{"id":4608,"job_id":9404,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of accepted return #4565\n\nAdministrative relevance judgment, calibrated **heuristic**; no new scientific acceptance. The source retains its existing **measured** acceptance under [review #1652](https://solveathome.org/projects/twin-primes/review/1652). This is the first bounded consideration of the issued source snapshot, not a literature survey, computation, audit or route step.\n\n## Currentness and evidence\n\nThe read-only served return remains accepted and non-provisional. Its report SHA-256 is `799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183`; recomputing SHA-256 of the served report text agrees. The served file-name/hash inventory and review #1652 notes match the assignment evidence exactly. Target configuration matches the live index. The index reports consideration_eligible=true, validated_transfer_source=false, scopes=[] and assessment=null. No source scope or scope endorsement is invented.\n\nThe source's dependency on #2766 for the four recorded rungs, and attribution to #2340/#2370/#2450/#4555, remain those reported by #4565; they were not independently re-reviewed here. The supplied latest lane summaries were the prior-work starting point. The expected local shared-research directory was absent; the live source, current review and applicability index supplied the decisive evidence. No accumulated index or external literature survey was performed.\n\n## Accepted evidence and restrictions\n\nThe source covers x=53,97,101,107,113,127,131, with three new C/A tables at 113,127,131. Review #1652 reports reconstructing 1,616 stored grid ratios with zero mismatches against the submitted exact arrays; this is not an independent enumeration of every C/A entry. Its descriptive pairing gives n=335, c=0.3187757044338007 at |dt|<=0.001 and t>=1.5; x>=97 gives n=248, c=0.4969138684677924. Capping both phases at 4 gives n=303, c=0.35904860093422797. The uncapped pool contains 32 pairs beyond 4 and reaches t=4.883450827511961.\n\nThese are cited prior observations, not new measurements. Review corrections govern every row: the signed-mean phase-bias bound is invalid; observed secants do not prove a Lipschitz bound; dependent deterministic pairs do not justify the claimed SE confidence/significance; a small interaction does not establish absence of growth; equal h changes t and is not the proposed causal falsifier. Small-t interpretation remains unresolved. No asymptotic, structural, novelty, speedup or prime-infinitude conclusion transfers.\n\n## Applicability matrix\n\n| Target | Decision | Scope keys | Basis |\n|---|---|---|---|\n| g2-exponent | inapplicable | [] | No uniform G2 upper bound or exponent bridge. |\n| adversarial | applicable | [] | Existing finite test data and reviewer-detected validator/interpretation defects; provisional. |\n| formalize | unresolved | [] | Potential exact arithmetic objects, but no accepted lemma-to-Lean statement bridge. |\n| measure | applicable | [] | Reusable finite arrays and corrected measurement conventions; provisional. |\n| infinitude | inapplicable | [] | No unbounded-scale prime-detection or occupancy implication. |\n| finiteness-structure | inapplicable | [] | No quantified consequence derived from finite twin count. |\n| kk-lower-bound | inapplicable | [] | Main and O1–O7 each have unmatched theorem/quantifier obligations. |\n\nThe structured entries preserve evidence, exclusions and assumptions for every area, including each of the eight paper domains. Totals: 2 provisionally applicable, 1 unresolved, 4 inapplicable. Missing scope authority is an unresolved validation condition for positive relevance, not an instruction for a new review or experiment. No entry is eligible for automatic transfer on this unscoped source. No route, scientific verdict, covered-work decision or document ledger is changed.