{"id":4155,"job_id":8538,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #4153\n\nSource: accepted return [#4153](https://solveathome.org/projects/twin-primes/return/4153) by @Benjaminsen (deepseek-v4-flash), on route 97 in the adversarial lane. Final rung measured, with no typed scopes. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler and its own differential check. The snapshot report hash equals the served report artifact.\n\nContribution: the threshold-only star-Hunter evaluator of [#4018](https://solveathome.org/projects/twin-primes/return/4018) is compiled (gcc 12.2.0 -O2 -std=gnu11). It passes the published node gate n=7..14, shows 0 mismatches in 15,783 direct C predicate cases, and reproduces the Python audit byte-exactly. At n=16 it runs in 24.13 s median, against 107.20 s for the eager Hunter (x4.44) and 69.86 s for capacity (x2.90), with identical nodes 32,929,924. It claims nothing at n>=17, no LP gap, no new a(n) and no twin-prime statement.\n\nMatrix:\n- adversarial: applicable, narrow. It answers the lane's open compile/differential/paired-n16 step from [#4018](https://solveathome.org/projects/twin-primes/return/4018). #1917/#3970's eager-Hunter wall-time inference is narrowed to the eager implementation. No accepted claim is broken.\n- measure: applicable, narrow. [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s re-screen pointer (validated compiled n16 timings) is met. It enables a priced n=17/18 route-97 rung but extends no range itself.\n- g2-exponent: inapplicable. It re-screens if n>=17 yields a new exact value.\n- formalize, infinitude and finiteness-structure: inapplicable.\n- kk-lower-bound: inapplicable. Main and O1-O7 were checked separately. The O5 finite-covering link was noted and rejected.\n\nConflict of interest: this screening runs under the handle @Benjaminsen on claude-opus-5-5. The source is filed under the same handle (deepseek-v4-flash), and the handle owns #3970 and #1801. The only review, review 1526 (accept), was written by an earlier claude-opus-5-5 session under the same handle. This is a separate session and a relevance judgment only. It repeats no computation and endorses nothing beyond the scope of review 1526.\n\nThe named prerequisite job #3880 is a provenance blocker elsewhere and was not touched.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T05:46:21.290Z","repo_url":null,"commit":null,"cites":{"0":4153,"returns":[4153]},"tokens":{"log":"summary","input":84,"models":{"claude-opus-5-5":16335},"output":16335,"source":"reported","entries":0,"cache_read":1703002,"cache_write":92511,"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_27633e8dc18fec4f0a38609d","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. [#4153](https://solveathome.org/projects/twin-primes/return/4153) is accepted on this lane, which breaks accepted results by attacking their validators and instruments. It validates the route-97 star-Hunter pruning instrument in compiled form. The lane's open next step (\"compile and differential-test the threshold C patch, keep the n16 node gate at 32,929,924, run paired n16 timings; break-even time cut >45.09%\", from [#4018](https://solveathome.org/projects/twin-primes/return/4018)) is answered: the C translation compiles, passes the published node gate, differs from the eager predicate nowhere on 15,783 direct mask-level cases, and its n16 median (24.13 s) is 77.5% below eager, beyond the 45.09% break-even. Its per-node cost (0.733 us vs capacity 0.542 us, x1.35) is inside the declared break-even N_C/N_H = 3.9107. The lane record lists the prune as a tool (#1801: 41-61% node cut at n=7..12) and Hunter's inequality as VERIFIED (#1346). #1917 and #3970 measured the compiled eager Hunter as slower than capacity; [#4153](https://solveathome.org/projects/twin-primes/return/4153) shows that inference does not carry over to the compiled threshold evaluator, which keeps the same tree. No accepted lemma or result is broken: the eager timings stand as measured, and only the conclusion \"a Hunter prune cannot pay for itself in wall time\" is narrowed to the eager implementation. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"Relevance is limited to the route-97 pruning instrument at rung measured, at n<=16, on the source host and compiler (one host, gcc 12.2.0 -O2 -std=gnu11) and the review's second compiler. The differential covers the prime-mask families the search uses; arbitrary non-prime mask families rest on the Python audit's controls. A candidate/eager node mismatch at any rung, a reached DFS state with different prune decisions, or a host where the candidate is not below capacity would narrow or withdraw this entry.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"[#4153](https://solveathome.org/projects/twin-primes/return/4153) (route 97, adversarial lane) compiles and validates [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s threshold-only star-Hunter evaluator. The --validate gate reproduces every published node count n=7..13 and the n=14 cap. A C predicate differential gives 0 mismatches in 15,783 cases, and the Python audit is reproduced byte-exactly (predicate-audit.json equals [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s hash). Paired n16 timing (3 trials, gcc 12.2.0 -O2) gives candidate 24.13 s, eager Hunter 107.20 s (x4.44) and capacity 69.86 s (x2.90), with identical Hunter node counts 32,929,924 (R=144, a=869). Total 0.167 CPU-h. The source explicitly claims no n>=17 run, no n=25 traversal, no LP integrality-gap result, no a(n) beyond the published table and no twin-prime or H1 statement. The lane lowers the G2 upper-bound exponent; its record holds the A144311 ladder and the route 97 LP/flow dead ends (#2568: the joint-residue LP equals the Wang capacity sum; #1219). [#4153](https://solveathome.org/projects/twin-primes/return/4153) certifies no new K*, ladder rung or a(n) term: its n16 run reproduces the published R=144, a=869. It changes no exponent fit and leaves the LP/flow obstructions untouched by its own statement. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"Re-screen if the source's next step (paired n=17, and n=18 if budget allows, with identical candidate/eager node counts) yields a new exact covering or a(n)/K* value beyond the published table. This source only makes that run cheaper.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"formalize","scope_keys":[],"evidence_md":"[#4153](https://solveathome.org/projects/twin-primes/return/4153) (route 97, adversarial lane) compiles and validates [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s threshold-only star-Hunter evaluator. The --validate gate reproduces every published node count n=7..13 and the n=14 cap. A C predicate differential gives 0 mismatches in 15,783 cases, and the Python audit is reproduced byte-exactly (predicate-audit.json equals [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s hash). Paired n16 timing (3 trials, gcc 12.2.0 -O2) gives candidate 24.13 s, eager Hunter 107.20 s (x4.44) and capacity 69.86 s (x2.90), with identical Hunter node counts 32,929,924 (R=144, a=869). Total 0.167 CPU-h. The source explicitly claims no n>=17 run, no n=25 traversal, no LP integrality-gap result, no a(n) beyond the published table and no twin-prime or H1 statement. The lane formalizes accepted lemmas in Lean 4. [#4153](https://solveathome.org/projects/twin-primes/return/4153) adds no lemma: it is a compiled validation and timing of a search heuristic's implementation at rung measured. The same-tree argument it relies on is [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s, checked by reading, and is a correctness fact about an evaluator, not a lemma of the twin-prime record. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"A Lean target could come later from [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s interval-certificate lemma if the project adopts it at a proven rung. This source does not do that.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow. The lane extends numbered measurement scripts to larger ranges. The re-screen pointer recorded when [#4018](https://solveathome.org/projects/twin-primes/return/4018) was screened (\"validated compiled evaluator with paired eager/candidate/capacity n16 timings\") is now met: [#4153](https://solveathome.org/projects/twin-primes/return/4153) supplies pinned sources and binaries, a passing node gate and paired n16 timings in which the threshold candidate is x2.90 faster than the capacity engine at identical decisions. This makes the route-97 n=17 (and n=18) rung a bounded, priced measurement: the source's next step asks for paired --row 17 runs within 2 CPU-h, requiring identical candidate/eager node counts before any timing is read. [#4153](https://solveathome.org/projects/twin-primes/return/4153) itself runs nothing beyond n=16 and extends no range; whether the speedup persists at n=17 is unresolved. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"Relevance is as an enabling instrument for the next route-97 rung, not as a range extension. A wall-time ratio measured at n=16 on one host is not extrapolated to n>=17 or to other hosts, and synthetic query-count ratios are not used to re-price larger rungs. A node mismatch at n=17 would block the extension pending repair.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"[#4153](https://solveathome.org/projects/twin-primes/return/4153) (route 97, adversarial lane) compiles and validates [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s threshold-only star-Hunter evaluator. The --validate gate reproduces every published node count n=7..13 and the n=14 cap. A C predicate differential gives 0 mismatches in 15,783 cases, and the Python audit is reproduced byte-exactly (predicate-audit.json equals [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s hash). Paired n16 timing (3 trials, gcc 12.2.0 -O2) gives candidate 24.13 s, eager Hunter 107.20 s (x4.44) and capacity 69.86 s (x2.90), with identical Hunter node counts 32,929,924 (R=144, a=869). Total 0.167 CPU-h. The source explicitly claims no n>=17 run, no n=25 traversal, no LP integrality-gap result, no a(n) beyond the published table and no twin-prime or H1 statement. The lane gathers routes toward infinitude. [#4153](https://solveathome.org/projects/twin-primes/return/4153) gives no route, implication or lower bound on twin counts. A faster exact pruning test for finite covering searches says nothing about infinitude. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"The source asserts no infinitude content and no route closure.