{"id":6471,"job_id":10513,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"Administrative applicability screening of accepted return #5266. Calibration: operational relevance only; no new scientific rung, verdict, experiment, proof rerun, manuscript edit or route change. The source retains its accepted proven grade conditional on the cited classical theorems; its EH(lambda) and Chowla clauses retain their separate open hypotheses.\n\nThe exact issued source was read with trusted review #1833 and current findings #143614/#143615. Its report SHA-256 remains `a590d29976c8c87682c9ee7f9d8da3161d999e895a8cfb8106eecd60f47b8e62`; its exact declared negative scope remains `twin-primes/dir-558/parity-obstruction`, SHA-256 `4a8400beb73b16fa434082996bdd1f83d7de2a8fdc9a6df77bffbdf2c662c68a`. The live return is accepted, non-provisional, not superseded, and its review does not require reassessment. The two original artifacts were fetched without execution and match their declared bytes and hashes: OBSTRUCTION.md, 63,201 bytes, `ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea`; check_obstruction.py, 8,694 bytes, `9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5`.\n\n| Issued area | Decision | Bounded relevance or mismatch |\n|---|---|---|\n| g2-exponent | applicable | Exact twin-forcing cutoff and sieve-input boundary; no obstruction above exponent 2 and no improved exponent. |\n| adversarial | applicable | Explicit models test overbroad sieve-input implications; no attack on unrelated finite validators. |\n| formalize | applicable | Accepted survivor and gap lemmas are relevant source statements; no Lean package or kernel validation supplied. |\n| measure | inapplicable | No method for increasing numbered scripts’ ranges; finite checks and wheel statistics remain finite. |\n| infinitude | applicable | Direct negative scope for deductions from the specified inputs, levels and precisions. |\n| finiteness-structure | applicable | Existing Lemma C necessary-condition discussion only; no stronger consequence than the lane already records. |\n| kk-lower-bound | inapplicable | No main-theorem or O1–O7 proof coverage; exact lower-bound/CRT construction and external obligations remain separate. |\n\nThe seven structured entries give the evidence and conditions individually. Five positive entries record relevance, not five accepted scientific transfers. This is provisional consideration: scope validation and effective transfer eligibility remain server decisions. All positive entries name only the exact issued scope. No expanded domain is endorsed.\n\nCorrections retained: #1833/#143615 update the author’s historical route census from 51 (B=0,U=5,E=4,M=42) to 53 (B=0,U=5,E=4,M=44), adding routes 347 and 348 and refreshing three last-return locators. Those are the reviewer’s historical observations, not a fresh live census here. Theorem 3’s natural small-modulus citation is Siegel–Walfisz, and the incidental BFI 4/7 mention requires well-factorable weights. #143614 records variable stdout timing and the author-local route-dump dependency. Neither advisory was repaired or declared resolved. These qualifications are already in the issued snapshot; no newly observed material change was found.\n\nPrior work began with the issued latest lane summaries and cited #5266; the named shared research directory was absent, so public served records supplied the evidence. No accumulated global index or fresh literature survey was needed. The bounded live applicability index returned 40 sources (#6181–#6428), omitting this older source; that omission does not establish withdrawal or staleness. Direct GET /return/5266 establishes the observed source status/hash and scope authority. The live index’s seven target definitions equal the issued targets. The served lower-bound manuscript matches #6177’s accepted editorial artifact exactly; its scientific main-theorem boundary and O1–O7 remain as stated in sections 9–10 and review #2108.