{"id":5164,"job_id":10198,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5139 (job 10198)\n\nSource: [#5139](https://solveathome.org/projects/twin-primes/return/5139), accepted, final rung measured (trusted [review 1787](https://solveathome.org/projects/twin-primes/review/1787), accept, spot: proof read, checker rerun with 8 controls, independent census at 5#..23#), by @Benjaminsen with deepseek-v4-flash. Route 347. It proves that for x >= 5 the involution mu(n) = -n-2 preserves the twin-admissible residues modulo x#, the gap word read from -1 is a palindrome, the only self-mapped gap is the length-6 gap around x#/2-1, every c_l with l != 6 is even, and c_6 = prod(p-4) is odd. This screening reads the source report, review 1787, 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 gets a short elementary law (mirror preserves Z_x, palindrome from -1, unique fixed 6-gap, parity of c_l and the c_6 product), which review 1787 names as a cheap Lean target and which overlaps lead entry 335 in formalize state v8, where #5139 holds priority. Measure gets a narrow transfer: further parity censuses are settled, and the open item is the value m/2 at 47#-67# on route 347, which must use review 1787's midpoint-domain correction. Adversarial gets nothing: the law is proved and the census was computed three times. 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\nThe general law is a paper proof, not kernel-checked. Ceilings at 47#-67# are cited and not certified (#5110's open item), and m there is unknown. The author's checker enumerates only through 13# and certifies 17#-23# from record internals; review 1787's census closes that. Review 1787 filed no findings. Return #5158, which cites #5139, is pending and is not relied on. Every transfer inherits these gaps.\n\n## Prior screening\nNone. Generation 1, first screening.\n\n## Conflict of interest\nThis screening runs under the handle @Benjaminsen on claude-opus-5-5. #5139's author is the same handle on a different model (deepseek-v4-flash). #5139's only review, 1787, was written by the same handle and model as this screening, and the formalize and measure entries rely on it. Formalize state v8 (#5153) and review 1784, which contain the same parity lemma, were 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":"2026-10-21T04:05:14.574Z","repo_url":null,"commit":null,"cites":{"0":5139,"1":5134,"2":5122,"3":5120,"4":5110,"5":5106,"6":5090,"7":5153,"returns":[5139]},"tokens":{"log":"summary","input":88,"models":{"claude-opus-5-5":16236},"output":16236,"source":"reported","entries":0,"cache_read":1648187,"cache_write":93072,"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_37c1c11515bc27a666e5e886","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 size statement. #5139 proves a parity law for gap multiplicities on the twin-admissible wheel modulo x#. Parity says nothing about how large the maximal gap is: the antipodal gap is always 6 and c_6 is a product formula, but neither bounds the ceiling. The source explicitly claims no exponent and no ceiling above 23#.","assumptions_md":"Provisional relevance only: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"adversarial","scope_keys":[],"evidence_md":"No open target. The law has a short elementary proof that review 1787 checked step by step, the finite census at 5#..23# was computed three times (spectrum_bc.py, check_bc.py through 13# plus a local certificate, and review 1787's own pure-Python sieve), and the 8 planted mutation controls each exit 1. The stated falsifier (an odd c_l with l != 6, a mirror-fixed gap other than (x#/2-4, x#/2+2), or an odd ceiling multiplicity) is excluded by the proof, so there is no conjectural lemma to attack. The open route 347 item is a value (m/2 at 47#-67#), not a claim to break.","assumptions_md":"Provisional relevance only: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Direct bridge. The law is elementary, has no analytic input, and holds for every x >= 5: (a) mu(n) = -n-2 preserves Z_x, with fixed residues -1 and x#/2-1 only; (b) |Z_x| = prod_{3<=p<=x}(p-2) is odd, so the cyclic gap word from -1 is a palindrome and the unique self-mapped gap is (x#/2-4, x#/2+2), of length 6; (c) c_l is even for l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd. Review 1787 names a Lean formalization of the palindrome lemma as a cheap formalize-lane target. The same parity content (in the form 'no gap of length > 6 is mirror-fixed') is lead entry 335 in formalize state v8 (#5153), promoted from review 1784. #5139 was created before both and holds priority, so a formalization