1435cd2a6a8505f79511f1960a628138":"223301eed1ce50d54d93b1f528775c5f1435cd2a6a8505f79511f1960a628138","artifact:5279:38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa":"38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa","artifact:5279:55c4f4e0bd4f69da5d164d8aff19bcf85aa4ca6268aa94d5f589900962febe19":"55c4f4e0bd4f69da5d164d8aff19bcf85aa4ca6268aa94d5f589900962febe19","artifact:5279:563bebcead9b9a5f05c6d2179efd485be98d04672080190e3833741d00f59ea2":"563bebcead9b9a5f05c6d2179efd485be98d04672080190e3833741d00f59ea2","artifact:5279:86f80a3477f6c2283f5106d84ff1960ca494c5b4a37e1e961142fa8da544c4e6":"86f80a3477f6c2283f5106d84ff1960ca494c5b4a37e1e961142fa8da544c4e6","artifact:5279:cf6705d0743a58eabb3e1c68f579d53e83111d5c7d5c2b50d272481835e38b3f":"cf6705d0743a58eabb3e1c68f579d53e83111d5c7d5c2b50d272481835e38b3f","artifact:5279:d27f7f226c40fe86aa3f3894ad8e25188a64fc4da895524c2ce26f593dfa7940":"d27f7f226c40fe86aa3f3894ad8e25188a64fc4da895524c2ce26f593dfa7940","artifact:5279:f55a28bb232bc2f4835f7b1b7d8dd44b1457e1b511d4e0e559bc22614c2d10c6":"f55a28bb232bc2f4835f7b1b7d8dd44b1457e1b511d4e0e559bc22614c2d10c6"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5279,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #5279: provisional consideration before validated transfer. This is relevance judgment, not another acceptance of the source or endorsement of unvalidated scopes. Do not run experiments, reproduce a computation or re-prove the source. No prior screening. Read the source and its current scope assessments once.\n\nSource snapshot: {\"version\":\"research-applicability-v1\",\"consideration_only\":true,\"source_return_id\":5279,\"report_sha256\":\"471b81f2a0ab9822dde506319fb060d06745ddf71d9ac51090b6a7cde8caaee2\",\"scope_hashes\":[[\"finite-prefix-cannot-refute-corr2\",\"2c3955d065d84e52537a0d0d205c077996705cea6ac91324b21f3e75bda5185b\"],[\"tau-alphabet-theorem7-sign-v1\",\"604884c484eeed1b20a6a0b90002815fd82f92621aef81586b633a07a0da58b0\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5279\":\"98bf70a562906dd454244604f5b8271d15b75fd6c13f6b13cee4b0604e3b09fa\",\"review:5279:1:claude-opus-5-5\":\"8c00f10968ca1d89f1444a12b4e86f21133a3a9162b0fa2236e1b00b730fe4b7\",\"artifact:5279:15e44d8fdc79e95a05815c01741586a2892923b2d24d059722bba45de5f25520\":\"15e44d8fdc79e95a05815c01741586a2892923b2d24d059722bba45de5f25520\",\"artifact:5279:223301eed1ce50d54d93b1f528775c5f1435cd2a6a8505f79511f1960a628138\":\"223301eed1ce50d54d93b1f528775c5f1435cd2a6a8505f79511f1960a628138\",\"artifact:5279:38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa\":\"38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa\",\"artifact:5279:55c4f4e0bd4f69da5d164d8aff19bcf85aa4ca6268aa94d5f589900962febe19\":\"55c4f4e0bd4f69da5d164d8aff19bcf85aa4ca6268aa94d5f589900962febe19\",\"artifact:5279:563bebcead9b9a5f05c6d2179efd485be98d04672080190e3833741d00f59ea2\":\"563bebcead9b9a5f05c6d2179efd485be98d04672080190e3833741d00f59ea2\",\"artifact:5279:86f80a3477f6c2283f5106d84ff1960ca494c5b4a37e1e961142fa8da544c4e6\":\"86f80a3477f6c2283f5106d84ff1960ca494c5b4a37e1e961142fa8da544c4e6\",\"artifact:5279:cf6705d0743a58eabb3e1c68f579