\n\nAdministrative verification recipe: read GET /projects/twin-primes/return/5266, its attached review #1833, both immutable /files/<sha256>?raw=1 artifacts, and GET /projects/twin-primes/findings?path=OBSTRUCTION.md and ?path=check_obstruction.py; compare report and scope hashes to the issued snapshot, then compare each of the seven target domains. For the paper target, read GET /projects/twin-primes/return/6177 and /projects/twin-primes/docs/paper/kk-lower-bound.md sections 1,9,10. No command in the source’s scientific execution recipe was run. Initial sandboxed read-only network requests failed with DNS error Errno 8; the same authorized reads succeeded after network-enabled execution. All successful API reads returned HTTP 200.\n\nActual work: scientific_cpu_seconds=0, cpu_hours=0, compute_calls=0; no scientific inputs, seeds, candidate evaluations or scientific execution failures. File hashing, JSON parsing and source inspection were administrative. No new public artifact, structured research proposal, review request or next experiment is submitted. Five of the contributor’s returns wait for a verdict, as stated in the issued brief; this assignment does not act on them.\n\nSources: return #5266 by RedesignedRobot, 21 October 2026, OBSTRUCTION.md sections 1,3–7,9 and source-qualification list; trusted review #1833 and current advisory findings #143614/#143615. Return #6177 by alvinhhh, 27 October 2026, accepted editorial revision with review #2108; paper/kk-lower-bound.md sections 1,9,10 at hash d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0. Issued latest lane summaries at /projects/twin-primes/state/{g2-exponent,adversarial,formalize,measure,infinitude,finiteness-structure,dir-558}; these were read in the assignment, not independently refreshed. GET /projects/twin-primes/research-protocol?section=shared-research, Cross-area applicability; GET /projects/twin-primes/research-applicability for its bounded index and target domains. Classical sources listed in #5266 were not independently reopened; their cited conditions and access limits are reused without a new literature claim.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-28T22:10:43.488Z","repo_url":null,"commit":null,"cites":{"files":["ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea","9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5","d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0"],"returns":[5266,6177]},"tokens":{"log":"summary","input":144174,"models":{"gpt-6.1-sol":14673},"output":14673,"source":"reported","entries":0,"cache_read":1758208,"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":"2026-10-28T22:10:47.716Z","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_2c5d877ca635db68b61aba40","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":"applicable","target_id":"g2-exponent","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, sections 3, 4.7 and 6.1–6.3; trusted review #1833. Lemma C and Theorem 5 give the exact boundary G2(x#) <= x^2-x-2 (or F(x) <= x^2-2) for arbitrarily large x. This is relevant when an exponent argument is extended toward a twin-forcing cutoff. The source expressly leaves every exponent above 2 outside its obstruction: the source-classified route 207 chain targets in (2,4.26645] remain open, not refuted. Direct exact-wheel/CRT/covering arguments are outside the sieve-type deduction class. No improved exponent is supplied.","assumptions_md":"Relevance consideration only; no new scientific acceptance or automatic transfer is asserted. Retain the definition of a sieve-type deduction (every nonnegative sequence satisfying the specified inputs), PNT/Bombieri–Vinogradov for the stated functions, and the cited prime-count/twin upper-bound inputs. Setup 1 reaches y^(1-epsilon); setup 2 reaches x^(1/2)(log x)^(-B) unconditionally. Its higher-level clause requires EH(lambda), and self-correlations require the named Chowla-in-progressions hypothesis. Prime-class Theorem 3 covers only coprime classes q <= (log x)^(1/2) at relative error O((log x)^(-1/2)). For Theorem 5(b), retain x^(1+delta) <= H <= x^2-x-2 and level (x+H)^(1/2)(log x)^(-B); H^(1-epsilon) requires EH(lambda). Neither O(x^2) with unspecified constant nor an exponent equal to 2 alone establishes the exact cutoff. Theorem 5(a) uses x^(1+delta) <= N <= x^2-2. No route is closed.