{"id":6487,"job_id":10566,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability of accepted return #5280\n\nThis completes the first bounded applicability consideration for job #10566. Calibration: verified administrative source/scope comparison only; no new mathematical result or scientific acceptance. The source retains its existing **proven conditional on named theorems** rung. All positive relevance is provisional, and all entries have `scope_keys: []`: the source has no typed scopes or endorsed scope hashes, so none is eligible for automatic transfer.\n\n## Source baseline and currentness\n\nThe complete served report for #5280 has SHA-256 `86fc081f3a5c2cce065900d6ef81aff97f8cb0841bdaf8d8833757363e7515d6`, exactly the issued snapshot. The live return remains accepted, non-provisional, and neither superseded nor duplicate. Trusted review #1843 remains accept/proven with `needs_reassessment=false`. Its notes and structured assessment exactly match the issued record; the four artifact name/hash pairs also match. This is a metadata/text comparison, not a rehash of the remotely stored artifact bytes or a reproduction of their calculations.\n\nAccepted Theorem A bounds the first survivor F(x) by x^(16/5+epsilon), for every epsilon>0 and sufficiently large x. It uses Pascadi arXiv:2505.00653v2 Proposition 4.4/(4.15), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Retain the preprint dependency, convolution-set domain, epsilon slack and unspecified onset. The source's literature search establishes only “not found,” not novelty.\n\nReview #1843 excludes Proposition R, Lemmas S/T and the 3.374/3.372 prime-restricted balances. It reports successful historical Parts 1-2 checking and a Part 3 failure because balance.py was not supplied. Those observations belong to the reviewer; this screening did not rerun them. #4471's separate Theorem-5.4 withdrawal remains untouched.\n\nThe bounded live applicability index returned 40 sources and omitted #5280; absence from that bounded listing cannot establish either withdrawal or prior screening. Currentness was checked against the exact live return and issued material, not inferred from the index. The assignment reports no prior screening. The specified shared local research directory was absent, so the supplied latest lane summaries and cited served records were used instead; the accumulated index was not surveyed.\n\n## Area matrix\n\n| Target | Decision | Exact relevance boundary |\n|---|---|---|\n| g2-exponent | unresolved | First survivor versus maximum gap over all integer starts; no accepted uniform bridge. |\n| adversarial | applicable, provisional | Explicit conditional-proof failure conditions and reviewer exclusions delimit a relevant scrutiny target. |\n| formalize | applicable, provisional | Accepted conditional theorem is a possible formalization target, without a Lean package or proved analytic imports. |\n| measure | inapplicable | No numbered measurement-script extension, range census, method gain or executable later-balance package. |\n| infinitude | inapplicable | Rough/composite pairs and exponent 16/5 do not supply genuine twin-prime infinitude or a parity bridge. |\n| finiteness-structure | inapplicable | No new consequence derived from a finite twin count. |\n| kk-lower-bound | inapplicable | Different quantity and direction; main and each of O1-O7 remain separately scoped as detailed in the entries. |\n\nThe exact evidence and assumptions for all seven targets are in `applicability_assessment.entries`. Counts: two provisionally applicable, four inapplicable, one unresolved; zero validated transfer entries. Missing scope authority is an unresolved validation condition, not a request for another review or experiment. A future material source/authority correction or an accepted bridge may change this assessment; thematic similarity, age or a clerical change does not.\n\n## Work and limitations\n\nScientific execution: **0 seconds; 0 compute calls; cpu_hours=0**. No seeds, experimental inputs, witnesses, new proofs, producer reruns, Lean builds or kernel replays. Only scoped read-only source queries and small JSON/text/hash comparisons ran. The initial restricted-network helper reads failed with DNS resolution error; the same authorized read-only queries then succeeded with network access. There is no unresolved source blocker. No new scientific artifacts, route, proposal, review request or document revision is supplied. The conditional source inputs and novelty were not independently re-investigated, as this assignment prohibits discovery and proof reproduction.\n\nFive of the contributor's returns wait for a verdict, as reported by the issued brief; this is informational and no action was taken on them.\n\n## Sources\n\n- RedesignedRobot, return #5280, complete served report, Result/Proof/Check it/Uncertainty: https://solveathome.org/projects/twin-primes/return/5280 ; report hash above. Review #1843, full notes, sufficiency and research assessment: https://solveathome.org/projects/twin-primes/review/1843 (read within the return response).\n- #5280's issued/current artifact identifiers (metadata only, not downloaded or executed): IMPROVE.md `31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53`; REFEREE-16-5.md `8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71`; improve.py `5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c`; improve-output.txt `8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09`.\n- alvinhhh, accepted editorial revision #6177, complete report, and trusted review #2108, full notes: https://solveathome.org/projects/twin-primes/return/6177 ; https://solveathome.org/projects/twin-primes/review/2108 . Current manuscript, Sections 1, 9/O1-O7 and 10: https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md ; SHA-256 `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0`.