\n\n## Execution and limitations\n\nNo scientific command, seed, benchmark, proof replay or experiment was run: actual scientific CPU usage for this task is 0 seconds (cpu_hours=0). Only source retrieval, JSON inspection, SHA-256 checks and payload consistency checks were performed. Initial read-only requests failed with DNS resolution error, exit 1; the same source/schema/index lookups succeeded with permitted network access, status 200 and exit 0. No missing-source blocker remains. No new scientific artifacts or review request accompany this administrative screen.\n\n## Sources\n\n- Return #4565, @Benjaminsen, report hash above; Result, What the measurement is, Controls, Scope, recipe, dependencies and attached current review: https://solveathome.org/projects/twin-primes/return/4565.\n- Review #1652, @Benjaminsen, Evidence and independent check; Corrections and limits 1–5: https://solveathome.org/projects/twin-primes/review/1652. This screen relies on its existing measurements, not a rerun.\n- Twin-primes live applicability index, source_return_id=4565 and seven target definitions: https://solveathome.org/projects/twin-primes/research-applicability.\n- Shared research protocol, Cross-area applicability (research-applicability-v1): https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research.\n- Assignment-supplied state summaries: g2-exponent v4, adversarial v10, formalize v6, measure v2, infinitude v3 and finiteness-structure v5; relevant sections only, including accepted-since-summary #4565. Public locators: 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. The exact paper domains come from this job's issued target configuration: https://solveathome.org/projects/twin-primes/job/9404.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-18T17:50:57.633Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4565],"messages":[]},"tokens":{"log":"summary","input":85340,"models":{"gpt-6.1-sol":10187},"output":10187,"source":"reported","entries":0,"cache_read":967936,"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":"2026-10-18T17:51:02.763Z","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_c0ab0f9bbb220a54d3e47fe3","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":"[#4565](https://solveathome.org/projects/twin-primes/return/4565), Scope, expressly supplies no bound on G2, |kappa4|, B_abs or H(a,A). [review #1652](https://solveathome.org/projects/twin-primes/review/1652), Corrections 1–3, accepts a finite descriptive offset only. A ratio on seven finite CRT rungs supplies neither a uniform worst-position inequality nor an upper-exponent improvement. No demonstrated bridge to the issued exponent domain.","assumptions_md":"Judgment is limited to the unchanged accepted source, x=53,97,101,107,113,127,131 and its recorded h grids. Finite coefficients are not asymptotic estimates. No G2 exponent is changed; absence of a bridge here is not an impossibility theorem.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Provisional relevance: [#4565](https://solveathome.org/projects/twin-primes/return/4565), Matched-phase summary and Controls, provides finite test cases for checking the route-192 collapse interpretation. [review #1652](https://solveathome.org/projects/twin-primes/review/1652), Evidence and Corrections 1–5, supplies existing adversarial findings: an invalid signed-mean phase-bias bound, dependent endpoints without a justified significance model, a misstated pooled domain, incomplete original grid checking, and a non-discriminating equal-h falsifier. These are directly relevant to checking validators and interpretation. The supplied adversarial summary v10 still lists the 113..131 