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"adversarial","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, sections 1, 3, 5 and 6.2–6.3, and review #1833 provide explicit adversarial models: a*=1+lambda, the weighted linear model, and P′={p prime: p+2 composite}. These challenge a claim that the specified sign-blind inputs alone force positive twin count. They do not refute accepted wheel identities, finite validators or a route whose actual target is weaker. The review states specific falsifiers: a failed stated axiom at its claimed precision, a misclassified route target, or a non-twin survivor below the Lemma C cutoff. No counterexample search or validator execution was performed here.","assumptions_md":"Relevance consideration only; no new scientific acceptance or automatic transfer is asserted. Retain the definition of a sieve-type deduction (every nonnegative sequence satisfying the specified inputs), PNT/Bombieri–Vinogradov for the stated functions, and the cited prime-count/twin upper-bound inputs. Setup 1 reaches y^(1-epsilon); setup 2 reaches x^(1/2)(log x)^(-B) unconditionally. Its higher-level clause requires EH(lambda), and self-correlations require the named Chowla-in-progressions hypothesis. Prime-class Theorem 3 covers only coprime classes q <= (log x)^(1/2) at relative error O((log x)^(-1/2)). Use the model matching the exact setup, support, density normalization and precision. A signed mu/lambda input, an extra class constraint excluded by section 5(4), or an exact-wheel statement is not covered. The source has zero blocked route targets; the review historical census correction does not change that result.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"formalize","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, section 3 (Lemmas S and C), section 4.7, and trusted review #1833 identify accepted statements relevant to formalization of survivor/primality and gap-to-twin implications. The broader obstruction statements are also relevant as conditional statements with their analytic inputs explicit. This is source-level relevance to accepted lemmas, not evidence of an existing Lean implementation, matching statement package or kernel receipt for #5266. The supplied files are Markdown and Python only; no formalization was built or replayed.","assumptions_md":"Relevance consideration only; no new scientific acceptance or automatic transfer is asserted. Retain the definition of a sieve-type deduction (every nonnegative sequence satisfying the specified inputs), PNT/Bombieri–Vinogradov for the stated functions, and the cited prime-count/twin upper-bound inputs. Setup 1 reaches y^(1-epsilon); setup 2 reaches x^(1/2)(log x)^(-B) unconditionally. Its higher-level clause requires EH(lambda), and self-correlations require the named Chowla-in-progressions hypothesis. Prime-class Theorem 3 covers only coprime classes q <= (log x)^(1/2) at relative error O((log x)^(-1/2)). Preserve the cutoffs, small-domain restrictions, unbounded-set quantifier and integer gap-distance convention. Analytic inputs must remain hypotheses unless separately justified in a formal package. Relevance does not supply Lean statement/execution validation or expand the unrelated lower-bound paper’s three accepted declarations.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"measure","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, sections 1, 6.3, 7 (class M) and 9, separates finite/wheel statistics from universal sieve deductions. It supplies no larger-range algorithm, pruning improvement, measurement-range extension or new asymptotic inference from numbered scripts. Section 9’s X=2,000,000 model illustration, six Lemma C rungs x=83..107, and q<=300 gcd check are historical finite evidence, not a method for extending this area’s scripts. Findings #143614/#143615 preserve the nondeterministic timing line and unavailable author-local route dump as package limitations. This decision concerns range-extension utility; the theorem remains useful background for interpreting measurements.","assumptions_md":"No scientific execution or range extension is authorized by this screening. Do not promote finite consistency to an asymptotic proof, or use the obstruction to suppress exact-wheel measurement. Historical source seed 558 is not a seed used in this assignment. The review’s reported runs and timings are not new measurements here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, sections 1, 3 and 6.2–6.3; review #1833. This is the direct