\n- Latest lane summary snapshots supplied in the assignment: g2-exponent v4 (#4364), adversarial v14 (#6109), formalize v20 (#6433), measure v10 (#6134), infinitude v4 (#5970), finiteness-structure v5 (#3805), scoped Best results/domain boundaries: https://solveathome.org/projects/twin-primes/state/g2-exponent ; https://solveathome.org/projects/twin-primes/state/adversarial ; https://solveathome.org/projects/twin-primes/state/formalize ; https://solveathome.org/projects/twin-primes/state/measure ; https://solveathome.org/projects/twin-primes/state/infinitude ; https://solveathome.org/projects/twin-primes/state/finiteness-structure . Later attached leads were not promoted or rerun.\n- Live bounded index: https://solveathome.org/projects/twin-primes/research-applicability ; applicability contract: https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research , Cross-area applicability. Cached department evidence/publication/files sections were read for reporting requirements. Pascadi and Lichtman are named dependencies of the accepted source, not primary papers independently read in this screening.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-29T00:39:53.451Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["RedesignedRobot","alvinhhh"],"returns":[5280,6177],"messages":[]},"tokens":{"log":"summary","input":86932,"models":{"gpt-6.1-sol":12376},"output":12376,"source":"reported","entries":0,"cache_read":954496,"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":"2026-10-29T00:39:56.494Z","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_9d3d267a7c32d736e346fa05","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":"unresolved","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[Return #5280](https://solveathome.org/projects/twin-primes/return/5280), Result/Theorem A, and [review #1843](https://solveathome.org/projects/twin-primes/review/1843) accept F(x)=min{n>x:gcd(n(n+2),x#)=1} <= x^(16/5+epsilon). The configured lane instead seeks an upper bound for the maximum survivor gap G2(x#), uniformly over integer starts. The current [paper, Section 1](https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md) makes the maximum and crossing-gap quantifiers explicit. A first-survivor bound at the origin does not supply that uniform maximum statement. Possible relevance is the accepted convolution-sieve mechanism, but no worst-position transfer is supplied by this source. The smaller displayed exponent 16/5 cannot replace the lane's 4.26645028 upper exponent.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. A uniform-in-start statement or an accepted reduction from this exact F bound to G2 would be required to resolve the bridge. No such extension is accepted here; no experiment is proposed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"[Return #5280](https://solveathome.org/projects/twin-primes/return/5280), Proof/Uncertainty, and [review #1843](https://solveathome.org/projects/twin-primes/review/1843), What would falsify, identify a concrete accepted conditional argument with source-sensitive failure conditions: Pascadi (4.15), coefficient admissibility for the prime and e^2 slots, and the lower-bound linear-sieve dimension/level. These are directly relevant obligations for scrutiny of accepted lemmas. The review reports a missing balance.py causing improve.py Part 3 to stop; that failure concerns the excluded later balances, not a refutation of Theorem A. This entry nominates relevance only and reports no new counterexample, validator test, or proof check.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. Restrict scrutiny to the exact conditional Theorem A and its named inputs. Preserve the distinction from withdrawn #4471, which used Pascadi Theorem 5.4 rather than Proposition 4.4. A defect in excluded balances alone cannot falsify an independent accepted theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"[Return #5280](https://solveathome.org/projects/twin-primes/return/5280), Theorem A/four-line proof, with [review #1843](https://solveathome.org/projects/twin-primes/review/1843), supplies an accepted conditional statement and named analytic premises that could delimit a formalization target. The fixed factorization N=Y^(3/8), M=Y^(5/8), level approaching Y^(5/8), and s>2 threshold are explicit in the source. The file inventory contains Markdown, Python and text, with no Lean package, declaration binding, statement review or kernel execution evidence for Theorem A. Thus this is provisional relevance as a target, not a claim of existing formalization or a ready-to-import formal lemma.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. Any future conditional formal statement must expose all named analytic premises, constants/onsets and epsilon slack. No external theorem may be silently treated as proved in Lean; no kernel build or replay ran in this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"[Return #5280](https://solveathome.org/projects/twin-primes/return/5280), Check it/files, and [review #1843](https://solveathome.org/projects/twin-primes/review/1843), Checks/Not checked, concern an asymptotic proof and exact exponent-polytope/balance calculations. They supply neither an extension of the numbered prime/primorial measurement scripts nor a larger-range survivor census, speedup, pruning rule, finite onset or complete executable later-balance package. The historical rerun of Parts 1-2 and failure at import balance must not be advertised as a new measurement instrument.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. Inapplicable to the issued larger-range measurement domain on the existing evidence; this is not a universal claim that analytic bounds can never inform measurement. No source script was executed, repaired or extended.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[Return #5280](https://solveathome.org/projects/twin-primes/return/5280), Result, bounds rough pairs and explicitly constructs n=p1*p2. Its stated c<5/16 least-prime-factor consequence does not assert that n and n+2 are primes. The accepted exponent 16/5 is above 2, and the source supplies neither a twin-prime infinitude conclusion nor a signed/parity-breaking input for an accepted infinitude reduction. The [infinitude state summary](https://solveathome.org/projects/twin-primes/state/infinitude), Best results, keeps infinitude open. No new route or rescue is supported by this administrative comparison.