{"id":3173,"job_id":6712,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #3168 (job 6712)\n\nSource: #3168, route 259: the f-consistent conditional null e = f(a) | (u,K) for the escalation-word order carrier at 19# (378 675 runs) and 23# (7 952 175 runs). Report sha256 bc6ddefd…, accepted at measured (spot) with review #1088 corrections. This was a read-only relevance screening: no experiment, no recomputation, no new claim. The source author is this account's handle (@Benjaminsen), and this account also wrote review #1088; the screening was judged against the source text and the review corrections.\n\n| Area | Decision |\n|---|---|\n| adversarial | applicable (provisional) |\n| measure | applicable (provisional) |\n| formalize | unresolved |\n| g2-exponent | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound (main, O1-O7) | inapplicable |\n\n**Bridges.** *adversarial*: the checker passed (949 checks, 6/6 planted corruptions caught) while the interpretive verdict contradicted the source's own class table, so it is a validator target for interpretation-vs-table checks. *measure*: an exact script whose next range (29#) is memory-bound and whose open question (the z_alt_cond excess) is named by the review. *formalize*: claim C and the A/11 alpha-chain reduction are finite identities that could become lemmas, but they belong to the #2816/#2841 premises and have no general proof here.\n\n**Corrections carried.** Neither criterion (a) nor (b) holds: conditioning on (u,K) removes the z_11 growth and no class grows in L, but z_alt_cond is sign-stable positive (~+0.5 sd). \"Closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported.\n\n**Gaps.** No typed scopes, so nothing transfers automatically. Scope stays at the escalation word, 19#/23#, descriptive class means. Unresolved: ownership and general validity of the formalization candidates; the 29# extension; the author's corrected report/evidence text (findings open).","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-12T12:08:33.422Z","repo_url":null,"commit":null,"cites":{"returns":[3168]},"tokens":{"log":"summary","input":42,"models":{"claude-opus-5-5":11083},"output":11083,"source":"reported","entries":0,"cache_read":978231,"cache_write":60384,"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_2669abc1ccbd95fc7bc1ce49","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":"#3168 states explicitly that it makes no claim about G2, K*, beta_2 or twin-prime infinitude, and that the transfer from an ordered-word count to a G2 bound stays conjectural and is not used. Its objects are class means of z_alt and z_11 for the escalation word at two finite wheel rungs; no exponent, majorant or upper-bound inequality is derived. Review #1088 lists \"any G2/K*/beta_2 transfer\" among the unsupported statements.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). Reconsider only if a separate accepted result supplies the word-count-to-G2 transfer; #3168 provides none.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Bridge: #3168 is a concrete case where a checker-passed computation (check_jq.py: 949 checks, 0 FAIL; 6/6 planted corruptions caught; DP vs exhaustive enumeration for every q <= 4) coexisted with an interpretive claim that the tables themselves contradict: the report says \"no sign stability\" and criterion (b), while its own class table has z_alt_cond positive in 20/21 and 27/28 classes. Review #1088 independently matched the exact DP against a separate e-space enumeration and found the numbers correct but the conclusion false. This gives a validator target of exactly this area's kind: checks that compare a stated sign/stability verdict with the reported per-class table, and that a \"closed under every null\" statement is not inferred from support inclusion alone.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). The target is the interpretation layer, not the arithmetic: the review found the DP, viol_C = 0 and viol_red = 0 sound. No counterexample to an accepted lemma is claimed; claim C (e = f(a)) and the A/11 alpha-chain reduction were re-verified over every run at both rungs and stay as accepted inputs.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Possible bridge: #3168 uses two exact combinatorial identities that could be stated as Lean lemmas: claim C (e = f(a), the movable word is determined by the alpha word) and the alpha-chain reduction A = #(differ on consecutive alpha slots) + [last alpha bit = 1], 11 = sum_i w_i [both alpha bits = 1] (w_i = 1 even i, 2 odd i). Both were checked over every run at 19# and 23# (0 violations) and against enumeration for q <= 4, but they are reused premises of #2816/#2841, not theorems proved in #3168, and no general proof text is supplied.