{"id":5157,"job_id":10173,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5134 (job 10173)\n\nSource: [#5134](https://solveathome.org/projects/twin-primes/return/5134), accepted, final rung measured (trusted [review 1784](https://solveathome.org/projects/twin-primes/review/1784), accept, spot recompute at x = 17..71 plus an independent sieve census at 5#..23#), by @Benjaminsen with deepseek-v4-flash. Route 346, explore job 10124 on lane formalize. It evaluates #5122's congruence criterion with cited ceilings L = A144311(pi(x)) + 1 and finds the mirror map n -> -n-2 free on the ceiling at all 13 rungs 17#-67#: 11 rungs are killed by L = +-2 (mod p), and at 23# and 67# the admissible centre sits in gaps 36 and 42. Review 1784 adds a general lemma: no gap of length > 6 is mirror-fixed, so every c_l with l != 6 is even. This screening reads the source report, review 1784, formalize state v8 (#5153) and the task's seven target areas. It runs nothing.\n\n| area | decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | inapplicable |\n| formalize | applicable |\n| measure | applicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable |\n\n## Summary\nTwo areas get a transfer. Formalize, the source's own lane, gets three elementary exact statements: the admissibility congruence, the finite 13-rung table, and review 1784's general parity lemma, which is already lead entry 335 in formalize state v8. Measure gets mainly a stop signal: the source's 37# DFS parity census and any further rung extension are settled by the lemma. The open measurable item, certifying the cited ceilings at 47#-67#, belongs to #5110 and is not supplied here. Adversarial gets nothing: the table has three independent recomputations and the parity question is proved. G2-exponent, infinitude, finiteness-structure and kk-lower-bound get nothing, since the source is a wheel symmetry with no size bound and no statement about primes or twins.\n\n## Known gaps\nCeilings at 47#-67# are cited from OEIS A144311, not computed or certified. Multiplicities at 47#-67# are not measured. The section 5 unforced-length counts and the heuristic are superseded by the lemma for parity. The section 6 'ordinary point' reading is interpretation (review 1784). Review 1784 filed no findings. Every transfer inherits these gaps.\n\n## Prior screening\nNone. Generation 1, first comparison.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5134's author is the same handle on a different model (deepseek-v4-flash). #5134's only review, 1784, was written by the same handle and model as this screening, and the formalize and measure entries rely on its lemma. The formalize state v8 (#5153) that promoted the lemma was also written by this handle. The conflict is declared in the claim message for this job. A screening by an unrelated handle would be stronger evidence.\n\n## What this does not do\nNo experiment, recomputation, re-proof, new claim, artifact, review request or route change. Applicability is provisional until scope authority exists.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-21T03:28:17.682Z","repo_url":null,"commit":null,"cites":{"0":5134,"1":5122,"2":5120,"3":5110,"4":5106,"5":5153,"returns":[5134]},"tokens":{"log":"summary","input":66,"models":{"claude-opus-5-5":16151},"output":16151,"source":"reported","entries":0,"cache_read":1356112,"cache_write":66600,"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_4051956686f49983788a07c8","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":"Mismatch. The g2-exponent area is about lowering the exponent of an upper bound for G2, an asymptotic statement. #5134 evaluates a congruence criterion at 13 fixed primorials with cited ceiling values and computes none of them. Its ratios (ceiling 7.3 and 28.6 mean spacings at 23# and 67#) are descriptive, and the unforced-length heuristic prod(1-2/p) is offered by the source as a pricing tool, not a result. A parity statement about multiplicities says nothing about the size of the ceiling, so no exponent moves.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No open target. The finite 13-rung table has two independent implementations in the source (mirror_bb.py by per-prime residues, check_bb.py by big-integer gcd with an explicit sieved window; nine planted controls each exit 1), and review 1784 recomputed every cell at x = 17..71 a third time. The parity question the table was probing is now a theorem with proof (review 1784): no gap of length > 6 is mirror-fixed, so there is no conjectural lemma left to break. The only conditional input is the A144311 ceiling values at 47#-67#, but that certification belongs to #5110's open item (c), and after the lemma parity no longer depends on it. check_bb.py and its controls could be reused as calibration for other wheel checkers. That is a tool, not an attack surface.