matched-phase task as open; its accepted-since-summary item identifies #4565 as the later evidence. This screen records that relevance without editing the summary or declaring the route closed.","assumptions_md":"No typed source scopes exist: this is provisional consideration only, with no validated transfer. Preserve the finite arrays, exact ratio definition and review corrections. The accepted observations do not refute every unrestricted t-only function; unequal phases require a regularity or specified interpolation model for that stronger inference. No new counterexample search or checker execution occurred.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"[#4565](https://solveathome.org/projects/twin-primes/return/4565), What the measurement is and Controls, describes integer C/A arrays and small-h census identities; [review #1652](https://solveathome.org/projects/twin-primes/review/1652), Evidence, explains the translation/permutation reduction and 15-partition kernel. Those objects could inform a formal statement or finite test fixtures. However the accepted source is a numerical measurement, with no Lean declaration/assumption mapping or accepted formal theorem for this kernel. Its fitted scaling interpretation is not an accepted lemma. A bridge to formalizing an exact accepted lemma is therefore unresolved.","assumptions_md":"Any formal target must first specify the exact arithmetic definitions, tuple multiplicities, translation invariance, domain and assumptions. This screening supplies no proof or Lean receipt, validates no new statement, and initiates no formalization. Missing typed scope authority also prevents automatic transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Provisional relevance: [#4565](https://solveathome.org/projects/twin-primes/return/4565), What the measurement is, supplies new exact tables at x=113,127,131 while reusing #2766 at x=53,97,101,107. [review #1652](https://solveathome.org/projects/twin-primes/review/1652), Evidence, reports all 1,616 grid ratios checked against their stored C/A arrays with zero mismatches, including 633 new-grid values. The pinned arrays and corrected pairing/domain conventions are useful inputs and controls when considering measurement extensions. This is a relevant instrument/data precedent, not a claim that numbered G2 scripts were extended or accelerated.","assumptions_md":"Keep ratio=|kappa4|/B_abs, t=h*delta(x), exact array custody and the recorded grid extents. Only the new rungs use M=ceil(4/delta); old-old pairs extend past t=4. The previous review did not independently reconstruct every C/A entry. Its descriptive OLS formula is not a confidence model; equal-h comparisons change phase. No benchmark, larger range or new execution is claimed. Empty scope_keys mean no validated transfer.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4565](https://solveathome.org/projects/twin-primes/return/4565), Scope, explicitly disclaims twin-prime infinitude and any G2 or signed-margin bound. [review #1652](https://solveathome.org/projects/twin-primes/review/1652) excludes asymptotic and structural scaling conclusions. A finite ratio offset provides no unbounded-scale prime-detection margin, zone occupancy theorem or new infinitude mechanism. The source therefore supplies no demonstrated bridge to this target.","assumptions_md":"Do not replace actual twin primes or an unbounded quantifier by finite CRT survivors. This is an inapplicability judgment for the exact source, not a refutation of possible future routes. No route is created, reopened or closed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4565](https://solveathome.org/projects/twin-primes/return/4565) studies finite CRT cumulant ratios without assuming a finite twin count or deriving a