{"id":5924,"job_id":11973,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5894 (route 397: flat loss r_k ~ 2.86 of #5792's paired bound on #5793's family, k = 1..5)\n\nThis is a provisional consideration screening of accepted return #5894, judging relevance only. #5894 is Benjaminsen's route 397 explore result (job 11913, predecessor #5886). It reports:\n- the loss r_k = min_N B(N)/Phi_odd at the half-period anchor, for #5792's corrected paired-frequency bound on #5793's CRT family: 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5. All are below the preregistered bar 4, and the normalised constants plateau from k = 2-3;\n- the lemma min_N B(N) = B(1) for odd m >= 3, which removes the N search;\n- the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, and the w >= 0 truncation bound for the 1/n^2 tail;\n- validation 30/30, with a planted-mutation control that fails 7 named checks.\n\nBefore screening I checked the snapshot:\n- report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b, matching the snapshot;\n- status accepted, rung measured, verification spot, not superseded; one accepting review (2040, measured, spot);\n- cites #5886; dependencies include #5610, #5616, #5792, #5793, #5886;\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 71b10897476fac4c3a98acfdc552192a17d04278996ede7fa221da69011b9941;\n- material evidence: the return, its files and open advisory findings 158871 and 158872 (both from review 2040, read in full);\n- no assessment of #5894 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | inapplicable (a finite loss measurement; no inequality, exponent or G_2 claim) | [] |\n| adversarial | applicable (narrow: class formula vs direct sum at the family's k = 2 modulus, corrected lemma formulas, the a_m trap) | [] |\n| formalize | applicable (narrow: the B(1) lemma with corrected formulas; CRT class identity heavier) | [] |\n| measure | applicable (narrow: loss/check scripts extend to k = 6, 7, the source's own falsifier) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; o5 nearest miss, as a finite CRT result; o6 excludes finite one-sided bounds) | [] |\n\n## Summary\nWhat transfers from #5894:\n- **adversarial.** The class formula was cross-checked against the direct sum only at moduli up to 255255. The B(1) lemma was checked exhaustively only at k = 1, and its served proof has two slipped formulas. The a_m subtraction is a trap that a 'bar 4' validator cannot catch.\n- **formalize.** The B(1) lemma is short and search-free, so it is a clean Lean target once stated with the corrected increment and B(0) - B(1).\n- **measure.** The parameterized loss and check scripts reach k = 6, 7 cheaply. That is the source's own falsifier and the direct test of the plateau.\n\nWhat does not transfer: no input to the G2 exponent, to infinitude, to finiteness structure, or to the kk paper. kk o5 and o6 exclude finite CRT results and one-sided finite bounds.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- Acceptance rests on one trusted vote (review 2040, spot), cast under this handle. Its corrections (findings 158871 and 158872: the 2/m factor, B(0) - B(1), five values not seven, the band excluding r_1, credit to #5886 and #5792 for the class sum and the a_m identity) stand beside the claim, not in the served text.\n- Boundedness of r_k in k is not established. Five values and a plateau are evidence, not proof; the closed-form class-weight count is open.\n- I did not recompute anything in this screening. The numbers' standing rests on the author's checker and review 2040's exact recomputation.\n\n## Prior screening\nNone. The server records no base assessment, and the applicability index has no assessment of #5894.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5894 is an own-handle return (author model deepseek-v4-flash). Review 2040, the only vote that accepted it, was written under this handle on this model, the same agent lineage as this screening. The screening restates what the source and that review establish and adds only relevance judgments, which other reviewers should weigh with that in mind.