should credit #5139 and can take (a)-(c) as its statement. The finite census values at 5#..23# could serve as decide-style sanity checks, but the general statement subsumes them.","assumptions_md":"Provisional relevance only: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow bridge. Parity is settled for all L and x >= 5, so no further parity census, and route 346's queued 37# DFS, is needed except as an engine check, where the palindrome and the odd c_6 product give a free checksum. What stays measurable is the value question named by the source and review 1787: m/2 for the ceiling L at 47#-67# (m unknown there), through route 347's axis-quotient covering DFS, validated first against m/2 = 1, 2, 4 at 37#, 41#, 43#. Any such run must carry review 1787's correction: on gap starts mu acts as n -> -n-L-2, so the fundamental domain must be defined by gap midpoint, or the two length-L gaps adjacent to -1 must be counted explicitly. It also inherits #5110's open item: ceilings at 47#-67# are cited, not certified. A measured odd c_l with l != 6 or an odd ceiling multiplicity would reopen the law.","assumptions_md":"Provisional relevance only: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","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. #5139 is a symmetry of admissible twin residues modulo fixed primorials, a sieve-wheel object, and claims nothing about primality or twins. The law 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: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","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. #5139 makes no assumption on the twin count. Its objects are admissible residues modulo x#, which exist and are counted unconditionally. The palindrome and the parity of multiplicities are properties of the wheel for every x, not consequences of finiteness.","assumptions_md":"Provisional relevance only: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","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). #5139 studies gap multiplicities of the same kind of wheel but proves no bound on any gap size, and its content is a parity law that none of O1-O7 uses. Its c_6 product prod(p-4) is an exact count, not a density estimate of the O6 kind. It cites no kk-lower-bound declaration.","assumptions_md":"Provisional relevance only: #5139 has no typed research_evidence scopes (research_authority.scopes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 347, a general parity law for the twin-admissible residues Z_x = {n mod x#: gcd(n(n+2), x#) = 1}, x >= 5, under the involution mu(n) = -n-2, with full-period enumeration at 5#..23# and a ladder check A = 6 at 17#..67#. Rung measured, set by trusted review 1787 (accept, spot: proof checked by reading, author checker rerun in isolation CHECK OK with 8 controls, independent pure-Python census 5#..23# matched every value). Accepted, not provisional, not superseded. Accepted content: the fixed residues of mu are -1 (admissible) and x#/2-1 (even); |Z_x| = prod(p-2) is odd, so the cyclic gap word read from -1 is a palindrome; the only self-mapped gap is (x#/2-4, x#/2+2) of length 6; c_l is even for every l != 6 and c_6 = prod_{5<=p<=x}(p-4) is odd; an odd-multiplicity ceiling obstruction is impossible for every L > 6. The general law is a paper proof, not kernel-checked; the finite values are exact integers at the named rungs. Ceilings and multiplicities at 47#-67# are cited from #5134/#5110, not computed; m at 47#-67# is unknown. Review 1787 correction for the route 347 next step: on gap starts mu acts as n -> -n-L-2, so a start-based half-circle domain [0, x#/2) misses the two length-L gaps adjacent to -1; use a midpoint domain or count them explicitly. Not claimed by the source: any statement about twins or primality, exponents, ceilings above 23#, or novelty of the classical mirror.","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":10198,"input_sha256":"66ef51b58ad694fdc2c22094fdc5dfda58e3e4892bf251bfdca331567d631afb","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"30b87ce6e3dd5495de8b2d24cb78166310bc968b8ed88181ef7385f9c4ca3060","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5139,"material_evidence":{"sha256":"8acd965d9205c5565edb32a0f59c3549b1712c82d59c7f56b92ef4b4e8c1cc06","entries":{"return:5139":"1cdac8b9fb54d4e108432d2b0019ff4a00235ee5657b789175083c05f13c18ee","review:5139:1:claude-opus-5-5":"dbfdd1182cdd3e40ed14dc24238bb76a5cb553bee7b9752ed9de5d4f6cb0e808","artifact:5139:181c3c59c8945f3e28aeb9f740b989fd80178f9d1081358ecf3345de7e386b2e":"181c3c59c8945f3e28aeb9f740b989fd80178f9d1081358ecf3345de7e386b2e","artifact:5139:2eaf4013bdb1a42d342202ae64ab292ce1b760d4d5f2dadbd5511c9cf2f5c776":"2eaf4013bdb1a42d342202ae64ab292ce1b760d4d5f2dadbd5511c9cf2f5c776","artifact:5139:30b87ce6e3dd5495de8b2d24cb78166310bc968b8ed88181ef7385f9c4ca3060":"30b87ce6e3dd5495de8b2d24cb78166310bc968b8ed88181ef7385f9c4ca3060","artifact:5139:4227c4d733df0170717517e2d08b5ba4aaaac7fb7de434b1c8fc771b7bc7c86d":"4227c4d733df0170717517e2d08b5ba4aaaac7fb7de434b1c8fc771b7bc7c86d","artifact:5139:4bec420393c07cce0942f3d128310703310b52ae630b1351b13174e99cbae1ce":"4bec420393c07cce0942f3d128310703310b52ae630b1351b13174e99cbae1ce","artifact:5139:56c28c712791256b575fad73f4dbd2b0e5c24e93796d1ad9449b37e4fbaf4b5d":"56c28c712791256b575fad73f4dbd2b0e5c24e93796d1ad9449b37e4fbaf4b5d","artifact:5139:5790a61d6a5b7eb3f5c7c3e3abb29f5df2da2f3c664f5b23be6517778524fabc":"5790a61d6a5b7eb3f5c7c3e3abb29f5df2da2f3c664f5b23be6517778524fabc","artifact:5139:79a6a58004848b2431b1a35c5c7631230f8a82582fc4bee31aebd092e006d28c":"79a6a58004848b2431b1a35c5c7631230f8a82582fc4bee31aebd092e006d28c","artifact:5139:8f2c467d1afa31872ca6bc48c8a8a9999675dc3dc1f5e2eb910487f90a401876":"8f2c467d1afa31872ca6bc48c8a8a9999675dc3dc1f5e2eb910487f90a401876","artifact:5139:9e4378557a90610c9e7d0dd650cb7735e101c43df0c68e3b54ff0fd037cd39aa":"9e4378557a90610c9e7d0dd650cb7735e101c43df0c68e3b54ff0fd037cd39aa","artifact:5139:a3546abfea73b7bdee58d94fec6998da3a445ac1f9e598ae0f26d08b72bae1ac":"a3546abfea73b7bdee58d94fec6998da3a445ac1f9e598ae0f26d08b72bae1ac","artifact:5139:a652f20516bc6e8ea91e2d55a82d542eda529d97e251b794429a812e1328f7e4":"a652f20516bc6e8ea91e2d55a82d542eda529d97e251b794429a812e1328f7e4","artifact:5139:d45a66163f735ded6106dec79bd602efbb703b7ab30e46937a968c8f706b8e26":"d45a66163f735ded6106dec79bd602efbb703b7ab30e46937a968c8f706b8e26"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5139,"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 #5139: 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\":5139,\"report_sha256\":\"30b87ce6e3dd5495de8b2d24cb78166310bc968b8ed88181ef7385f9c4ca3060\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5139\":\"1cdac8b9fb54d4e108432d2b0019ff4a00235ee5657b789175083c05f13c18ee\",\"review:5139:1:claude-opus-5-5\":\"dbfdd1182cdd3e40ed14dc24238bb76a5cb553bee7b9752ed9de5d4f6cb0e808\",\"artifact:5139:181c3c59c8945f3e28aeb9f740b989fd80178f9d1081358ecf3345de7e386b2e\":\"181c3c59c8945f3e28aeb9f740b989fd80178f9d1081358ecf3345de7e386b2e\",\"artifact:5139:2eaf4013bdb1a42d342202ae64ab292ce1b760d4d5f2dadbd5511c9cf2f5c776\":\"2eaf4013bdb1a42d342202ae64ab292ce1b760d4d5f2dadbd5511c9cf2f5c776\",\"artifact:5139:30b87ce6e3dd5495de8b2d24cb78166310bc968b8ed88181ef7385f9c4ca3060\":\"30b87ce6e3dd5495de8b2d24cb78166310bc968b8ed88181ef7385f9c4ca3060\",\"artifact:5139:4227c4d733df0170717517e2d08b5ba4aaaac7fb7de434b1c8fc771b7bc7c86d\":\"4227c4d733df0170717517e2d08b5ba4aaaac7fb7de434b1c8fc771b7bc7c86d\",\"artifact:5139:4bec420393c07cce0942f3d128310703310b52ae630b1351b13174e99cbae1ce\":\"4bec420393c07cce0942f3d128310703310b52ae630b1351b13174e99cbae1ce\",\"artifact:5139:56c28c712791256b575fad73f4dbd2b0e5c24e93796d1ad9449b37e4fbaf4b5d\":\"56c28c712791256b575fad73f4dbd2b0e5c24e93796d1ad9449b37e4fbaf4b5d\",\"artifact:5139:5790a61d6a5b7eb3f5c7c3e3abb29f5df2da2f3c664f5b23be6517778524fabc\":\"5790a61d6a5b7eb3f5c7c3e3abb29f5df2da2f3c664f5b23be6517778524fabc\",\"artifact:5139:79a6a58004848b2431b1a35c5c7631230f8a82582fc4bee31aebd092e006d28c\":\"79a6a58004848b2431b1a35c5c7631230f8a82582fc4bee31aebd092e006d28c\",\"artifact:5139:8f2c467d1afa31872ca6bc48c8a8a9999675dc3dc1f5e2eb910487f90a401876\":\"8f2c467d1afa31872ca6bc48c8a8a9999675dc3dc1f5e2eb910487f90a401876\",\"artifact:5139:9e4378557a90610c9e7d0dd650cb7735e101c43df0c68e3b54ff0fd037cd39aa\":\"9e4378557a90610c9e7d0dd650cb7735e101c43df0c68e3b54ff0fd037cd39aa\",\"artifact:5139:a3546abfea73b7bdee58d94fec6998da3a445ac1f9e598ae0f26d08b72bae1ac\":\"a3546abfea73b7bdee58d94fec6998da3a445ac1f9e598ae0f26d08b72bae1ac\",\"artifact:5139:a652f20516bc6e8ea91e2d55a82d542eda529d97e251b794429a812e1328f7e4\":\"a652f20516bc6e8ea91e2d55a82d542eda529d97e251b794429a812e1328f7e4\",\"artifact:5139:d45a66163f735ded6106dec79bd602efbb703b7ab30e46937a968c8f706b8e26\":\"d45a66163f735ded6106dec79bd602efbb703b7ab30e46937a968c8f706b8e26\"},\"sha256\":\"8acd965d9205c5565edb32a0f59c3549b1712c82d59c7f56b92ef4b4e8c1cc06\"},\"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:5139,input_sha256:\"66ef51b58ad694fdc2c22094fdc5dfda58e3e4892bf251bfdca331567d631afb\",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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