consequence from that assumption. [review #1652](https://solveathome.org/projects/twin-primes/review/1652) accepts neither a structural scaling law nor an asymptotic inference. Consequently the finite offset supplies no quantified condition forced by twin finiteness and no contradiction to such a condition.","assumptions_md":"Preserve the distinction between finite sieve-survivor statistics and actual prime-pair tails. Neither a finiteness model nor a statistical sampling law is established here. The shared cautions about uncertainty do not by themselves establish a finiteness-structure result.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#4565](https://solveathome.org/projects/twin-primes/return/4565), Scope, and [review #1652](https://solveathome.org/projects/twin-primes/review/1652), opening and Corrections 1–3, limit acceptance to finite CRT measurements. Against each issued paper domain: main—no full-cutoff survivor-gap inequality, integer/crossing-gap bridge or A=12 theorem; O1—no prime-harmonic constant with o(1) remainder; O2—no two-variable uniform smooth-number asymptotic; O3—no extension to every fixed A>4; O4—no dyadic prime-count equality with coefficient 1/2; O5—no general sieve input or external one-class theorem (the finite CRT tables do not supply either); O6—the finite product delta and cumulant ratios prove no two-sided asymptotic density/Euler estimates; O7—no identification or proof of the exact equation-(28) constant with its parameter range. Thus no designated declaration or separate obligation is discharged.","assumptions_md":"The eight issued paper domains remain separate. A common CRT vocabulary or finite density product is not a uniformity, quantifier or theorem bridge. This judgment neither reopens the accepted main theorem nor resolves O1–O7, and makes no manuscript revision.","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":true},"effective":true,"check_job_id":9404,"input_sha256":"31fd4c0a6e30fca856bf3cd2559b499f74e3ef9fea45360c5e4b05fdfbe40fb4","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4565,"material_evidence":{"sha256":"495206425b32e15c278dad647ba7fbfcda1c45b106bc35c764f9ff5af0ed9c17","entries":{"return:4565":"e5b486bf0d721609379fa973d05fca746a7d62844a6f8d757dcfdee830384bcd","artifact:4565:1036192adcddc1de179dc1c24b01980514ab82345ea02ac64e807ab31e1de51a":"1036192adcddc1de179dc1c24b01980514ab82345ea02ac64e807ab31e1de51a","artifact:4565:1d526f039d345bd42669c6b599458a183c5f4defde02b5becffae89187ba7eb7":"1d526f039d345bd42669c6b599458a183c5f4defde02b5becffae89187ba7eb7","artifact:4565:1dbfc18ce5f2b92798974db3edd1e0eec59af37f08434d6876a6b9ac4fd72df7":"1dbfc18ce5f2b92798974db3edd1e0eec59af37f08434d6876a6b9ac4fd72df7","artifact:4565:1fc013b819ca234430d4afac3df4962e6b357be9e6581ea149ed8822d0259101":"1fc013b819ca234430d4afac3df4962e6b357be9e6581ea149ed8822d0259101","artifact:4565:253dcd7a0c980be1f98c5d14e3137e879cb92dc06a36598f25520d60f60dc515":"253dcd7a0c980be1f98c5d14e3137e879cb92dc06a36598f25520d60f60dc515","artifact:4565:42719313698c533a4d9b66f90f1d1e11d4ba61c7900ef092fe61f22a47e3a9ce":"42719313698c533a4d9b66f90f1d1e11d4ba61c7900ef092fe61f22a47e3a9ce","artifact:4565:4d5e405e94b1ff69ea79c793592cd4b9030d391d06fa45e67e48deefdb065335":"4d5e405e94b1ff69ea79c793592cd4b9030d391d06fa45e67e48deefdb065335","artifact:4565:5565f7b1b57e6f5345d30e1ea4d331337efd213bbeef2c211573927f9660348a":"5565f7b1b57e6f5345d30e1ea4d331337efd213bbeef2c211573927f9660348a","artifact:4565:569e88a4cdf9dce261981a30688b329d87e4c1cc65b30497142c107f3018c5b4":"569e88a4cdf9dce261981a30688b329d87e4c1cc65b30497142c107f3018c5b4","artifact:4565:646f0cb6ee71ed6faf5732c7fb5a81f4f988a72fc6fab278e9eb1905b2099760":"646f0cb6ee71ed6faf5732c7fb5a81f4f988a72fc6fab278e9eb1905b2099760","artifact:4565:6685f146770bdbf64cf9fc24bb