{"id":6549,"job_id":10725,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Provisional applicability of accepted return #5365\n\nThis is the first bounded administrative matrix for the exact issued source and seven configured targets. Calibration: heuristic relevance judgments only, with no new scientific result, acceptance, scope endorsement, proof execution, review request or route change. The source retains its accepted **proven conditional on the named theorems** rung from trusted review #1866.\n\n## Source and currentness\n\nGET /projects/twin-primes/return/5365 returned accepted, trusted, not superseded, with review #1866 still a trusted accept and needs_reassessment=false. Independently hashing its UTF-8 report reproduced the issued and served report SHA256 f667f65bdbb1631b33c67532be8a07081113b1b45565d9428267e73cb9d3e56c. All 14 served file name/hash references match the issued inventory; this was a metadata comparison, not a download-and-rehash of their bodies. The review notes match the issued notes exactly. The three scoped finding queries reproduce open advisories #146570-146572, with notes matching the review. The seven live target objects equal the issued targets. These checks revealed no changed source restriction. I did not independently reconstruct the server's composite material-evidence digest.\n\nThe bounded GET /projects/twin-primes/research-applicability index does not include #5365. Its absence is not treated as withdrawal or a currentness verdict; the exact return, issued snapshot and scoped correction records supply the checks above. Both issued and served source scope lists are empty. Every entry therefore uses scope_keys:[]; even positive relevance is provisional and establishes no automatic validated transfer.\n\n## Preserved scientific evidence\n\nReturn #5365 proves, conditional on its named versioned inputs, that for all large X at least (2 C2 exp(-gamma)/600) X/(log X)^2 pairs have min(P^-(n),P^-(n+2))>(X/3)^(40/119), hence both members are P2. It gives F(x)<3x^2.975, not a bound uniform over gap positions. Its reported headline certificate is Phi>=0.011722; E3 alone gives exponent 2.9995 and Phi>=0.011348. Review #1866 reports an independent enclosure [0.014770,0.015581] at 2.975. These are cited prior observations, not fresh measurements.\n\nKeep Pascadi arXiv:2505.00653v2 Propositions 4.4/5.2 (preprint), Maynard arXiv:2006.07088v1 Proposition 5.2 and Lemmas 5.3/5.4/6.1 through Proposition R, and Lichtman arXiv:2109.02851v2 Theorem 2.10 and Iwaniec-weight support. The specialized 3/5 switch is on 1/5<=t<=1/3, one complete upper bound is selected per q-cell, and lower-sieve terms retain their own levels. Review #1866 credits #5281 for Proposition R and H inputs. This screening inherits that attribution without independently rereading #5281 or the external papers.\n\nPreserve all three open advisories: certify.py writes timing to stdout (#146570); AUDIT-EXTRACT.md names an earlier 45a674e7 version instead of shipped main.tex 58f0da78 (#146571); manifest-pinned auxiliary/build files are absent from the return (#146572). The extract and 3.054 build cannot be treated as fully rebuildable from this package. No human reading of S1/Proposition R or literature-wide novelty is asserted. These restrictions do not themselves revoke the accepted theorem.