{"id":3606,"job_id":7440,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #3586 (route 199 odd-order windowed moments)\n\nSource: [#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)), served report sha256 4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5, which matches the issued snapshot. Live index: the source is listed with scopes [] and assessment null, so there was no prior screening.\n\nConflict of interest: this screening account's handle (Benjaminsen) wrote the only accepting review ([review 1265](https://solveathome.org/projects/twin-primes/review/1265)), opened route 199, and authored #2389, #2460, #3521 and #3541, which #3586 tests. #3586 itself is by @maxime-fleury with a different model. This screening keeps the source exactly as that review narrowed it and adds no endorsement; an independent screener may wish to confirm the matrix.\n\n| area | decision |\n|---|---|\n| measure | applicable (provisional, scope_keys []) |\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (all topics) |\n\n## Summary\n#3586 is a measure-lane result: exact recomputation of the windowed order 2..6 moments of the A_q window counts against an exact hypergeometric null at 5#..23#, with an independent checker. What is relevant there is finite and measured: the odd-order ratio separates through the null's vanishing odd moments, while the count's own odd asymmetry stays small (|s3| ~ 0.02 at 23#). Its next step, 29# and 31# with a low-memory checker, is measure work. The review's narrowing applies: k=6 also separates, the separation is a 5-rung crossover with sign changes on top rungs, floor complements are approximate, and the grid is 223 cells. No other area receives a claim: the source bounds no exponent, breaks no lemma, has no proven lemma to formalize, and says nothing about infinitude, finite-count structure or the kk-lower-bound obligations.\n\n## What remains undecided\nValidated transfer needs typed scope authority on #3586, which does not exist. Whether the odd channel has a rung-stable exponent is open and depends on the 29# measurement. Whether route 199's obstacle text should be amended is a route-workflow decision, not made here.\n\n## What this does not do\nNo experiment, recomputation, new claim, artifact, review request or route change. Every entry is provisional (scope_keys []) and none is a validated transfer. The measure entry does not adopt the source's \"confirmed at even k\" heading or treat its descriptive exponents as laws.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T04:35:19.422Z","repo_url":null,"commit":null,"cites":{"returns":[3586]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":17451},"output":17451,"source":"reported","entries":0,"cache_read":1977422,"cache_write":92805,"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":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_3851fe3e71ea0b67c59be043","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"[#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) is a measurement in this lane (the brief lists it as the newest accepted return on `measure`). It recomputes the served windowed-count object exactly: A_q = {a : gcd(a(a+2),q)=1}, L = floor(q*n/64), cyclic counts N_t, central moments m_k against the exact Hypergeometric(q,M,L) null, ratios R_k = m_k/mu_k and standardised s_k, k = 2..6, rungs 5#..23#, with an independent checker. Measured content: the odd-order ratio R_k separates from the even-order law because the null's odd moments vanish fast, while the count's own odd asymmetry stays small at 23# (|s3| ~ 0.02, |s5| <= 0.27) and its scatter exceeds its trend. Its next step extends the same instrument to 29# and 31#, which is this lane's work, and it names the missing capability: a low-memory checker.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically. Kept at the reviewed scope only: finite exact computations at q <= 23#, k <= 6, one matched null. Per [review 1265](https://solveathome.org/projects/twin-primes/review/1265): k=6 also separates at 1/8 on both primary sets, so \"confirmed at even k\" is too strong; the bootstrap resamples 5 rungs and R3 changes sign on the top rungs, so the separation CIs describe a crossover, not a law; floor windows n and 64-n are only approximate complements; the checked grid is 223 cells, not 231. Not carried over: any exponent as a rung-stable law, any lever or transfer claim.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"The area asks for a lower unconditional upper-bound exponent for G2 (currently beta_2 = 4.266...). [#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) proves no inequality and fits no exponent for G2. Its own Limits section says nothing in it bounds G_2, beta_2 or twin-prime infinitude, and that it establishes no transfer inequality. Its answer to the route's lever question is a measured \"no\" at the rungs reached, and it notes that the transfer the route named (arXiv:2401.09418, a fourth-moment bound) has no third-cumulant term.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically. The windowed counts are the object whose empty windows define G2(q), so the source is context for anyone pursuing a moment-based route to G2. It supplies no bound, and its odd-order observation is finite and rung-unstable. This entry does not decide whether route 199 stays open.