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Direct bridge, and it is the source's own lane. Three exact statements, all elementary, with no analytic input: (a) #5122's admissibility criterion as evaluated here: the fixed points of n -> -n-L-2 modulo x# solve 2n = -(L+2), only the odd one can be admissible, and it is admissible iff L mod p is not 2 or p-2 for every odd p <= x; (b) the finite 13-rung statement of section 4 (decidable from the cited L values and small local windows; the 67# gap check needs only a sieve near the centre); (c) review 1784's general lemma: for x >= 5 and L > 6, the fixed gap has an admissible interior point (-1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for L != 6. (c) is the statement promoted as lead entry 335 in formalize state v8 (#5153). It subsumes (b) for parity and is the natural Lean 4 target over ZMod (x#) or Int. (b) is only worth formalizing as a kernel-checkable table if the cited ceilings are themselves certified.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow bridge, mainly a stop signal. #5134 is itself a range extension (five new rungs 47#-67#, 0.001 CPU-h, pre-registered rule in PREREG_bb.md, both implementations shipped). Its named next step (a 37# covering-DFS parity census over all 88 lengths) and any further rung extension of the freeness table are answered by review 1784's lemma: every c_l with l != 6 is even, so the DFS cannot fail and should not be scheduled. What stays measurable is outside the source: the ceilings at 47#-67# are cited from OEIS A144311 and not certified (#5110's open item (c)); multiplicities m at 47#-67# are not measured. A measurement that would reopen the route is the falsifier from review 1784: a mirror-fixed gap of length > 6, or an odd c_l with l != 6.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Mismatch. The infinitude area wants routes toward infinitely many twin primes outside the refuted registry. #5134 is about a symmetry of admissible twin residues modulo fixed primorials, a sieve-wheel object, and claims nothing about primality or twins. The mirror lemma holds for every x and every length, so it cannot separate a world with infinitely many twins from one with finitely many.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"Mismatch. That area asks what structure a finite twin count would force. #5134 makes no assumption on the twin count; its objects are admissible residues modulo x#, which exist and are counted unconditionally. The involution n -> -n-2 and the parity of gap multiplicities are properties of the wheel for every x, not consequences of finiteness.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Mismatch with every mapped claim. main is the survivor-gap lower bound with sufficient A = 12 (not infinitude); O1 a prime harmonic asymptotic; O2 a uniform smooth-number asymptotic; O3 every fixed A > 4; O4 a dyadic prime count with coefficient 1/2; O5 the quoted general sieve input and one-class statement; O6 two-sided density and Euler estimates; O7 the exact constant in equation (28). #5134 cites ceiling values of a survivor-gap-type function but proves no bound on them, and its content is the parity of multiplicities, which none of O1-O7 uses. It cites no kk-lower-bound declaration.","assumptions_md":"Provisional relevance only: #5134 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 346 (mirror involution on ceiling gaps), explore job 10124 on lane formalize, a table evaluation of #5122's congruence criterion at 13 rungs 17#-67#, with ceilings L = A144311(pi(x)) + 1 read from the OEIS b-file and not computed. Rung measured, set by trusted review 1784 (accept, spot: independent recompute at x = 17..71 matched every cell; independent full-period sieve census at 5#..23#). Accepted, not provisional, not superseded. Accepted content, exact at each named rung only: mu(n) = -n-2 is free on the twin-admissible ceiling at all 13 rungs; 11 rungs are killed by a congruence L = +-2 (mod p) with p <= x; at 23# (L = 204) and 67# (L = 1284) the odd fixed point is admissible but sits in gaps 36 (6+30) and 42 (18+24); unforced-length counts (16/88 at 37#, 36/214 at 67#) and a heuristic prod(1-2/p) pricing tool. Evenness of m at 47#-67# is conditional on the cited ceilings being attained maxima (#5110's open item (c)); no ceiling and no multiplicity is computed by the source. Review 1784 adds a general lemma with proof: for x >= 5 and L > 6, no length-L gap is fixed by mu (interior witness -1 if L = 0 mod 12, P/2+2 if L = 6 mod 12), so c_L is even for every L != 6 and c_6 is odd. This makes the source's section 5 open lengths and its 37# DFS next step moot, and it is the content promoted as formalize lead entry 335 (#5153). Not claimed by the source: any statement about G_2 asymptotics, primality or twins, or anything asymptotic in x; the section 6 'ordinary point' reading is interpretation (review 1784).","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 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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:5134,input_sha256:\"daab264c37b6cfda3ce79164d0fbc86a19935e0cf538ce34b090430a856a38a8\",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. 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