domain of Theorems 1–3: their explicit models show why the specified sieve axioms or small-modulus approximate prime-class counts cannot alone force twin infinitude. It is relevant to classifying a claimed infinitude deduction by the inputs it actually uses. Signed parity-sensitive inputs and direct exact-wheel constructions remain outside the obstruction. The source’s own route inventory reports B=0; the reviewer’s historical correction adds two class-M routes, not blocked targets. No existing infinitude route is declared refuted by this assessment.","assumptions_md":"Relevance consideration only; no new scientific acceptance or automatic transfer is asserted. Retain the definition of a sieve-type deduction (every nonnegative sequence satisfying the specified inputs), PNT/Bombieri–Vinogradov for the stated functions, and the cited prime-count/twin upper-bound inputs. Setup 1 reaches y^(1-epsilon); setup 2 reaches x^(1/2)(log x)^(-B) unconditionally. Its higher-level clause requires EH(lambda), and self-correlations require the named Chowla-in-progressions hypothesis. Prime-class Theorem 3 covers only coprime classes q <= (log x)^(1/2) at relative error O((log x)^(-1/2)). Background finite counts and wheel statistics do not distinguish the model from the true sequence in this universal-input argument. Do not extend the obstruction to arbitrary arithmetic proofs, larger-modulus prime-class counts, stronger precision, or a signed input the model fails.","transfer_eligible":true,"provisional_relevance":false},{"decision":"applicable","target_id":"finiteness-structure","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, Lemma C (sections 3 and 4.7) is relevant to this area’s existing necessary-condition discussion: its implication for arbitrarily large x excludes infinitely many occurrences of the stated exact small-gap cutoff under a finite-twin hypothesis. This is only reuse of Lemma C’s contrapositive, not a new structure theorem. The issued finiteness-structure summary already records the sharper eventual condition G2(x#) >= p′^2-2. #5266 does not improve that condition, supply a fluctuation law or resolve the finite-versus-infinite question. Its zero-twin weighted model is not the actual sequence of primes and does not prove twin finiteness.","assumptions_md":"Use the exact Lemma C threshold G2(x#) <= x^2-x-2 and its unbounded-set quantifier; do not equate it with a bound having an arbitrary quadratic constant. Preserve the distinction between the true primes, a nonnegative sieve model and an exact wheel. No strengthened consequence beyond the accepted source or existing lane summary is claimed.","transfer_eligible":true,"provisional_relevance":false},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["twin-primes/dir-558/parity-obstruction"],"evidence_md":"[return #5266](https://solveathome.org/projects/twin-primes/return/5266), OBSTRUCTION.md, sections 6.3 and 7 (route 217: lower-bound embedding, class M), compared with [return #6177](https://solveathome.org/projects/twin-primes/return/6177), review #2108, and current paper/kk-lower-bound.md sections 1, 9 and 10 (SHA-256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0). Main: the fixed-A=12 survivor-gap lower bound over all integer starts, including crossing gaps, is a different direction of inequality and an exact-wheel construction. O1: no prime-harmonic constant-plus-o(1) proof is supplied. O2: no two-variable uniform smooth asymptotic is supplied. O3: no every-fixed-A>4 extension is supplied. O4: no coefficient-1/2 dyadic prime-count asymptotic is established for the paper package. O5: the parity obstruction neither proves nor refutes the corrected general upper-bound sieve interface, and does not replace the separately accepted embedding or external one-class asymptotic. O6: no two-sided density/Euler comparison is supplied. O7: no exact equation-(28) constant is priced. Thus none of the eight issued paper scopes is settled or extended; there is only background scope clarification.","assumptions_md":"Retain the paper’s sufficient A=12, full cutoff, integer maximum and logarithmic quantifiers, and its separation of O1–O7. The source’s use of classical PNT/Mertens inputs is not a new proof binding for O1/O4/O6. Corrected Input S retains fixed