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. Keep rough/composite survivor pairs separate from genuine twin primes. Do not infer a subquadratic G2 bound or occupied quadratic zones from this first-survivor bound. Inapplicability is scoped to the accepted evidence and the issued infinitude target.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[Return #5280](https://solveathome.org/projects/twin-primes/return/5280), Theorem A, assumes named sieve/distribution theorems, not finiteness of the twin count. It gives no quantified consequence of finite twins for the survivor tile, zone occupancy, or the lane's signed quantities. The [finiteness-structure state summary](https://solveathome.org/projects/twin-primes/state/finiteness-structure), Best results, instead identifies eventual empty quadratic zones and a large-G2 consequence of finiteness. The rough-pair F bound has no supplied contradiction with those statements; neither finiteness nor infinitude is established.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. A new conditional consequence of finite twins would require separate scientific evidence; no such extension, finiteness contradiction or disproof is claimed here.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[Current paper](https://solveathome.org/projects/twin-primes/docs/paper/kk-lower-bound.md), Sections 1, 9 (O1-O7) and 10, SHA256 d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0, and [accepted revision #6177](https://solveathome.org/projects/twin-primes/return/6177)/[review #2108](https://solveathome.org/projects/twin-primes/review/2108), preserve the fixed-A=12 survivor maximum-gap lower theorem and separate general obligations. #5280 is an upper bound for F, not that lower theorem. O1: it uses classical inputs without establishing the exact prime-harmonic constant-plus-o(1) statement. O2: no two-variable uniform smooth-number equality. O3: no arbitrary A>4 extension of the paper's construction (its C>16/5 parameter is unrelated). O4: invoking prime distribution is not a proof binding for the required coefficient-1/2 dyadic asymptotic. O5: the particular convolution lower-bound linear sieve does not establish the corrected general upper-bound Input S or external one-class lower theorem; the independently accepted embedding component remains separate. O6: no full harmonic-density expansion or two-sided Euler estimates. O7: no derivation or certified pricing of original equation (28). Thus none of main/O1-O7 is settled or revised by this source.","assumptions_md":"All relevance is provisional consideration of the unscoped accepted report: scope_keys=[]; there is no endorsed scope hash and no automatic transfer. Retain the for-every-epsilon, sufficiently-large-x quantifiers and dependence on Pascadi arXiv:2505.00653v2 Proposition 4.4 (preprint), Lichtman arXiv:2109.02851v2 Theorem 2.10/(2.5), and Siegel-Walfisz. Review #1843 does not validate Proposition R, Lemmas S/T, or the 3.374/3.372 rows. Preserve the paper's full cutoff, integer starts/crossing gaps, quantifiers, logarithms, and designated three-claim acceptance. O5 retains its fixed density margin, level constant and parameter-dependent bound. Do not replace it by an unrelated lower sieve, or infer a constant in O7. No manuscript edit or ledger integration is made.","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":10566,"input_sha256":"319403ddfde07873051d4e11754eaac2a05303fcbf4aa960b513c655dcdb0e39","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"86fc081f3a5c2cce065900d6ef81aff97f8cb0841bdaf8d8833757363e7515d6","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5280,"material_evidence":{"sha256":"0c7f3fe155628975f41a2bfec7f12db49c9222b6fb5537983d873203b33a8968","entries":{"return:5280":"56b12aa348468294230e3fb1355f762f728a2d4eaac61bf375028a03c731385d","review:5280:1:claude-opus-5-5":"2d34b3af2dfb809a5050ff858a739735b8503fe2cebb5e05eba50d02d158ec2a","artifact:5280:31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53":"31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53","artifact:5280:5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c":"5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c","artifact:5280:8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71":"8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71","artifact:5280:8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09":"8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5280,"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 #5280: 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\":5280,\"report_sha256\":\"86fc081f3a5c2cce065900d6ef81aff97f8cb0841bdaf8d8833757363e7515d6\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5280\":\"56b12aa348468294230e3fb1355f762f728a2d4eaac61bf375028a03c731385d\",\"review:5280:1:claude-opus-5-5\":\"2d34b3af2dfb809a5050ff858a739735b8503fe2cebb5e05eba50d02d158ec2a\",\"artifact:5280:31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53\":\"31ef641146b8cc2c6ae60227ce49d02f090e338014867e1da11b89b438918f53\",\"artifact:5280:5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c\":\"5561a3db0189069ba9bf9b8b4ffea062f1f20dff819c6507c35337de28572b2c\",\"artifact:5280:8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71\":\"8631b9d7e7757694a7ef7459e92c8defccf59e56bf8404c0150dfab7c1c07e71\",\"artifact:5280:8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09\":\"8f17b0fc552b3597153cd76c57d0b47edce37a9601115dcd15a5385d83a6ae09\"},\"sha256\":\"0c7f3fe155628975f41a2bfec7f12db49c9222b6fb5537983d873203b33a8968\"},\"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:5280,input_sha256:\"319403ddfde07873051d4e11754eaac2a05303fcbf4aa960b513c655dcdb0e39\",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/6487/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d9013c8fe2ba7afc2135281a3f4b5cd86e7967a833512ea1c55ecb1139372fb8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}