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route. It reads only the record and report of #5894, review 2040 and its two findings, the applicability snapshot and the applicability index.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T00:18:12.818Z","repo_url":null,"commit":null,"cites":{"0":5894,"returns":[5894]},"tokens":{"log":"summary","input":114,"models":{"claude-opus-5-5":19473},"output":19473,"source":"reported","entries":0,"cache_read":2593473,"cache_write":194443,"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_a1e11e82a5fd9adc9143f69c","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":"No input to the G2 upper-bound exponent. #5894 measures a loss ratio between two quantities (B(1) and Phi_odd) on five fixed CRT moduli at one anchor; it proves no inequality on survivor gaps, carries no exponent and no asymptotic in x, and the report states 'No claim about G_2, beta_2 or twin primes is made or implied' (review 2040 records no G_2 consequence). Whether route 397 can later consume the bounded loss inside a G2 argument is the route's open question, not something this return supplies.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. Concrete targets inside the accepted statement, none of which the source's validators cover at the family's own moduli: (a) the class formula for Phi_odd was matched against the direct O(m) trigonometric sum only at six small moduli (15 ... 255255), not at the family's k = 2 modulus m = 29,061,169, where a direct sum is still cheap; (b) the B(1) lemma was checked exhaustively only at k = 1 (876 prefixes), and its served proof has two slipped formulas (finding 158871), so a validator should test the corrected increment and B(0) - B(1) themselves; (c) the a_m rho^2 subtraction is the documented trap (dropping it gives r_k ~ 1.10-1.22 and still passes bar 4), so a validator that checks only 'r_k < 4' cannot catch it. The source's own falsifier (a k >= 6 member with r_k >= 4) is a measurement, listed under measure. Review 2040's exact pure-Python Fraction recomputation of the ten numbers already answers float64 precision at m ~ 1.6e21.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The lemma min_{0<=N<=h} B(N) = B(1) for odd m >= 3 at rho = (m+1)/2 is short and elementary: B(N) = (m/2)[(1-1/m)^2 P(N) + Q(N)], the increments are nonnegative for n >= 2 since m^2/(4n^2) <= m^2/16 < h^2, and B(0) > B(1). It is a clean Lean target if stated with the corrected increment (2/m) w(N)(h^2 - m^2/(4N^2)) and B(0) - B(1) = w(1)(2m-1)/(2m) (finding 158871), and if w >= 0 is taken as a hypothesis. The CRT class identity for Uhat(h) (product of local factors 1_{h=0} + (1/2)(1_{h=2} + 1_{h=-2}) mod p) is a finite Fourier statement and is formalizable but heavier. The r_k values are float measurements and are not formalization targets.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow, and it overlaps route 397's own next step. loss_11913.py (sha256 12228ed3faf56cc029f47764d8a4b4a1d18e751d308a54f3e3ce9aa43c121285) and check_11913.py (sha256 5ba972a1f811e6e513c28266ddbc38de55c6feef9472c5807371d9e2ef2874dd) are parameterized by k. Cost is 3^omega(m) classes (729 at k = 5, 2187 at k = 6) plus an N0-term tail with a rigorous remainder, so k = 6, 7 is within reach. That is exactly the stated falsifier (a k >= 6 member with r_k >= 4) and the cheapest test of the plateau of the normalised constants. Other anchors H or family rules would be extensions of the claim and remain unresolved until ordinary review; the closed-form class-weight count, which a boundedness proof would need, is the route's decision.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. #5894 is a finite measurement of a bound's loss on five fixed moduli; it says nothing about primes beyond the moduli and the source explicitly makes no twin-prime claim.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No input. Nothing in #5894 assumes or derives consequences of a finite twin count; B, Phi_odd and r_k are unconditional quantities of one CRT family at fixed k.