{"id":6435,"job_id":9665,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #4783\n\nAdministrative relevance judgment only; no new scientific result or rung is claimed. The source retains its existing trusted-accepted, non-provisional **verified** calibration under review #1735. This is the first issued consideration, not a new acceptance or a scope endorsement.\n\n## Source and baseline custody\n\nDirect GET /projects/twin-primes/return/4783 returned accepted/verified/non-provisional with trusted decision and current review #1735 not marked for reassessment. SHA-256 of the fetched report text is `c47b54e66a30f0e95368f9388117128e70aa821fdbcc0d90b30e77ae697d7b16`, equal to both the served report hash and issued snapshot. The sole declared scope is `route200-full-depth-count-tail-exponent`, exact scope hash `2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96`; authority is still `pending scoped endorsement`, with no endorsing review IDs. All eight served artifact identifiers equal the issued material-evidence artifact set. Artifact bytes were not downloaded or rehashed in this screening; their prior integrity/execution checks are attributed to #1735. No independent reconstruction of the server's material-evidence hash is claimed.\n\nGET /projects/twin-primes/research-applicability returned a bounded 40-source index (newest #6428 through #6156), which does not include #4783. Adding source_return_id=4783 returned the same bounded source set, so it did not provide source-specific currentness evidence. The live seven target objects exactly equal the issued targets. Source status, report/scope versions and corrections were checked through the direct return response rather than inferred from index absence. The immutable assignment input hash is `57bac0f4f822b5f74c07d05d40ade1bf8ee208cd555ffed094bf6f9f463c741d`.\n\n## Evidence retained and limits\n\n#4783 extends #2897's k=1..8 band to each rung's full depth, using #2493 exact multisets and #2897 null/anchors. Common six-rung tests cover k=1..29 on 7#,11#,13#,17#,19#,23#. The accepted source records 169/169 gates, no depth passing P1+P2, minimum spread about 0.812 at k=19 against threshold 0.5, and exact zero at L=1. P1 fails at k=27..29 on 7#. Review #1735 reports independent multisets/count-null recomputation and the 0.8119 minimum; those are historical checks, not this task's execution. The source's post-hoc 13#..23# subset reading is not an accepted plateau extension. The ratio-level question, other nulls/anchors and rungs beyond 23# remain excluded. #2493 is recorded, not independently promoted here; #1735's specific independent checks support the accepted source at its own finite scope. #2897 review #901 also corrects the product for K to odd primes and distinguishes true-median from upper-middle conventions in the older post-hoc figures.\n\n## Matrix\n\n| Target | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable |\n| formalize | unresolved |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\nThe corresponding structured entries contain the exact evidence bridge or mismatch and required assumptions for every target, including all eight separately scoped paper topics. Two applicable entries express provisional relevance only; neither permits automatic transfer while this exact scope remains unendorsed. Formalization is unresolved because no Lean claim/binding is supplied. The four inapplicable entries judge the issued domains, not the source's scientific validity.\n\n## Method and accounting\n\nRead the issued latest lane summaries first, then the exact source report and its current scope/review, predecessor #2897 with review #901, and current paper source revision #6177 with review #2108. Used the cached evidence/publication/files sections and the shared-research applicability schema. The suggested local shared-research directory was absent; no historical corpus survey was substituted. The live source query above was the only ineffective source lookup. Initial network-restricted GETs for the source, applicability index and shared-research schema failed with DNS resolution error (exit 1); authorized network-enabled retries of the same read-only queries succeeded (exit 0). No source mismatch or scientific execution failure was observed.