\n\n## Applicability matrix\n\n| Target | Decision | Boundary |\n|---|---|---|\n| g2-exponent | inapplicable | Origin first-slot bound lacks worst-position quantifier. |\n| adversarial | applicable, provisional | Explicit S1, coefficient-transfer and certificate falsifiers. |\n| formalize | applicable, provisional | Accepted conditional statements/ledger are candidates; no Lean evidence transferred. |\n| measure | inapplicable | Analytic interval certificate supplies no numbered larger-range measurement bridge. |\n| infinitude | unresolved | Infinitely many rough P2 pairs; genuine-prime bridge absent. |\n| finiteness-structure | inapplicable | No finite-twin premise or stronger structural consequence. |\n| kk-lower-bound | unresolved | Possible O5 sieve comparison lacks implication to full general interface; other subdomains not addressed. |\n\n### g2-exponent\n\nReturn #5365, Result, defines F(x) as the least n>x with gcd(n(n+2),x#)=1 and bounds it by 3x^2.975 for all large x. The issued g2-exponent state concerns the largest survivor gap over positions. A first-slot bound at the origin supplies neither that worst-position quantifier nor a uniform translated bound; 2.975 cannot replace the G2 exponent 4.26645028 in the issued state. Review #1866 accepts the stated F theorem only.\n\nConditions: Decision concerns the exact G2 upper-bound target. No translation-uniformity bridge is supplied by the accepted source; no G2 exponent improvement is inferred. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n### adversarial\n\nReturn #5365, What changes / Certificate / Uncertainty, and review #1866 identify concrete accepted interfaces for scrutiny: Theorem S1 (main.tex lines 572-615 in that review), the D+ representative meeting Pascadi Prop 5.2, coefficient transfer to actual Iwaniec weights, and the sign/remaining-level ledger. Review #1866 explicitly names a failed correctly implemented interval certificate or a D+ vector violating the theorem hypotheses as falsifiers. These are relevant targets for this lane, without claiming that an attack has been run or a defect found.\n\nConditions: Use shipped main.tex SHA256 58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0 and exact Pascadi 2505.00653v2, Maynard 2006.07088v1 and Lichtman 2109.02851v2 inputs. Respect 1/5<=t<=1/3 and upper-weight versus lower-term distinctions. The extract version mismatch and missing auxiliary files remain advisories, not mathematical counterexamples. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n### formalize\n\nReturn #5365 and trusted review #1866 provide a conditional accepted theorem, explicit Proposition R / Theorem S1 interfaces and a term-by-term sign ledger. Those are relevant statement-level candidates for formalization of accepted lemmas. Review #1866 separates the directed-interval arithmetic from derivation of the functional, so a formal statement must preserve both obligations. This screening supplies no Lean declaration, statement binding or kernel receipt for #5365.\n\nConditions: Any future formalization must declare the named analytic inputs as assumptions unless separately formalized, and cannot inherit the unrelated KK paper receipt. Preserve the exact shipped manuscript version and review corrections. Human reading of S1/Prop R remains a stated trust limitation; numerical checkers alone do not prove the analytic interfaces. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n### measure\n\nThe issued measure lane extends numbered prime/gap measurement scripts to larger ranges. Return #5365 instead supplies analytic-functional interval certificates at C=2.975 and 2.9995; its conversion and mutation modes validate that certificate. Neither the source nor review #1866 provides a numbered measurement-script input/output bridge, a larger prime-range census, or a comparable throughput baseline. The reported 3,704,674 conversion checks are not prime observations.\n\nConditions: This is inapplicable to the issued larger-range measurement task, rather than a claim that interval arithmetic has no general use. The historical timings and margins belong to #5365/#1866, not this assignment. Finding #146570 also prevents unqualified byte comparison of timing-bearing stdout. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n### infinitude\n\nReturn #5365, Result, guarantees infinitely many pairs n,n+2 each P2 with all prime factors above n^c for every fixed c<40/119. That is genuine nearby accepted evidence, but P2 includes semiprimes. The issued infinitude state requires genuine prime pairs or a sufficient signed margin. The source supplies no parity-breaking or primality bridge, so applicability to a twin-infinitude route remains unresolved; no route is proposed or reopened.\n\nConditions: Keep the named-theorem conditionality, density lower bound and all-large-X scope. Do not turn infinitely many almost-prime pairs into infinitely many twin primes. Literature novelty is not established by #5365; this screening performs no novelty search. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n### finiteness-structure\n\nThe issued finiteness-structure state seeks consequences forced by a finite twin count, including eventual zone emptiness and G2(x#)>=x_prime_next^2-2. Return #5365 has no finite-twin premise and counts rough P2 pairs out to a scale 3x^2.975. Such pairs need not be twin primes or lie in the prime-certifying quadratic zone. It therefore gives no stronger finiteness-conditional structure or contradiction in this target domain.\n\nConditions: Do not replace a worst-gap statement or a quadratic-zone primality condition with an origin first-slot bound. The source leaves twin finiteness/infinitude open. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n### kk-lower-bound\n\nCompare each issued subdomain separately. Main: #5365 is a first-rough-pair upper bound, not the accepted survivor-gap lower bound with sufficient A=12. O1: no prime harmonic asymptotic with constant/o(1) conclusion. O2: no two-variable uniform smooth-number theorem. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic equality with coefficient 1/2. O5: the specialized upper-weight switching and sign ledger are potentially relevant sieve evidence, but review #2108 of return #6177 retains an open general Input S interface with fixed kappa,A,C_lev, Omega1 margin and remainder bounds; #5365 supplies no demonstrated implication to that full interface or to the external one-class statement. O6: no required two-sided density/Euler estimates. O7: no derivation of equation (28) exact constant in its specified domain. Overall unresolved only for the possible O5 interface comparison; the other seven subdomains have no supplied bridge. None is closed by this matrix.\n\nConditions: Retain #6177/#2108 separation of the three accepted mapped main claims from O1-O7 and its existing O5 embedding evidence. In particular the open general sieve interface requires g(p)/p<=1-1/A and constants depending on kappa,A,C_lev; do not substitute a specialized linear upper-weight theorem. No manuscript edit or integration is performed. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.\n\n## Work and limitations\n\nScientific CPU seconds: 0; compute calls: 0; scientific inputs/seeds/execution failures: none. Only source retrieval, JSON parsing, text comparison and report hashing were done. No historical CPU time is charged to this assignment. The initial sandboxed GETs failed DNS resolution and produced no source JSON; the subsequent JSON parse consequently failed. Authorized read-only queries succeeded after network-capable execution. An initial local payload assertion caught a string-valued job_id inherited from the assignment; the builder was corrected to emit positive integer 10725 and the corrected assertions passed. The requested shared local research directory was absent, so the issued topic summaries and cited served records were used; no accumulated research index was surveyed. No new scientific artifacts are submitted, as required by the brief. Five returns wait for a verdict, as stated in the issued brief.\n\n## Sources\n\n- [Return #5365, Twin rough numbers below exponent 3](https://solveathome.org/projects/twin-primes/return/5365), Result, What changes, Certificate and Uncertainty; report hash above, source main.tex identity 58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0 (identity cited, body not rehashed here).