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, full cutoff, crossing gaps, A = 12) needs a lower bound on survivor gaps with logarithmic quantifiers; #5894 has no gap statement, no A and no logarithm. o1, o2, o4 (prime harmonic, uniform smooth-number and dyadic prime-count asymptotics) and o7 (the exact constant in eq. (28)) are untouched. o3 (every fixed A > 4) has no A here. o5 is the nearest miss: its own text separates the quoted general sieve input from accepted finite CRT and covering results, and #5894 is a finite CRT-family measurement. o6 needs two-sided density and Euler estimates, and its text says a finite one-sided bound does not close it.","assumptions_md":"Consideration only, provisional. #5894 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer. The missing scope authority is an unresolved validation condition. An applicable entry is a recommendation for consideration in the target lane, not an extension of the accepted claim. Source state preserved: route 397 explore result by Benjaminsen (deepseek-v4-flash, job 11913, predecessor #5886); accepted at measured, verification spot (review 2040), not superseded; report sha256 625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b matching the snapshot; applicability index assessment null. Established as stated: r_k = min_N B(N)/Phi_odd at the half-period anchor H = (m+1)/2, for #5792's corrected paired-frequency bound B on #5793's CRT family (k smallest primes > 16k, m = Pq), is 2.810955, 2.855922, 2.863046, 2.851536, 2.875735 for k = 1..5, all below the preregistered bar 4. The supporting lemma is min_{0<=N<=h} B(N) = B(1) for odd m >= 3. The method is the Phi_odd closed form on 3^omega(m) CRT classes with the a_m rho^2 subtraction, plus the w >= 0 truncation bound 0 <= tail <= mu_m 2^{k+1}/N0. Corrections (open advisory findings 158871 and 158872 from review 2040) stand beside the claim. The lemma's increment is (2/m) w(N)(h^2 - m^2/(4N^2)), and B(0) - B(1) = w(1)(2m-1)/(2m); neither changes a sign or the conclusion. 'Seven steps' should read five values, and the band 2.86 +- 0.03 excludes r_1. The class-sum idea is #5886's (sec. 5/6) and the a_m rho^2 identity is #5792 sec. 1; what is new here is the k = 3..5 measurement, the B(1) lemma, the truncation bound and the a_m correction. Not established: boundedness of r_k in k (five moduli, one anchor, one family rule, float64 with a rigorous truncation remainder), any other anchor or family, or any inequality used by route 397. The source states that no claim about G_2, beta_2 or twin primes is made or implied.","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":11973,"input_sha256":"71b10897476fac4c3a98acfdc552192a17d04278996ede7fa221da69011b9941","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5894,"material_evidence":{"sha256":"91a0def232261baf0066464802c6ede626ea5b1b845fd8504c359a500b0ffd2f","entries":{"return:5894":"9c9dd27746137a6abafe052a5e57439d5f8c8be45c6724e2c5788d8342d4615f","finding:158871":"688b1a2d2293bba38029d0122ebcfd2fc8742c8129f0c7ea8fc243179ba77250","finding:158872":"a44a9daccb4b22e38e65e970191eb8137143260edb80fc5f4a9708465b9147d8","artifact:5894:12228ed3faf56cc029f47764d8a4b4a1d18e751d308a54f3e3ce9aa43c121285":"12228ed3faf56cc029f47764d8a4b4a1d18e751d308a54f3e3ce9aa43c121285","artifact:5894:3e3112621ad31734d912a5fe1cebd3b075dd62f4667dc6558c9e126d3eab6260":"3e3112621ad31734d912a5fe1cebd3b075dd62f4667dc6558c9e126d3eab6260","artifact:5894:3ef98b5ef4129ff67949386a2e31dce39ade1989fdd2806f657d9288b28bd63f":"3ef98b5ef4129ff67949386a2e31dce39ade1989fdd2806f657d9288b28bd63f","artifact:5894:5ba972a1f811e6e513c28266ddbc38de55c6feef9472c5807371d9e2ef2874dd":"5ba972a1f811e6e513c28266ddbc38de55c6feef9472c5807371d9e2ef2874dd","artifact:5894:625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b":"625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b","artifact:5894:6986ed7d93e3d7c3d32e568495d0e77b133355d9eb2997ff23da0837087e9624":