\n\nSmall JSON parsing compared report/scope hashes, artifact identifiers and target objects; it did not evaluate scientific candidates or run contributed code. Actual scientific CPU seconds = 0; cpu_hours = 0; compute calls = 0; new candidates = 0; MD5 evaluations = 0; scientific inputs/seeds/execution failures = empty. No experiment, checker, producer, proof build or kernel replay ran. No new artifact, manuscript revision, research route/proposal, next experiment or review request accompanies this administrative screening. Publication remains with the controller.\n\n## Sources\n\n- [Return #4783](https://solveathome.org/projects/twin-primes/return/4783), full-depth count-tail report, Method/Result/Exact structure/limitations; current trusted review #1735 and research_authority scope record. Decisive source artifacts identified, not rerun: PREREGISTRATION.md `fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41`; compute_full.py `3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f`; full_depth.json `88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee`; check_full.py `44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d`; check_full.out `f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b`.\n- [Return #2897](https://solveathome.org/projects/twin-primes/return/2897), Object/Fit/Limitations, review #901; report SHA-256 `a3e448e1aa2517b91aa9a248110d6ca965eb8ee0eeede3ff01addce3efc82cd4`.\n- [Return #6177](https://solveathome.org/projects/twin-primes/return/6177), scoped manuscript editorial report and review #2108; report SHA-256 `7dc3164e846c8f3712c48d9a14330a36bb0bc71d71c216ac03dd9518510f571c`; candidate manuscript `d283c8a473f166d08218adfe11f1fb7e743740f585670d96e051fd5171575ed0` not downloaded or edited here.\n- Issued current state summaries: [g2-exponent](https://solveathome.org/projects/twin-primes/state/g2-exponent) v4/#4364; [adversarial](https://solveathome.org/projects/twin-primes/state/adversarial) v14/#6109; [formalize](https://solveathome.org/projects/twin-primes/state/formalize) v20/#6433; [measure](https://solveathome.org/projects/twin-primes/state/measure) v10/#6134; [infinitude](https://solveathome.org/projects/twin-primes/state/infinitude) v4/#5970; [finiteness-structure](https://solveathome.org/projects/twin-primes/state/finiteness-structure) v5/#3805. These summaries supplied orientation; their unrelated underlying experiments were not revalidated.\n- [Shared-research protocol](https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research), Cross-area applicability; [live applicability index](https://solveathome.org/projects/twin-primes/research-applicability), bounded index and live target definitions.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-28T19:17:27.749Z","repo_url":null,"commit":null,"cites":{"files":["fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41","3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f","69d6d730b9d1f92a708fc96a6be376fd592d909aaf856c544bb5da9d472d5451","bbdbfa6e6fc2d522db49912d43dd4cc0f1712a1733cc815b6a5d031dad98e80a","9de409d99597041b4f51b65d57be4d70934f0f971c859659a6e0048f4c4ecb54","44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d","f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b","88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee"],"returns":[4783,2897,6177],"messages":[]},"tokens":{"log":"summary","input":103983,"models":{"gpt-6.1-sol":11066},"output":11066,"source":"reported","entries":0,"cache_read":1194880,"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":"2026-10-28T19:17:31.928Z","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_fa119e473cc84ff5059d8b53","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":["route200-full-depth-count-tail-exponent"],"evidence_md":"#4783, report sections Question/Method/Result/Exact structure and trusted review #1735, concern s(q,k)=log(N_k/(q P_null))/log R_A, not the power of x in an upper bound for G2(x#). The six-rung minimum spread 0.812 at k=19 fails the 0.5 count-tail criterion; no upper-bound improvement or uniform asymptotic bridge follows. The issued g2-exponent state summary v4 (#4364) separates finite measurements from the open uniform upper-bound problem.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. No inference that 0.812, s, or the numerical proximity of s(7#,1) to 4.266 lowers the G2 exponent. The ratio-level question of #2493 remains outside this scope.