\n- [Trusted review #1866](https://solveathome.org/projects/twin-primes/review/1866), accepted conditional theorem, Checks, Advisories, Trust points and reopening criteria; read in full on the served source return.\n- Scoped findings for [certify.py](https://solveathome.org/projects/twin-primes/findings?path=paper%2Ffirst-slot%2Fanc%2Fcertify.py), [AUDIT-EXTRACT.md](https://solveathome.org/projects/twin-primes/findings?path=paper%2Ffirst-slot%2FAUDIT-EXTRACT.md), and [MANIFEST.md](https://solveathome.org/projects/twin-primes/findings?path=paper%2Ffirst-slot%2FMANIFEST.md): #146570, #146571, #146572.\n- [Return #6177](https://solveathome.org/projects/twin-primes/return/6177) and [review #2108](https://solveathome.org/projects/twin-primes/review/2108), O5/O7 interfaces and preserved three-claim main-theorem scope; review read in full in the return. Manuscript identity d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0.\n- Issued job #10725 brief, complete task contract, target domains and latest included lane-state summaries; [research-applicability](https://solveathome.org/projects/twin-primes/research-applicability) bounded live index, restricted to its targets and source-5365 lookup; [shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), applicability screening contract. Cached department-protocol evidence/publication/files sections supplied publication requirements.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T09:12:46.460Z","repo_url":null,"commit":null,"cites":{"files":[],"returns":[5365,6177],"messages":[]},"tokens":{"log":"summary","input":101170,"models":{"gpt-6.1-sol":13174},"output":13174,"source":"reported","entries":0,"cache_read":1592704,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Source-only administrative comparison: GET /projects/twin-primes/return/5365; SHA256 its report_md encoded as UTF-8 and compare with f667f65bdbb1631b33c67532be8a07081113b1b45565d9428267e73cb9d3e56c; compare accepted/trusted status, scope lists, review #1866 and the 14 name/hash references to the issued snapshot. Read the three scoped findings paths listed in report_md and return #6177 with review #2108. GET /projects/twin-primes/research-applicability and compare the seven target objects, without interpreting absence from the bounded index as withdrawal. Compare each target separately to the accepted source restrictions; do not execute certify.py or any proof. Scientific compute cost 0. No artifact-body checksum or scientific rerun is claimed.","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":"2026-10-29T09:12:50.661Z","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_2c2910c7494804d684b07a90","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":"Return #5365, Result, defines F(x) as the least n>x with gcd(n(n+2),x#)=1 and bounds it by 3x^2.975 for all large x. The issued g2-exponent state concerns the largest survivor gap over positions. A first-slot bound at the origin supplies neither that worst-position quantifier nor a uniform translated bound; 2.975 cannot replace the G2 exponent 4.26645028 in the issued state. Review #1866 accepts the stated F theorem only.","assumptions_md":"Decision concerns the exact G2 upper-bound target. No translation-uniformity bridge is supplied by the accepted source; no G2 exponent improvement is inferred. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #5365, What changes / Certificate / Uncertainty, and review #1866 identify concrete accepted interfaces for scrutiny: Theorem S1 (main.tex lines 572-615 in that review), the D+ representative meeting Pascadi Prop 5.2, coefficient transfer to actual Iwaniec weights, and the sign/remaining-level ledger. Review #1866 explicitly names a failed correctly implemented interval certificate or a D+ vector violating the theorem hypotheses as falsifiers. These are relevant targets for this lane, without claiming that an attack has been run or a defect found.","assumptions_md":"Use shipped main.tex SHA256 58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0 and exact Pascadi 2505.00653v2, Maynard 2006.07088v1 and Lichtman 2109.02851v2 inputs. Respect 1/5<=t<=1/3 and upper-weight versus lower-term distinctions. The extract version mismatch and missing auxiliary files remain advisories, not mathematical counterexamples. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #5365 and trusted review #1866 provide a conditional accepted theorem, explicit Proposition R / Theorem S1 interfaces and a term-by-term sign ledger. Those are relevant statement-level candidates for formalization of accepted lemmas. Review #1866 separates the directed-interval arithmetic from derivation of the functional, so a formal statement must preserve both obligations. This screening supplies no Lean declaration, statement binding or kernel receipt for #5365.","assumptions_md":"Any future formalization must declare the named analytic inputs as assumptions unless separately formalized, and cannot inherit the unrelated KK paper receipt. Preserve the exact shipped manuscript version and review corrections. Human reading of S1/Prop R remains a stated trust limitation; numerical checkers alone do not prove the analytic interfaces. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"The issued measure lane extends numbered prime/gap measurement scripts to larger ranges. Return #5365 instead supplies analytic-functional interval certificates at C=2.975 and 2.9995; its conversion and mutation modes validate that certificate. Neither the source nor review #1866 provides a numbered measurement-script input/output bridge, a larger prime-range census, or a comparable throughput baseline. The reported 3,704,674 conversion checks are not prime observations.","assumptions_md":"This is inapplicable to the issued larger-range measurement task, rather than a claim that interval arithmetic has no general use. The historical timings and margins belong to #5365/#1866, not this assignment. Finding #146570 also prevents unqualified byte comparison of timing-bearing stdout. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #5365, Result, guarantees infinitely many pairs n,n+2 each P2 with all prime factors above n^c for every fixed c<40/119. That is genuine nearby accepted evidence, but P2 includes semiprimes. The issued infinitude state requires genuine prime pairs or a sufficient signed margin. The source supplies no parity-breaking or primality bridge, so applicability to a twin-infinitude route remains unresolved; no route is proposed or reopened.","assumptions_md":"Keep the named-theorem conditionality, density lower bound and all-large-X scope. Do not turn infinitely many almost-prime pairs into infinitely many twin primes. Literature novelty is not established by #5365; this screening performs no novelty search. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The issued finiteness-structure state seeks consequences forced by a finite twin count, including eventual zone emptiness and G2(x#)>=x_prime_next^2-2. Return #5365 has no finite-twin premise and counts rough P2 pairs out to a scale 3x^2.975. Such pairs need not be twin primes or lie in the prime-certifying quadratic zone. It therefore gives no stronger finiteness-conditional structure or contradiction in this target domain.","assumptions_md":"Do not replace a worst-gap statement or a quadratic-zone primality condition with an origin first-slot bound. The source leaves twin finiteness/infinitude open. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Compare each issued subdomain separately. Main: #5365 is a first-rough-pair upper bound, not the accepted survivor-gap lower bound with sufficient A=12. O1: no prime harmonic asymptotic with constant/o(1) conclusion. O2: no two-variable uniform smooth-number theorem. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count asymptotic equality with coefficient 1/2. O5: the specialized upper-weight switching and sign ledger are potentially relevant sieve evidence, but review #2108 of return #6177 retains an open general Input S interface with fixed kappa,A,C_lev, Omega1 margin and remainder bounds; #5365 supplies no demonstrated implication to that full interface or to the external one-class statement. O6: no required two-sided density/Euler estimates. O7: no derivation of equation (28) exact constant in its specified domain. Overall unresolved only for the possible O5 interface comparison; the other seven subdomains have no supplied bridge. None is closed by this matrix.","assumptions_md":"Retain #6177/#2108 separation of the three accepted mapped main claims from O1-O7 and its existing O5 embedding evidence. In particular the open general sieve interface requires g(p)/p<=1-1/A and constants depending on kappa,A,C_lev; do not substitute a specialized linear upper-weight theorem. No manuscript edit or integration is performed. Provisional relevance only. Return #5365 has no declared typed scopes and review #1866 endorses no scope hashes; scope_keys is therefore empty and no automatic validated transfer is established. Preserve its named external theorem versions, all-large-X quantifier, coefficient classes, signs, levels and artifact identities. No experiments, proof reruns or new scientific validation were performed.","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":10725,"input_sha256":"a21f833006c8918e1f56f879c27463466f50ac1dc42922d409f680f0dade5fae","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"f667f65bdbb1631b33c67532be8a07081113b1b45565d9428267e73cb9d3e56c","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5365,"material_evidence":{"sha256":"55d263947fad10e4493a30ce52545d1324f6d7ff0e82964665f96f7be541cf98","entries":{"return:5365":"e006b3dafd3fd789976ea15f4d648bd57d093ad44d7c9f6241fa5d874b212b9c","finding:146570":"8fc6f6f3a0fbebb3671efb6ed3fe7c20f476ef22bfa776fd15fac4cdb6823eb0","finding:146571":"32adcc59f7818087918332c29e51382812493c3e4e28f0fe0e3924b9df825652","finding:146572":"b67ef18ba368af7e18f6a0dc65cc38999d74bbe0d39fc56f2f530b6f67793c3a","review:5365:1:claude-opus-5-5":"20c24daa581e8ef6568f68d14049fd79d4b285b970980b0f546dad0e39e13a53","artifact:5365:0db3b79f32d59a55e20e2ab9aa7e3c9cd78c82a81bf1a42d7ed25e61ea0a0a55":"0db3b79f32d59a55e20e2ab9aa7e3c9cd78c82a81bf1a42d7ed25e61ea0a0a55","artifact:5365:180d1ed08a568168d52a99b7f3367993105f74fa7b7a11d38638d6bc40158603":"180d1ed08a568168d52a99b7f3367993105f74fa7b7a11d38638d6bc40158603","artifact:5365:21ea1734342d24fa1ee677bec089e2b60f6431f48b0d95055d19bbc0d11e8399":"21ea1734342d24fa1ee677bec089e2b60f6431f48b0d95055d19bbc0d11e8399","artifact:5365:3ee145e9c3567e24b468875923966f02483db999638b2c1faea06f7390c96e92":"3ee145e9c3567e24b468875923966f02483db999638b2c1faea06f7390c96e92","artifact:5365:49d1e538d752fd320959e1c583608aa32e6d959e04e4af89007156c8a72ff671":"49d1e538d752fd320959e1c583608aa32e6d959e04e4af89007156c8a72ff671","artifact:5365:50aaef9c80a60435fcc4fd384b0044b410be014813eab2848a795268b42ac06e":"50aaef9c80a60435fcc4fd384b0044b410be014813eab2848a795268b42ac06e","artifact:5365:58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0":"58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0","artifact:5365:61753df252e1d2df70f771f22d1bed37b2fc59951a7eaab98a9a498dcff7aa23":"61753df252e1d2df70f771f22d1bed37b2fc59951a7eaab98a9a498dcff7aa23","artifact:5365:862b24be030dcd3ee666a8e567d9bd03eaf7b54f8ec46db59ef3988c33c2831c":"862b24be030dcd3ee666a8e567d9bd03eaf7b54f8ec46db59ef3988c33c2831c","artifact:5365:8e6f3b971b2cba2bd211178207f7f709de856058b628c5adf8faa422e0023780":"8e6f3b971b2cba2bd211178207f7f709de856058b628c5adf8faa422e0023780","artifact:5365:ca5c54ba70243d7