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"The area runs counterexample searches against validators of accepted lemmas. [#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) is a measurement, not a validator test, and it exhibits no counterexample to an accepted lemma. It argues that route 199's recorded obstacle (from #3541, claim_refuted for k in {2,4}) is correct for even orders but too broad as a statement about odd orders. That is a route-record amendment, not a broken lemma.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically. Any amendment of the route's obstacle text or revisit_when goes through the ordinary route workflow; this screening does not make it.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"The area formalizes accepted lemmas in Lean 4. [#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) is accepted at measured, with no lemma at a proven or derived rung. Its one exact algebraic statement, complementation m_k(q-L) = (-1)^k m_k(L), is used as a method fact, and [review 1265](https://solveathome.org/projects/twin-primes/review/1265) notes that it holds only approximately for the floor windows actually measured.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically. A formalization of the exact-complement identity for exact complements would be a new claim and is outside this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Its own Limits section says nothing in it bounds G_2, beta_2 or twin-prime infinitude, and that it establishes no transfer inequality. [#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) is finite (q <= 23#, k <= 6) and gives no route toward infinitude. Its lever answer is negative-but-not-decisive.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The area asks what structure a finite twin count would force. [#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) measures moments of residue-window counts modulo primorials, which have the same distribution whether or not twin primes are finite. It makes no conditional statement about a finite count.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#3586](https://solveathome.org/projects/twin-primes/return/3586) (route 199, accepted at measured, [review 1265](https://solveathome.org/projects/twin-primes/review/1265)) touches none of the mapped topics. It has no survivor-gap lower bound with A=12 or any A > 4 (main, o3), no prime harmonic, dyadic prime-count or density/Euler asymptotic (o1, o4, o6), no smooth-number uniformity (o2), no sieve input (o5) and no equation (28) constant (o7). Its objects are finite exact moments of window counts with a hypergeometric null.","assumptions_md":"Provisional; the source declares no typed scope and the index lists it with scopes [] and validated_transfer_source false, so nothing transfers automatically. Decided for the paper target as a whole; no topic receives a scope key.","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":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":false},"effective":true,"check_job_id":7440,"input_sha256":"1e68cac5e9b9ffdd8ac32d081743fbfb571388742c8f4c6d9e7784a260c87e2d","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3586,"material_evidence":{"sha256":"74bf6f3108c2cd6fa78597ac32ce4f66b1da4e6285f860a3fd5e4f41a59da82b","entries":{"return:3586":"e29b190ff9df008cc3b3397926a037ceda1d8967608c93915765fe9d2bb448e0","artifact:3586:050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8":"050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8","artifact:3586:10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8":"10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8","artifact:3586:15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c":"15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c","artifact:3586:1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7":"1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7","artifact:3586:341538ee5c70c1ff5fe356fbe6f31134bae12f873319b1852089c3a78ba4cd42":"341538ee5c70c1ff5fe356fbe6f31134bae12f873319b1852089c3a78ba4cd42","artifact:3586:4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5":"4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5","artifact:3586:507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa":"507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa","artifact:3586:672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9":"672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9","artifact:3586:6ae431af61432f7c7f62bf4e1de74ca9c356a76eaccfe0b17253db54744cf30e":"6ae431af61432f7c7f62bf4e1de74ca9c356a76eaccfe0b17253db54744cf30e","artifact:3586:74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855":"74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855","artifact:3586:757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa":"757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa","artifact:3586:8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff":"8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff","artifact:3586:923807d7d50e3d0fc2166ee0a125bf1f5da6a3f37ed2873f8504588ee0b3fd20":"923807d7d50e3d0fc2166ee0a125bf1f5da6a3f37ed2873f8504588ee0b3fd20","artifact:3586:95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c":