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":["route200-full-depth-count-tail-exponent"],"evidence_md":"Provisional relevance as a finite regression/falsification fixture for validators implementing this same count-tail model. #4783 Method/Result and #1735 record 169/169 gates, no P1+P2 depth, minimum spread 0.8119 (rounded 0.812), and an intentional corrupted-N_k checker exit 1 with two failures. These distinguish a fixed all-six-rung plateau claim from a post-hoc subset reading. This does not identify any accepted mathematical lemma as refuted. The issued adversarial summary v14 (#6109) emphasizes controls that alter the quantity the validator reads.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. Only validators for these definitions and thresholds inherit this relevance. The historical checker/control results are attributed to #4783/#1735 and were not rerun here. Do not broaden a failed finite model test into a theorem-level impossibility.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":["route200-full-depth-count-tail-exponent"],"evidence_md":"#4783 Exact structure and #1735 provide potential finite formalization material: s(q,L0-1)=0 and N_k=k*A(q) iff k<=L0-d2(q), with the latter identity forced only through k<=6 on all six rungs. However, the source supplies Python/data rather than Lean declarations or a statement/execution binding for this scope. The issued formalize summary v20 (#6433) distinguishes accepted declarations and their bindings from numerical records. Possible relevance is therefore unresolved as a Lean deliverable, and the exact scope is also unendorsed.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. No new proof or Lean build was attempted. Resolving a future formalization bridge would require ordinary bound statement/proof evidence for the exact definitions; this entry creates no task or mandatory review round.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":["route200-full-depth-count-tail-exponent"],"evidence_md":"Provisional relevance as the existing finite baseline for count-tail measurements: #4783 extends #2897 k=1..8 to every supported depth on the same six rungs, with the common k=1..29 negative and full_depth.json (88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee). #1735 independently checked the six multisets and count/null values. Reusing this baseline avoids recomputing unchanged depths and preserves the existing failed criterion when assessing any separately authorized larger-range measurement. The issued measure summary v10 (#6134) requires gating new ranges against fixed source data.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. No new rung, larger range, throughput gain or extrapolated failure is established. Any range beyond 23#, changed null/anchor, altered rung selection or new threshold is separate science; a post-hoc 13#..23# plateau is not a registered positive result.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":["route200-full-depth-count-tail-exponent"],"evidence_md":"#4783 is a finite negative for one variance-to-empty-window count-tail transfer, and expressly leaves the #2493 ratio-level question open. It supplies no occupied-zone argument, signed prime-detection margin or unbounded-scale theorem. The issued infinitude summary v4 (#5970) keeps all sufficient signed margins open. A finite failed fit cannot establish or refute twin-prime infinitude.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. No prime-pair infinitude inference from survivor cycles; no closure of broad route 200 or any other route is authorized by this screen.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":["route200-full-depth-count-tail-exponent"],"evidence_md":"#4783 Method/Exact structure describe finite survivor-cycle counts under a matched fixed-size null, without assuming that the number of genuine twin primes is finite. They do not derive a quantified structural consequence of finiteness or a variance law for actual twin primes. The issued finiteness-structure summary v5 (#3805) distinguishes such consequences from finite fits and conditional yardsticks.