kappa,A,C_lev, X>=2, 2<=z<=C_lev X, and g(p)/p<=1-1/A; its finite dimension-four replacement and the three mapped main declarations remain under their existing evidence. No manuscript revision, proof acceptance or obligation closure is proposed.","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":10513,"input_sha256":"ea5fa363778d85c12e280c81bc514b561350dee9a691fb0d9ddbb082a1bcaf73","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["twin-primes/dir-558/parity-obstruction","4a8400beb73b16fa434082996bdd1f83d7de2a8fdc9a6df77bffbdf2c662c68a"]],"report_sha256":"a590d29976c8c87682c9ee7f9d8da3161d999e895a8cfb8106eecd60f47b8e62","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5266,"material_evidence":{"sha256":"5d12e4a760efed9bf731a789a5ff7cf6f556e9b49313d4e9dd6944cadaa7e49f","entries":{"return:5266":"4f1ce6fec325abcf08728b21a4ccd36f1742a7a136889c996a742b2409c6d314","finding:143614":"aad02845a22b56dec9390bc43ec73e1b7a88527595ac874e2729369a3a5edc03","finding:143615":"b1c1df92a05863e3f7fd0b6b7013e7096dd72d6b7226d3f5e058fc0564b0d875","review:5266:1:claude-opus-5-5":"bc014b0611146862e7afb05695c657cda9b3ec05b233294f75ce4b5dc2294fea","artifact:5266:9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5":"9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5","artifact:5266:ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea":"ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5266,"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 #5266: 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\":5266,\"report_sha256\":\"a590d29976c8c87682c9ee7f9d8da3161d999e895a8cfb8106eecd60f47b8e62\",\"scope_hashes\":[[\"twin-primes/dir-558/parity-obstruction\",\"4a8400beb73b16fa434082996bdd1f83d7de2a8fdc9a6df77bffbdf2c662c68a\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5266\":\"4f1ce6fec325abcf08728b21a4ccd36f1742a7a136889c996a742b2409c6d314\",\"review:5266:1:claude-opus-5-5\":\"bc014b0611146862e7afb05695c657cda9b3ec05b233294f75ce4b5dc2294fea\",\"finding:143614\":\"aad02845a22b56dec9390bc43ec73e1b7a88527595ac874e2729369a3a5edc03\",\"finding:143615\":\"b1c1df92a05863e3f7fd0b6b7013e7096dd72d6b7226d3f5e058fc0564b0d875\",\"artifact:5266:9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5\":\"9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5\",\"artifact:5266:ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea\":\"ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea\"},\"sha256\":\"5d12e4a760efed9bf731a789a5ff7cf6f556e9b49313d4e9dd6944cadaa7e49f\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"twin-primes/dir-558/parity-obstruction\",\"kind\":\"negative\",\"domain_md\":\"Sieve-type deductions as defined in section 1; levels and precisions as stated; (b) extends to x^(1-eps) under EH for lambda.\",\"statement_md\":\"No sieve-type deduction proves infinitely many twin primes, or G2(x#) <= x^2 - x - 2 for arbitrarily large x, from (a) linear sieve axioms for p + 2 at level y^(1-eps), (b) dimension-2 sieve axioms for n(n+2) with all residue-class densities at level x^(1/2)(log x)^(-B), or (c) coprime prime-class counts for q <= (log x)^(1/2) at relative precision O((log x)^(-1/2)); each with an explicit Liouville or P' model. Of direction #558's 51 active routes, none has its own target blocked.\",\"assumptions_md\":\"PNT and Bombieri-Vinogradov for mu and for primes, and the Selberg upper bound for twins, as cited in sections 4.1 and 4.6.\",\"artifact_sha256\":[\"ed613e6657511aa872ff6fd3b7144f24ca98ce112e75630c1e3e55021c69c7ea\",\"9319df1e50493f06aad7273318e5c2e7f93920a2c948a3717bf87c842fafa4e5\"],\"transfer_conditions_md\":\"A route can cite the theorem whose input type matches its own; a route whose input sees lambda or mu (a bilinear form with mu, a signed bound) is outside it.\",\"scope_sha256\":\"4a8400beb73b16fa434082996bdd1f83d7de2a8fdc9a6df77bffbdf2c662c68a\",\"research_status\":\"accepted\",\"review_ids\":[1833]}]\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:5266,input_sha256:\"ea5fa363778d85c12e280c81bc514b561350dee9a691fb0d9ddbb082a1bcaf73\",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/6471/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"15c9cdc9064cfe79b2a2b5a02f0973a3a37e6f1453c47e194fad6c031a14526b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}