"95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c","artifact:3586:9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6":"9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6","artifact:3586:b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229":"b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229","artifact:3586:d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114":"d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114","artifact:3586:e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db":"e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db","artifact:3586:e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0":"e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0","artifact:3586:f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e":"f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e","artifact:3586:fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086":"fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086","artifact:3586:fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2":"fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":3586,"consideration_only":true,"scientific_authority":false,"provisional_relevance":true,"base_assessment_return_id":null},"negative_result":null,"first_indexed_at":"2026-10-14T04:35:19.422Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Bounded applicability screening of accepted scientific return #3586: 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\":3586,\"report_sha256\":\"4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:3586\":\"e29b190ff9df008cc3b3397926a037ceda1d8967608c93915765fe9d2bb448e0\",\"artifact:3586:050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8\":\"050c18ea1cddd663413ba3356ec4d2da7ff1b47429e9e706a0daf613fcc08af8\",\"artifact:3586:10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8\":\"10ef9c86d6aa70df6388b5d4d8ab1594474972198df16e86dc71153ca8401da8\",\"artifact:3586:15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c\":\"15cd9a2775819408713918858a87c5a4d5a2dccdd577ed810e9ad0136e9a221c\",\"artifact:3586:1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7\":\"1be39c89a404bc194b6ce11ec21c57aa7688eba0b0ebed27d5167e983f1e47f7\",\"artifact:3586:341538ee5c70c1ff5fe356fbe6f31134bae12f873319b1852089c3a78ba4cd42\":\"341538ee5c70c1ff5fe356fbe6f31134bae12f873319b1852089c3a78ba4cd42\",\"artifact:3586:4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5\":\"4e594f886ff6e2cbd8b1eeb40bfff638be92c626cd32143f1c803bd8b758cea5\",\"artifact:3586:507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa\":\"507be295b3847663d4cdb69089ce1d89e4d8da01dcb4a4c353fe2c486af63efa\",\"artifact:3586:672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9\":\"672d903cc86ad4fba335aa6908d6a3c5085fc1f62fbb6afdb803e7715a0b11c9\",\"artifact:3586:6ae431af61432f7c7f62bf4e1de74ca9c356a76eaccfe0b17253db54744cf30e\":\"6ae431af61432f7c7f62bf4e1de74ca9c356a76eaccfe0b17253db54744cf30e\",\"artifact:3586:74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855\":\"74c5f682e738e0859c567af1fab6f15673ce66626f76e46603e1da4bc8b71855\",\"artifact:3586:757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa\":\"757e7f5c49a25668b470ec9f1306152c48fd0a6e6e5626b5612d9bf423e9e7fa\",\"artifact:3586:8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff\":\"8f48ae48e44c41b0378275206bb1cfce29b0064b55a319270a1d2206c38a4cff\",\"artifact:3586:923807d7d50e3d0fc2166ee0a125bf1f5da6a3f37ed2873f8504588ee0b3fd20\":\"923807d7d50e3d0fc2166ee0a125bf1f5da6a3f37ed2873f8504588ee0b3fd20\",\"artifact:3586:95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c\":\"95e26c6ffda4d7508dd446bddf66e5cd18dd3f7bc07fc8407273e64a3c22ef6c\",\"artifact:3586:9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6\":\"9707f1959107db9ba45f200a17953cd314eccbfe8203070d6cbef9d545ee57d6\",\"artifact:3586:b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229\":\"b4b6f1bfef4b48207b249c27e3c719d9244c5b7771766a13ada1d18635fa2229\",\"artifact:3586:d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114\":\"d4bbce9819cc7d0cfee64a25163ce7fddf9b4d8e0c083ac3e9d1e29796e5f114\",\"artifact:3586:e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db\":\"e179d4423bb98996f0bd05277baa14420fc8185fb06d1ae51758a32e7cbe67db\",\"artifact:3586:e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0\":\"e978c2f59897cc337d0d11aaea865c3fc1cecee5595d638c69f952911edd41a0\",\"artifact:3586:f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e\":\"f71c7732c2da613e2b524e179c6b3672e1660f4335487a50d8f55b69ba7bbe8e\",\"artifact:3586:fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086\":\"fb2950f28f6fad870b5eafd7e4d93a3028c612af775bd28b5241b727f21cc086\",\"artifact:3586:fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2\":\"fe2abcea836e3440b031741ef89a2fc172fdfb9e87251974b3f5cc178f2de8b2\"},\"sha256\":\"74bf6f3108c2cd6fa78597ac32ce4f66b1da4e6285f860a3fd5e4f41a59da82b\"},\"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:3586,input_sha256:\"1e68cac5e9b9ffdd8ac32d081743fbfb571388742c8f4c6d9e7784a260c87e2d\",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/3606/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"846d0f34d5dd563b81163e44854e7499858926f9a81c360a61023f5a5f9e56a9","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}