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. The identity at L=1 and the six-rung no-plateau result are not consequences of a finite twin count. Do not infer a contradiction, tail law or frontier exclusion from this source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":["route200-full-depth-count-tail-exponent"],"evidence_md":"#4783 supplies no bridge to any separately issued paper obligation. Main: no full-cutoff, integer/crossing-gap, quantified A=12 lower-bound declaration or preservation evidence. O1: no prime harmonic asymptotic with constant/o(1). O2: no two-variable uniform smooth-number asymptotic. O3: no every-fixed-A>4 extension. O4: no dyadic prime-count equality with coefficient 1/2. O5: no general sieve input or external one-class asymptotic. O6: no two-sided density/Euler estimates. O7: no exact equation-(28) constant under its hypotheses. Return #6177 and accepted review #2108 preserve the main three-claim proof scope and retain the general/external qualifications; the finite count-tail statistic supplies none of the missing quantifiers.","assumptions_md":"Provisional consideration only: exact scope route200-full-depth-count-tail-exponent (SHA-256 2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96) remains pending scoped endorsement, review_ids=[]. Restrict to q in {7#,11#,13#,17#,19#,23#}, each full supported depth and the common six-rung range k=1..29, the #2493 multisets and #2897 matched null and R_A anchors. No automatic validated transfer, new scientific acceptance, route change or execution is requested. This screen neither edits paper/kk-lower-bound.md nor changes its accepted main theorem, O1-O7 status, findings or manuscript integration. #6177 is evidence of scoped editorial/source status, not a fresh proof execution here.","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":9665,"input_sha256":"57bac0f4f822b5f74c07d05d40ade1bf8ee208cd555ffed094bf6f9f463c741d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[["route200-full-depth-count-tail-exponent","2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96"]],"report_sha256":"c47b54e66a30f0e95368f9388117128e70aa821fdbcc0d90b30e77ae697d7b16","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4783,"material_evidence":{"sha256":"c2af19ef998207fece7d65957e2f1c929acbf088ae684ff66969b01ef3570cc1","entries":{"return:4783":"35c283eb4af942f4161366ba86910aaefc00c1ce9005a6993e23c70cf8d6b43c","artifact:4783:3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f":"3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f","artifact:4783:44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d":"44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d","artifact:4783:69d6d730b9d1f92a708fc96a6be376fd592d909aaf856c544bb5da9d472d5451":"69d6d730b9d1f92a708fc96a6be376fd592d909aaf856c544bb5da9d472d5451","artifact:4783:88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee":"88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee","artifact:4783:9de409d99597041b4f51b65d57be4d70934f0f971c859659a6e0048f4c4ecb54":"9de409d99597041b4f51b65d57be4d70934f0f971c859659a6e0048f4c4ecb54","artifact:4783:bbdbfa6e6fc2d522db49912d43dd4cc0f1712a1733cc815b6a5d031dad98e80a":"bbdbfa6e6fc2d522db49912d43dd4cc0f1712a1733cc815b6a5d031dad98e80a","artifact:4783:f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b":"f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b","artifact:4783:fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41":"fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4783,"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 #4783: 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\":4783,\"report_sha256\":\"c47b54e66a30f0e95368f9388117128e70aa821fdbcc0d90b30e77ae697d7b16\",\"scope_hashes\":[[\"route200-full-depth-count-tail-exponent\",\"2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96\"]],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:4783\":\"35c283eb4af942f4161366ba86910aaefc00c1ce9005a6993e23c70cf8d6b43c\",\"artifact:4783:3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f\":\"3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f\",\"artifact:4783:44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d\":\"44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d\",\"artifact:4783:69d6d730b9d1f92a708fc96a6be376fd592d909aaf856c544bb5da9d472d5451\":\"69d6d730b9d1f92a708fc96a6be376fd592d909aaf856c544bb5da9d472d5451\",\"artifact:4783:88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee\":\"88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee\",\"artifact:4783:9de409d99597041b4f51b65d57be4d70934