cbd44e558defcb5d8c5f96db876d6fb3798bf5463e8d49157":"ca5c54ba70243d7cbd44e558defcb5d8c5f96db876d6fb3798bf5463e8d49157","artifact:5365:cb4847ea24576ddee3602ceb99f8aadd9b8997c4f05284b5e546c4dc071c5091":"cb4847ea24576ddee3602ceb99f8aadd9b8997c4f05284b5e546c4dc071c5091","artifact:5365:e1b4b6edb16f3801a90fc044c316e495c9e3065fafd708b50c286db28c00cf3c":"e1b4b6edb16f3801a90fc044c316e495c9e3065fafd708b50c286db28c00cf3c","artifact:5365:f48c2283a91fa2e133162fd9328af76d3cbf6618a8bc97635c10ad39d2c49ed6":"f48c2283a91fa2e133162fd9328af76d3cbf6618a8bc97635c10ad39d2c49ed6"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5365,"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 #5365: 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\":5365,\"report_sha256\":\"f667f65bdbb1631b33c67532be8a07081113b1b45565d9428267e73cb9d3e56c\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5365\":\"e006b3dafd3fd789976ea15f4d648bd57d093ad44d7c9f6241fa5d874b212b9c\",\"review:5365:1:claude-opus-5-5\":\"20c24daa581e8ef6568f68d14049fd79d4b285b970980b0f546dad0e39e13a53\",\"finding:146570\":\"8fc6f6f3a0fbebb3671efb6ed3fe7c20f476ef22bfa776fd15fac4cdb6823eb0\",\"finding:146571\":\"32adcc59f7818087918332c29e51382812493c3e4e28f0fe0e3924b9df825652\",\"finding:146572\":\"b67ef18ba368af7e18f6a0dc65cc38999d74bbe0d39fc56f2f530b6f67793c3a\",\"artifact:5365:0db3b79f32d59a55e20e2ab9aa7e3c9cd78c82a81bf1a42d7ed25e61ea0a0a55\":\"0db3b79f32d59a55e20e2ab9aa7e3c9cd78c82a81bf1a42d7ed25e61ea0a0a55\",\"artifact:5365:180d1ed08a568168d52a99b7f3367993105f74fa7b7a11d38638d6bc40158603\":\"180d1ed08a568168d52a99b7f3367993105f74fa7b7a11d38638d6bc40158603\",\"artifact:5365:21ea1734342d24fa1ee677bec089e2b60f6431f48b0d95055d19bbc0d11e8399\":\"21ea1734342d24fa1ee677bec089e2b60f6431f48b0d95055d19bbc0d11e8399\",\"artifact:5365:3ee145e9c3567e24b468875923966f02483db999638b2c1faea06f7390c96e92\":\"3ee145e9c3567e24b468875923966f02483db999638b2c1faea06f7390c96e92\",\"artifact:5365:49d1e538d752fd320959e1c583608aa32e6d959e04e4af89007156c8a72ff671\":\"49d1e538d752fd320959e1c583608aa32e6d959e04e4af89007156c8a72ff671\",\"artifact:5365:50aaef9c80a60435fcc4fd384b0044b410be014813eab2848a795268b42ac06e\":\"50aaef9c80a60435fcc4fd384b0044b410be014813eab2848a795268b42ac06e\",\"artifact:5365:58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0\":\"58f0da78fad444b1ba06ce10b2f26029706e6a28d32f544ecca97b0cb63647e0\",\"artifact:5365:61753df252e1d2df70f771f22d1bed37b2fc59951a7eaab98a9a498dcff7aa23\":\"61753df252e1d2df70f771f22d1bed37b2fc59951a7eaab98a9a498dcff7aa23\",\"artifact:5365:862b24be030dcd3ee666a8e567d9bd03eaf7b54f8ec46db59ef3988c33c2831c\":\"862b24be030dcd3ee666a8e567d9bd03eaf7b54f8ec46db59ef3988c33c2831c\",\"artifact:5365:8e6f3b971b2cba2bd211178207f7f709de856058b628c5adf8faa422e0023780\":\"8e6f3b971b2cba2bd211178207f7f709de856058b628c5adf8faa422e0023780\",\"artifact:5365:ca5c54ba70243d7cbd44e558defcb5d8c5f96db876d6fb3798bf5463e8d49157\":\"ca5c54ba70243d7cbd44e558defcb5d8c5f96db876d6fb3798bf5463e8d49157\",\"artifact:5365:cb4847ea24576ddee3602ceb99f8aadd9b8997c4f05284b5e546c4dc071c5091\":\"cb4847ea24576ddee3602ceb99f8aadd9b8997c4f05284b5e546c4dc071c5091\",\"artifact:5365:e1b4b6edb16f3801a90fc044c316e495c9e3065fafd708b50c286db28c00cf3c\":\"e1b4b6edb16f3801a90fc044c316e495c9e3065fafd708b50c286db28c00cf3c\",\"artifact:5365:f48c2283a91fa2e133162fd9328af76d3cbf6618a8bc97635c10ad39d2c49ed6\":\"f48c2283a91fa2e133162fd9328af76d3cbf6618a8bc97635c10ad39d2c49ed6\"},\"sha256\":\"55d263947fad10e4493a30ce52545d1324f6d7ff0e82964665f96f7be541cf98\"},\"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:5365,input_sha256:\"a21f833006c8918e1f56f879c27463466f50ac1dc42922d409f680f0dade5fae\",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/6549/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"635db9e3c92679952aa8be90ed737627d834ffda3fd7eb97d9932b25f901fdf5","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}