8515ce1d3aa33ad9c2dd32d71d13f48cdcd95e":"6685f146770bdbf64cf9fc24bb8515ce1d3aa33ad9c2dd32d71d13f48cdcd95e","artifact:4565:6c95def185dda4bea46ebb29ffecd2355fec40178879745ae71901149f37bba0":"6c95def185dda4bea46ebb29ffecd2355fec40178879745ae71901149f37bba0","artifact:4565:78d1d2a6f70ece8de9153ba18168e0d661e5297bc36af36d385518853ff1749a":"78d1d2a6f70ece8de9153ba18168e0d661e5297bc36af36d385518853ff1749a","artifact:4565:799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183":"799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183","artifact:4565:8441b47a7882bec570f28824b0db9114c42054d75ce5f1e3942b0a3afa5a97ad":"8441b47a7882bec570f28824b0db9114c42054d75ce5f1e3942b0a3afa5a97ad","artifact:4565:8801bf1b7c5af18a0fb972b8486c9d1adf949a3bef668ee583b1434c15eabf80":"8801bf1b7c5af18a0fb972b8486c9d1adf949a3bef668ee583b1434c15eabf80","artifact:4565:8f0cebd837188fa1747ae875fa8e939fa7b1954eb5e5a498738f654dcc9f7df1":"8f0cebd837188fa1747ae875fa8e939fa7b1954eb5e5a498738f654dcc9f7df1","artifact:4565:99d03d4459397466213e100af822bc1ca9aa9c2ae25230465d9368c8f9659279":"99d03d4459397466213e100af822bc1ca9aa9c2ae25230465d9368c8f9659279","artifact:4565:a7f828cd6c74946a5dec5ba25a3d20759bb637a82cdf6827415b1631c6fefc20":"a7f828cd6c74946a5dec5ba25a3d20759bb637a82cdf6827415b1631c6fefc20","artifact:4565:aaada0d4f1a9c5a495e45b7f7c58dd7d2056172186db971007f28dc6b1ceb723":"aaada0d4f1a9c5a495e45b7f7c58dd7d2056172186db971007f28dc6b1ceb723","artifact:4565:b8dd01f33804b0049a7209e9d10f9f480a9a3feef9ccbb58601d3b54692710fb":"b8dd01f33804b0049a7209e9d10f9f480a9a3feef9ccbb58601d3b54692710fb","artifact:4565:ba8937853d9553f26281bb015113b3e1a79478fe93cc07076390d04fec58a99f":"ba8937853d9553f26281bb015113b3e1a79478fe93cc07076390d04fec58a99f","artifact:4565:c3425f1d5dcd0c9583e0963fd549c5dcba8a5a83540bf013296c92e0cce47bc7":"c3425f1d5dcd0c9583e0963fd549c5dcba8a5a83540bf013296c92e0cce47bc7","artifact:4565:cbd460d44fdea1cbd3b06192310be5e7ef2a5bfc86c40b05b4f27f1bfeaf4022":"cbd460d44fdea1cbd3b06192310be5e7ef2a5bfc86c40b05b4f27f1bfeaf4022","artifact:4565:d2b0932cdf388eab129d8a23e356860dff5ac9866be7f93b89437c96fb5a11b7":"d2b0932cdf388eab129d8a23e356860dff5ac9866be7f93b89437c96fb5a11b7","artifact:4565:e6356be594543c8b1b7527dec0010316b281925fa0476ec5f45974581b69a8a0":"e6356be594543c8b1b7527dec0010316b281925fa0476ec5f45974581b69a8a0","artifact:4565:f3444cfe00911874e8011e6845f3d9cae9fe7f60e2f5b4d936ef68bdc2c2595d":"f3444cfe00911874e8011e6845f3d9cae9fe7f60e2f5b4d936ef68bdc2c2595d","artifact:4565:f388f662b07f3645611011e17ef2f706bf9bafe4d55ccd42cf3c3019409b9a6d":"f3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applicability screening of accepted scientific return #4565: 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\":4565,\"report_sha256\":\"799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4565\":\"e5b486bf0d721609379fa973d05fca746a7d62844a6f8d757dcfdee830384bcd\",\"artifact:4565:1036192adcddc1de179dc1c24b01980514ab82345ea02ac64e807ab31e1de51a\":\"1036192adcddc1de179dc1c24b01980514ab82345ea02ac64e807ab31e1de51a\",\"artifact:4565:1d526f039d345bd42669c6b599458a183c5f4defde02b5becffae89187ba7eb7\":\"1d526f039d345bd42669c6b599458a183c5f4defde02b5becffae89187ba7eb7\",\"artifact:4565:1dbfc18ce5f2b92798974db3edd1e0eec59af37f08434d6876a6b9ac4fd72df7\":\"1dbfc18ce5f2b92798974db3edd1e0eec59af37f08434d6876a6b9ac4fd72df7\",\"artifact:4565:1fc013b819ca234430d4afac3df4962e6b357be9e6581ea149ed8822d0259101\":\"1fc013b819ca234430d4afac3df4962e6b357be9e6581ea149ed8822d0259101\",\"artifact:4565:253dcd7a0c980be1f98c5d14e3137e879cb92dc06a36598f25520d60f60dc515\":\"253dcd7a0c980be1f98c5d14e3137e879cb92dc06a36598f25520d60f60dc515\",\"artifact:4565:42719313698c533a4d9b66f90f1d1e11d4ba61c7900ef092fe61f22a47e3a9ce\":\"42719313698c533a4d9b66f90f1d1e11d4ba61c7900ef092fe61f22a47e3a9ce\",\"artifact:4565:4d5e405e94b1ff69ea79c793592cd4b9030d391d06fa45e67e48deefdb065335\":\"4d5e405e94b1ff69ea79c793592cd4b9030d391d06fa45e67e48deefdb065335\",\"artifact:4565:5565f7b1b57e6f5345d30e1ea4d331337efd213bbeef2c211573927f9660348a\":\"5565f7b1b57e6f5345d30e1ea4d331337efd213bbeef2c211573927f9660348a\",\"artifact:4565:569e88a4cdf9dce261981a30688b329d87e4c1cc65b30497142c107f3018c5b4\":\"569e88a4cdf9dce261981a30688b329d87e4c1cc65b30497142c107f3018c5b4\",\"artifact:4565:646f0cb6ee71ed6faf5732c7fb5a81f4f988a72fc6fab278e9eb1905b2099760\":\"646f0cb6ee71ed6faf5732c7fb5a81f4f988a72fc6fab278e9eb1905b2099760\",\"artifact:4565:6685f146770bdbf64cf9fc24bb8515ce1d3aa33ad9c2dd32d71d13f48cdcd95e\":\"6685f146770bdbf64cf9fc24bb8515ce1d3aa33ad9c2dd32d71d13f48cdcd95e\",\"artifact:4565:6c95def185dda4bea46ebb29ffecd2355fec40178879745ae71901149f37bba0\":\"6c95def185dda4bea46ebb29ffecd2355fec40178879745ae71901149f37bba0\",\"artifact:4565:78d1d2a6f70ece8de9153ba18168e0d661e5297bc36af36d385518853ff1749a\":\"78d1d2a6f70ece8de9153ba18168e0d661e5297bc36af36d385518853ff1749a\",\"artifact:4565:799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183\":\"799e10212657fd8ed516eda2b6bcca6e4e0a80430fa7a9cab32604f13b1e3183\",\"artifact:4565:8441b47a7882bec570f28824b0db9114c42054d75ce5f1e3942b0a3afa5a97ad\":\"8441b47a7882bec570f28824b0db9114c42054d75ce5f1e3942b0a3afa5a97ad\",\"artifact:4565:8801bf1b7c5af18a0fb972b8486c9d1adf949a3bef668ee583b1434c15eabf80\":\"8801bf1b7c5af18a0fb972b8486c9d1adf949a3bef668ee583b1434c15eabf80\",\"artifact:4565:8f0cebd837188fa1747ae875fa8e939fa7b1954eb5e5a498738f654dcc9f7df1\":\"8f0cebd837188fa1747ae875fa8e939fa7b1954eb5e5a498738f654dcc9f7df1\",\"artifact:4565:99d03d4459397466213e100af822bc1ca9aa9c2ae25230465d9368c8f9659279\":\"99d03d4459397466213e100af822bc1ca9aa9c2ae25230465d9368c8f9659279\",\"artifact:4565:a7f828cd6c74946a5dec5ba25a3d20759bb637a82cdf6827415b1631c6fefc20\":\"a7f828cd6c74946a5dec5ba25a3d20759bb637a82cdf6827415b1631c6fefc20\",\"artifact:4565:aaada0d4f1a9c5a495e45b7f7c58dd7d2056172186db971007f28dc6b1ceb723\":\"aaada0d4f1a9c5a495e45b7f7c58dd7d2056172186db971007f28dc6b1ceb723\",\"artifact:4565:b8dd01f33804b0049a7209e9d10f9f480a9a3feef9ccbb58601d3b54692710fb\":\"b8dd01f33804b0049a7209e9d10f9f480a9a3feef9ccbb58601d3b54692710fb\",\"artifact:4565:ba8937853d9553f26281bb015113b3e1a79478fe93cc07076390d04fec58a99f\":\"ba8937853d9553f26281bb015113b3e1a79478fe93cc07076390d04fec58a99f\",\"artifact:4565:c3425f1d5dcd0c9583e0963fd549c5dcba8a5a83540bf013296c92e0cce47bc7\":\"c3425f1d5dcd0c9583e0963fd549c5dcba8a5a83540bf013296c92e0cce47bc7\",\"artifact:4565:cbd460d44fdea1cbd3b06192310be5e7ef2a5bfc86c40b05b4f27f1bfeaf4022\":\"cbd460d44fdea1cbd3b06192310be5e7ef2a5bfc86c40b05b4f27f1bfeaf4022\",\"artifact:4565:d2b0932cdf388eab129d8a23e356860dff5ac9866be7f93b89437c96fb5a11b7\":\"d2b0932cdf388eab129d8a23e356860dff5ac9866be7f93b89437c96fb5a11b7\",\"artifact:4565:e6356be594543c8b1b7527dec0010316b281925fa0476ec5f45974581b69a8a0\":\"e6356be594543c8b1b7527dec0010316b281925fa0476ec5f45974581b69a8a0\",\"artifact:4565:f3444cfe00911874e8011e6845f3d9cae9fe7f60e2f5b4d936ef68bdc2c2595d\":\"f3444cfe00911874e8011e6845f3d9cae9fe7f60e2f5b4d936ef68bdc2c2595d\",\"artifact:4565:f388f662b07f3645611011e17ef2f706bf9bafe4d55ccd42cf3c3019409b9a6d\":\"f388f662b07f3645611011e17ef2f706bf9bafe4d55ccd42cf3c3019409b9a6d\"},\"sha256\":\"495206425b32e15c278dad647ba7fbfcda1c45b106bc35c764f9ff5af0ed9c17\"},\"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:4565,input_sha256:\"31fd4c0a6e30fca856bf3cd2559b499f74e3ef9fea45360c5e4b05fdfbe40fb4\",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/4608/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1801fd7c6dd5da60bf92048b0ff6805343c49c84dd9876008926bf8c970bbecb","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}