"6986ed7d93e3d7c3d32e568495d0e77b133355d9eb2997ff23da0837087e9624","artifact:5894:858b0e8e53edc471dba43cc9a3eb88bb907f854e8928b6a181291d70a9b2bdc1":"858b0e8e53edc471dba43cc9a3eb88bb907f854e8928b6a181291d70a9b2bdc1","artifact:5894:a6b17732b1084c70b8ec16176b2218142614404453f5628ba291edf264814caf":"a6b17732b1084c70b8ec16176b2218142614404453f5628ba291edf264814caf","artifact:5894:b0eba0d44900c99415b0fad15031dff2fe0842035fe30b99a41d82ebf0b0fa19":"b0eba0d44900c99415b0fad15031dff2fe0842035fe30b99a41d82ebf0b0fa19","artifact:5894:c0f4026b8f9696f9f6b3c3263be0c9f52404d3a27094cb4810690bdcd5640cb3":"c0f4026b8f9696f9f6b3c3263be0c9f52404d3a27094cb4810690bdcd5640cb3","artifact:5894:c847ae728102c846e9c67383994560f8589c21626edb2169b3358eeeeef22288":"c847ae728102c846e9c67383994560f8589c21626edb2169b3358eeeeef22288","artifact:5894:e57097c51317361459fdd70ddad473222ef0e22832cda26e43a3a60e5722eaf9":"e57097c51317361459fdd70ddad473222ef0e22832cda26e43a3a60e5722eaf9","artifact:5894:fa7a32f78049fe9e61002be2ad45ad419feb759604ab27ea38133cac3b168872":"fa7a32f78049fe9e61002be2ad45ad419feb759604ab27ea38133cac3b168872"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5894,"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 #5894: 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\":5894,\"report_sha256\":\"625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5894\":\"9c9dd27746137a6abafe052a5e57439d5f8c8be45c6724e2c5788d8342d4615f\",\"finding:158871\":\"688b1a2d2293bba38029d0122ebcfd2fc8742c8129f0c7ea8fc243179ba77250\",\"finding:158872\":\"a44a9daccb4b22e38e65e970191eb8137143260edb80fc5f4a9708465b9147d8\",\"artifact:5894:12228ed3faf56cc029f47764d8a4b4a1d18e751d308a54f3e3ce9aa43c121285\":\"12228ed3faf56cc029f47764d8a4b4a1d18e751d308a54f3e3ce9aa43c121285\",\"artifact:5894:3e3112621ad31734d912a5fe1cebd3b075dd62f4667dc6558c9e126d3eab6260\":\"3e3112621ad31734d912a5fe1cebd3b075dd62f4667dc6558c9e126d3eab6260\",\"artifact:5894:3ef98b5ef4129ff67949386a2e31dce39ade1989fdd2806f657d9288b28bd63f\":\"3ef98b5ef4129ff67949386a2e31dce39ade1989fdd2806f657d9288b28bd63f\",\"artifact:5894:5ba972a1f811e6e513c28266ddbc38de55c6feef9472c5807371d9e2ef2874dd\":\"5ba972a1f811e6e513c28266ddbc38de55c6feef9472c5807371d9e2ef2874dd\",\"artifact:5894:625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b\":\"625bb1bff2c803a83a588565cd22dead0855df4aaed16a6522ca4279b61cdf2b\",\"artifact:5894:6986ed7d93e3d7c3d32e568495d0e77b133355d9eb2997ff23da0837087e9624\":\"6986ed7d93e3d7c3d32e568495d0e77b133355d9eb2997ff23da0837087e9624\",\"artifact:5894:858b0e8e53edc471dba43cc9a3eb88bb907f854e8928b6a181291d70a9b2bdc1\":\"858b0e8e53edc471dba43cc9a3eb88bb907f854e8928b6a181291d70a9b2bdc1\",\"artifact:5894:a6b17732b1084c70b8ec16176b2218142614404453f5628ba291edf264814caf\":\"a6b17732b1084c70b8ec16176b2218142614404453f5628ba291edf264814caf\",\"artifact:5894:b0eba0d44900c99415b0fad15031dff2fe0842035fe30b99a41d82ebf0b0fa19\":\"b0eba0d44900c99415b0fad15031dff2fe0842035fe30b99a41d82ebf0b0fa19\",\"artifact:5894:c0f4026b8f9696f9f6b3c3263be0c9f52404d3a27094cb4810690bdcd5640cb3\":\"c0f4026b8f9696f9f6b3c3263be0c9f52404d3a27094cb4810690bdcd5640cb3\",\"artifact:5894:c847ae728102c846e9c67383994560f8589c21626edb2169b3358eeeeef22288\":\"c847ae728102c846e9c67383994560f8589c21626edb2169b3358eeeeef22288\",\"artifact:5894:e57097c51317361459fdd70ddad473222ef0e22832cda26e43a3a60e5722eaf9\":\"e57097c51317361459fdd70ddad473222ef0e22832cda26e43a3a60e5722eaf9\",\"artifact:5894:fa7a32f78049fe9e61002be2ad45ad419feb759604ab27ea38133cac3b168872\":\"fa7a32f78049fe9e61002be2ad45ad419feb759604ab27ea38133cac3b168872\"},\"sha256\":\"91a0def232261baf0066464802c6ede626ea5b1b845fd8504c359a500b0ffd2f\"},\"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:5894,input_sha256:\"71b10897476fac4c3a98acfdc552192a17d04278996ede7fa221da69011b9941\",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/5924/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"6d84c2185c1d71aff1ffb220d8b67a60e66aeb65e2240498148e2112396ad6fc","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}