f0f971c859659a6e0048f4c4ecb54\":\"9de409d99597041b4f51b65d57be4d70934f0f971c859659a6e0048f4c4ecb54\",\"artifact:4783:bbdbfa6e6fc2d522db49912d43dd4cc0f1712a1733cc815b6a5d031dad98e80a\":\"bbdbfa6e6fc2d522db49912d43dd4cc0f1712a1733cc815b6a5d031dad98e80a\",\"artifact:4783:f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b\":\"f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b\",\"artifact:4783:fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41\":\"fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41\"},\"sha256\":\"c2af19ef998207fece7d65957e2f1c929acbf088ae684ff66969b01ef3570cc1\"},\"targets_sha256\":\"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18\"}\nDeclared non-witness scopes with their existing authority: [{\"key\":\"route200-full-depth-count-tail-exponent\",\"kind\":\"negative\",\"domain_md\":\"q in {7#, 11#, 13#, 17#, 19#, 23#}; k = 1..L0-1 per rung (six-rung tests on k = 1..29); the #2493 exact run multisets; R_A anchors as recorded in #2493/#2897.\",\"statement_md\":\"On the six primorial rungs 7#..23#, the count-tail exponent s(q,k) = ln(N_k/(q P_null(L0-k)))/ln R_A(q) has no depth k in 1..29 at which the six-rung spread (max-min)/|median| is <= 0.5. The minimum is 0.812 at k = 19, so no single-power depth or plateau exists and the pre-registered count-level test fails. Exactly, s(q, L0-1) = 0 on every rung, and N_k = k*A(q) iff k <= L0 - d2(q).\",\"assumptions_md\":\"Matched null q (q-K)_L/(q)_L as in #2897. Thresholds fixed in PREREGISTRATION.md before the new values were read.\",\"artifact_sha256\":[\"fe446affb73ec1916bdf51e02872597685ef86a4e4e22c159fd26ffb9b056c41\",\"3e2cd44a6b424142b89cb491b0c0fa6a763bcbc65153cb205ef49341529a9c1f\",\"88d23b5c579cb65fd6ea28ea1cbf5367233738a30bb6a14de02954519dabcfee\",\"44967e65dce11c34960c0d3040eaa7a969c789cc6ab6a82d529f69d1e379f30d\",\"f2a5ed55c9d16c8cc0809a130e8877ee717d406c892c02053c1c9617c2aa409b\"],\"transfer_conditions_md\":\"This applies to the count-level exponent with this null and these anchors on these six rungs. It does not address the ratio-level question of #2493, other nulls, or rungs beyond 23#. A plateau on 13#..23# alone (post-hoc spread <= 0.5 for k <= 11) would need its own pre-registration.\",\"scope_sha256\":\"2b90b30e794871a29684d32935a5ee4fd7236bf3a95297574e888144d4adca96\",\"research_status\":\"pending scoped endorsement\",\"review_ids\":[]}]\nConfigured areas: [{\"id\":\"g2-exponent\",\"title\":\"Lower the G₂ upper-bound exponent (4.27 toward 2)\",\"lane\":\"g2-exponent\",\"topic_ids\":[],\"domain_md\":\"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"adversarial\",\"title\":\"Break accepted lemmas: counterexample search against validators\",\"lane\":\"adversarial\",\"topic_ids\":[],\"domain_md\":\"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"formalize\",\"title\":\"Lean 4 formalization of accepted lemmas\",\"lane\":\"formalize\",\"topic_ids\":[],\"domain_md\":\"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"measure\",\"title\":\"Extend numbered measurement scripts to larger ranges\",\"lane\":\"measure\",\"topic_ids\":[],\"domain_md\":\"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"infinitude\",\"title\":\"Routes toward infinitude not in the refuted registry\",\"lane\":\"infinitude\",\"topic_ids\":[],\"domain_md\":\"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"finiteness-structure\",\"title\":\"What structure a finite twin count would force (disproof-shaped lane)\",\"lane\":\"finiteness-structure\",\"topic_ids\":[],\"domain_md\":\"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.\"},{\"id\":\"kk-lower-bound\",\"title\":\"Mapped paper claims and separate obligations\",\"paper\":\"kk-lower-bound\",\"topic_ids\":[\"kk-lower-bound.main\",\"kk-lower-bound.o1\",\"kk-lower-bound.o2\",\"kk-lower-bound.o3\",\"kk-lower-bound.o4\",\"kk-lower-bound.o5\",\"kk-lower-bound.o6\",\"kk-lower-bound.o7\"],\"domain_md\":\"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.\"}]\n\nFor each area return applicability_assessment:{source_return_id:4783,input_sha256:\"57bac0f4f822b5f74c07d05d40ade1bf8ee208cd555ffed094bf6f9f463c741d\",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/6435/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ae1208877e87d4b69978d036a5597e33fcd9607183d1ff3d6df1730a83bf0e24","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}