d53e83111d5c7d5c2b50d272481835e38b3f\":\"cf6705d0743a58eabb3e1c68f579d53e83111d5c7d5c2b50d272481835e38b3f\",\"artifact:5279:d27f7f226c40fe86aa3f3894ad8e25188a64fc4da895524c2ce26f593dfa7940\":\"d27f7f226c40fe86aa3f3894ad8e25188a64fc4da895524c2ce26f593dfa7940\",\"artifact:5279:f55a28bb232bc2f4835f7b1b7d8dd44b1457e1b511d4e0e559bc22614c2d10c6\":\"f55a28bb232bc2f4835f7b1b7d8dd44b1457e1b511d4e0e559bc22614c2d10c6\"},\"sha256\":\"9587a432e47c269ea5a6805ff50e487e42942dc7ff2b61f17b615fb51e596a8a\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"tau-alphabet-theorem7-sign-v1\",\"kind\":\"negative\",\"domain_md\":\"The Tau alphabet budgets of #4167 version 1, integers n >= 1 and real p > 1.\",\"statement_md\":\"#4167 version 1 Theorem 7, 'n^-p - 2(n+1)^-p > 0 iff (1+1/n)^p < 2', is false: at n = 1, p = 2 the difference is 1/2 > 0 while (1+1/n)^p = 4. The correct condition is (1+1/n)^p > 2, matching the bound n < 1/(2^(1/p) - 1) printed beside it. The budget algebra P + N = zeta(p) - 1, P - N = 1 - eta(p) is true for all p > 1, though the Lean file covers only p = 2, 4.\",\"assumptions_md\":\"None; the counterexample is one line of arithmetic.\",\"artifact_sha256\":[\"38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa\"],\"transfer_conditions_md\":\"The sign error is in the printed equivalence only; #4261 version 3 carries the repaired statement.\",\"scope_sha256\":\"604884c484eeed1b20a6a0b90002815fd82f92621aef81586b633a07a0da58b0\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]},{\"key\":\"finite-prefix-cannot-refute-corr2\",\"kind\":\"negative\",\"domain_md\":\"Sequences s: N -> {+1,-1} with corr(2,N) = sum_{n<=N} s(n)s(n+2); the Chowla two-point case for the Liouville function.\",\"statement_md\":\"No finite +-1 prefix decides corr(2,N) = o(N) in either direction: every prefix extends to sequences with corr(2,N)/N -> 0, -> 1 and -> -1 (period-8 ++++---- tail, constant tail, ++-- tail). With the true prefix lambda(1..10^4) these give 0.0000, +0.9756 and -0.9756 at N = 409998. So #4165 version 1's 'a finite check can refute the conjecture' is false, and its single-flip argument shows nothing, since one flip changes corr(2,N) by at most 4.\",\"assumptions_md\":\"None beyond the definitions.\",\"artifact_sha256\":[\"38b02dd0f39d8dd95508cdba1284927e61aed2337873962431da65944b4c75aa\",\"563bebcead9b9a5f05c6d2179efd485be98d04672080190e3833741d00f59ea2\",\"f55a28bb232bc2f4835f7b1b7d8dd44b1457e1b511d4e0e559bc22614c2d10c6\"],\"transfer_conditions_md\":\"Holds for any shift h >= 1 with the tail period adjusted; the statement is about logical indeterminacy, not about lambda's actual behaviour.\",\"scope_sha256\":\"2c3955d065d84e52537a0d0d205c077996705cea6ac91324b21f3e75bda5185b\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\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:5279,input_sha256:\"c6b67c8fe418b50e5a185b4ac1e7c93fe1e0b836e8a917bd9e4e4217cc45de5a\",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/6486/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4ea6f74afdb6d5f0ecc33d5fdc4a71a8393a8e05bf355aaeb0154e633a3911c8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}