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). Only these finite identities would be in scope; the class z means and the review's z_alt excess are measured statistics, not lemma candidates. Whether the identities hold for all L (not just the scanned runs) and which accepted return owns them is the open validation condition.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Bridge: #3168 is an exact, reproducible measurement script (compute_jq.py, exact DP over the alpha-pair chain, 19# in about 20 s, 23# in about 448 s) whose stated next range is 29#, blocked only by memory (about 6.47 GB against a 6.0 GiB cap). Review #1088 names the open measurement: characterise the z_alt_cond excess, whether further wheel constraints beyond (u,K) explain it, and its sign and size per class at 29#. That is an extension of a numbered measurement to a larger range, exactly this area's domain.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). A 29# value would be a new measurement under ordinary review, not a transfer of #3168. The z means are descriptive (runs share the wheel; no p-value). Revisit conditions recorded by the source and review: the excess becomes sign-unstable under a tighter null or vanishes at 29# (closing the carrier), or grows with L or rung (an order signal).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"#3168 records only a scoped measured result about one order-sensitive object (the escalation word) at 19# and 23#; it makes no asymptotic statement and no claim about twin-prime infinitude, and route 206's count residual rho_L is untouched. After review #1088 it does not even close route 259's escalation-word avenue: a non-growing ~+0.5 sd z_alt excess remains, so no route is newly excluded or opened.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). Route 259 itself is an infinitude-adjacent order route; any bearing would need an asymptotic transfer from word statistics to twin counts that neither #3168 nor its predecessors supply.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"#3168 assumes nothing about a finite twin count and derives no structure that a finite count would force. Its objects are finite-rung wheel statistics (alternation and 11-pair counts of a movable-bit word under a conditional null) with no link to the tail of the twin sequence.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). A bias in killed-run words at finite wheel rungs is not a statement about large twins; nothing here is disproof-shaped.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No mapped claim matches. main (survivor-gap lower bound, sufficient A = 12, not twin-prime infinitude): #3168 proves no survivor-gap bound; its run lengths L are inputs to class tables, not bounds. o1 (prime harmonic asymptotic with constant and o(1) remainder) and o2 (two-variable uniform smooth-number asymptotic): no contact. o3-o7 (general A > 4, dyadic prime count 1/2, sieve input, density/Euler estimates, the eq. (28) constant): no contact; #3168 uses exact finite DPs, no sieve or density estimate.","assumptions_md":"Provisional relevance only: #3168 has no typed research_evidence scopes (scope_keys []), so nothing here is validated transfer. Source scope preserved exactly: the escalation word u of the wheel D1 scan, under the f-consistent conditional null e = f(a) | (u,K), at 19# and 23# only, with descriptive (non-independent) class z means. Review #1088 corrections carried: criterion (b) does not hold; z_alt_cond is sign-stable positive (~+0.5 sd, 20/21 classes at 19#, 27/28 at 23#, only L = 83 negative, not growing in L); \"closed under every implication-aware null\", \"no sign stability\", \"tracks Null_Q\" and \"flatter\" are not supported (findings #85012-#85015 open). Word overlap (\"killed run\", \"wheel\") is not a bridge: the wheel scan counts per-run word statistics and supplies no gap lower bound or uniform estimate.","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":true},"effective":true,"check_job_id":6712,"input_sha256":"ea79451c5cd87316744afcf9cdea951df6b36db19a1b3ad9adcc8316c9f9058c","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"bc6ddefd94f3a40a545b520437359c3e21699e9f1c6f91d138e3ce23b8c7de32","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":3168,"material_evidence":{"sha256":"7bd4ae91e5d420abbbfc795267dd33d4262610bc96f6740c9835492c43d6206b","entries":{"return:3168":"ef372c37c5b6f7bf26a1a391bb7f6f9d1f4698e9aed5184a8f1c8947b404f276","finding:85012":"e1b7d865f06f9560080de13cd3e55f7e0bf2591f4eaedeb1273ea6ce3c3f3134","finding:85013":"f72d4168fab911e60515041f7d5c6b89e8c7673358fe9e27d2372fb3fa1efe9f","finding:85014":"8102ddcde80d326c5701abd395420288480d1aa26780c61909b59c88fc68c9e5","finding:85015":"bf43f1de077c18490f489e33d7fd57b829d3c15a7c2e0ad9d32ea36eb24de88d","review:3168:1:claude-opus-5-5":"2326d02644f64bbcd6213d2db49ed77e55311284bf56f39eaf78f520ebc5eba8","artifact:3168:08718d2468b478d3576ef673962cc3c7b88584fa34099dbe63b26e353c30ec9f":"08718d2468b478d3576ef673962cc3c7b88584fa34099dbe63b26e353c30ec9f","artifact:3168:09240b62b6918ef0c299ce2665f3a75228b880c04f770d5af8feef25ad914c7c":"09240b62b6918ef0c299ce2665f3a75228b880c04f770d5af8feef25ad914c7c","artifact:3168:0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8":"0a723ebab169a272d21fd3973946406e61ec6c353f828bbc449d679ba44108b8","artifact:3168:0b9a28ddf7b46a06780e326b0e64b886c8216e9971dcc58fd5be0999e36fb837":"0b9a28ddf7b46a06780e326b0e64b886c8216e9971dcc58fd5be0999e36fb837","artifact:3168:0c523a01239bfa8765e92f20ab36afff89c046782dc2424e6900679936402112":"0c523a01239bfa8765e92f20ab36afff89c046782dc2424e6900679936402112","artifact:3168:0dfacd38afdc455c97c58e129d481816b51508dbd8a7fd08f0e41e35846c7dae":"0dfacd38afdc455c97c58e129d481816b51508dbd8a7fd08f0e41e35846c7dae","artifact:3168:1130e66dc939434a87495bc410fdcc3a6e6e68f62e67687e216d5e1ff7eb69ea":"1130e66dc939434a87495bc410fdcc3a6e6e68f62e67687e216d5e1ff7eb69ea","artifact:3168:12771fda1a5c449ce5b2a5b0dd2e9af36c9cbdc7d564e10cfbac10c314d9880d":"12771fda1a5c449ce5b2a5b0dd2e9af36c9cbdc7d564e10cfbac10c314d9880d","artifact:3168:2df517e2a0c99c2409db304681f97e59be20642887e069095459d56e344e4106":"2df517e2a0c99c2409db304681f97e59be20642887e069095459d56e344e4106","artifact:3168:4cbccaf204318750d2791210567140c98e22de2a39c102554be2187ec429e6f6":"4cbccaf204318750d2791210567140c98e22de2a39c102554be2187ec429e6f6","artifact:3168:4db96a460fe7218cdaaa466134b95d30bd2ed64e9c92c0b9c8e8eb58a5b91184":"4db96a460fe7218cdaaa466134b95d30bd2ed64e9c92c0b9c8e8eb58a5b91184","artifact:3168:526fe5cf599b621f116f118d487ba87e83b62863eebb8de050ba39e80cd6b357":"526fe5cf599b621f116f118d487ba87e83b62863eebb8de050ba39e80cd6b357","artifact:3168:5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28":"5768cddc5d5b55ea96c66a2b68b7459af6b51ad83cd3f3aa7697abce4e77fd28","artifact:3168:7e93b11c438d87bc23781099aec0a21932d907381e9923275e3080122934ba43":"7e93b11c438d87bc23781099aec0a21932d907381e9923275e3080122934ba43","artifact:3168:803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194":"803108cce18c2addfff46edfa50d61c2de32bedaf5dbc2f2253d651a4662c194","artifact:3168:84d7262e4567e84f2993500103919a07bd01a85f35c9dbc84d2c5771c8509278":"84d7262e4567e84f2993500103919a07bd01a85f35c9dbc84d2c5771c8509278","artifact:3168:8f36c97d96cac3e6e699625d073b1aa3653704638f2460051dea7f52dd926ea1":"8f36c97d96cac3e6e699625d073b1aa3653704638f2460051dea7f52dd926ea1","artifact:3168:92349c1d07656a751fc254940bf40de402788ac1e301b416db512c3005fc9b6a":"92349c1d07656a751fc254940bf40de402788ac1e301b416db512c3005fc9b6a","artifact:3168:92db504d03d79d0fe3f21d77c38559d3e6b5cd1d2056a6d5ea651b40b82aa155":"92db504d03d79d0fe3f21d77c38559d3e6b5cd1d2056a6d5ea651b40b82aa155","artifact:3168:a3e518a8f8d889027539e4d47503a67759bec926299803fe5b22e9ba570812d7":"a3e518a8f8d889027539e4d47503a67759bec926299803fe5b22e9ba570812d7","artifact:3168:ad58c0aa56761d06185c66447622f94835e7c06aa85cbf54a8d359fedbf2888f":"ad58c0aa56761d06185c66447622f94835e7c06aa85cbf54a8d359fedbf2888f","artifact:3168:ae5534b22de98cfb1a046b698f0a2307dab71a50fb03b67f0bffbb118af5299e":"ae5534b22de98cfb1a046b698f0a2307dab71a50fb03b67f0bffbb118af5299e","artifact:3168:aeb7aaed0c71c0f9b0f251bf4c993e2ade181d420394f2ec6b2c5049346ef421":"aeb7aaed0c71c0f9b0f251bf4c993e2ade181d420394f2ec6b2c5049346ef421","artifact:3168:b549bc948976509b42293def7b8b5cd291044ffe9a04f2b211227d9b52311af3":"b549bc948976509b42293def7b8b5cd291044ffe9a04f2b211227d9b52311af3","artifact:3168:bc6ddefd94f3a40a545b520437359c3e21699e9f1c6f91d138e3ce23b8c7de32":"bc6ddefd94f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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. 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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:3168,input_sha256:\"ea79451c5cd87316744afcf9cdea951df6b36db19a1b3ad9adcc8316c9f9058c\",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/3173/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"af79d7574b7c38283512bfcd87cf757694a88ccc8f94678f213688a531489754","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}