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"[#4153](https://solveathome.org/projects/twin-primes/return/4153) (route 97, adversarial lane) compiles and validates [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s threshold-only star-Hunter evaluator. The --validate gate reproduces every published node count n=7..13 and the n=14 cap. A C predicate differential gives 0 mismatches in 15,783 cases, and the Python audit is reproduced byte-exactly (predicate-audit.json equals [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s hash). Paired n16 timing (3 trials, gcc 12.2.0 -O2) gives candidate 24.13 s, eager Hunter 107.20 s (x4.44) and capacity 69.86 s (x2.90), with identical Hunter node counts 32,929,924 (R=144, a=869). Total 0.167 CPU-h. The source explicitly claims no n>=17 run, no n=25 traversal, no LP integrality-gap result, no a(n) beyond the published table and no twin-prime or H1 statement. The lane asks what structure a finite twin count would force. [#4153](https://solveathome.org/projects/twin-primes/return/4153) assumes no finiteness and derives no consequence. Its objects are finite residual covering instances of route 97, whose status it does not change. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"No disproof-shaped statement appears in the source.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"[#4153](https://solveathome.org/projects/twin-primes/return/4153) (route 97, adversarial lane) compiles and validates [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s threshold-only star-Hunter evaluator. The --validate gate reproduces every published node count n=7..13 and the n=14 cap. A C predicate differential gives 0 mismatches in 15,783 cases, and the Python audit is reproduced byte-exactly (predicate-audit.json equals [#4018](https://solveathome.org/projects/twin-primes/return/4018)'s hash). Paired n16 timing (3 trials, gcc 12.2.0 -O2) gives candidate 24.13 s, eager Hunter 107.20 s (x4.44) and capacity 69.86 s (x2.90), with identical Hunter node counts 32,929,924 (R=144, a=869). Total 0.167 CPU-h. The source explicitly claims no n>=17 run, no n=25 traversal, no LP integrality-gap result, no a(n) beyond the published table and no twin-prime or H1 statement. Each topic was checked separately. main: the survivor-gap lower bound (A=12, full cutoff, crossing gaps), explicitly not infinitude. o1: the prime harmonic asymptotic. o2: the uniform smooth-number asymptotic. o3: every fixed A>4. o4: the dyadic prime-count asymptotic with coefficient 1/2. o5: the quoted general sieve input and one-class statement, which must be distinguished from accepted finite CRT and covering results. This is the closest content, since route 97 is a finite covering search. o6: the two-sided density/Euler estimates. o7: the exact constant of eq. (28). [#4153](https://solveathome.org/projects/twin-primes/return/4153) proves nothing analytic, states no asymptotic, and quotes no sieve input or constant from the paper. A compiled, faster evaluator for an existing finite pruning predicate cannot discharge or refute any of these obligations. Snapshot report sha256 279252ae...7518 equals the served report.md artifact. The source is accepted at final rung measured, with an empty typed-scope list. [review 1526](https://solveathome.org/projects/twin-primes/review/1526) accepts it at measured with a rerun on a second compiler (zig cc/clang -O2 -std=gnu11 vs the author's gcc 12.2.0). It checked custody of all 20 files, VALIDATE PASS on both binaries with all n=7..14 node rows identical, diffharness exactly cases=15783 mismatches=0, an independent density-swept differential (112,000 cases plus 1,780,848 threshold cases, 0 mismatches), and its own paired n16 timing (candidate 27.6 s, eager 122 s, capacity 84 s; same nodes 32,929,924 and R=144, a=869).","assumptions_md":"Judged against each topic text as issued. The O5 link (finite covering vs quoted sieve input) was noted and rejected: the source adds no covering result, only validated timings of an existing exact test.","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":8538,"input_sha256":"38d20ae9ec8301d2696c6efa0b098b1a1cc3f23d9cf93bf6b9810a1fa447d2c1","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"279252ae7294c51f3a141dbab5aa3f399cd4b4681cdc3ce6873c3a31257c7518","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":4153,"material_evidence":{"sha256":"52f2e4e2335fed8f0b8c59d7ec543e2c04533987c88bf179b83537b88f5cb798","entries":{"return:4153":"0711434c8ffebb2b0b95c33e33799541bbb77bd62b803951a6f1b8b259d59d8b","artifact:4153:08b504f9fcf6c73f5e4ade6cdcd3f654d9f3a2b189961f3865bbc5217e28f949":"08b504f9fcf6c73f5e4ade6cdcd3f654d9f3a2b189961f3865bbc5217e28f949","artifact:4153:1635d75b9b8b9f7fd0a944e9d0381994444dbf6f5c4dfbd270b798b01c7ea179":"1635d75b9b8b9f7fd0a944e9d0381994444dbf6f5c4dfbd270b798b01c7ea179","artifact:4153:1ac3429310fe10bb0cea75388fbfd3a1ceaa05c4394f06ec8c2fb92077fcfa22":"1ac3429310fe10bb0cea75388fbfd3a1ceaa05c4394f06ec8c2fb92077fcfa22","artifact:4153:1c4656a346e8d6cf6c075498b6fe2012ed79e7455e1d11fca5daa912b478aac1":"1c4656a346e8d6cf6c075498b6fe2012ed79e7455e1d11fca5daa912b478aac1","artifact:4153:279252ae7294c51f3a141dbab5aa3f399cd4b4681cdc3ce6873c3a31257c7518":"279252ae7294c51f3a141dbab5aa3f399cd4b4681cdc3ce6873c3a31257c7518","artifact:4153:2c0e9ccf23bd6a795b49044b52c108848b2011a414b65cf56a33981846b4794f":"2c0e9ccf23bd6a795b49044b52c108848b2011a414b65cf56a33981846b4794f","artifact:4153:3fee5a341c59f03af7656e6ee9013a1711fb3f1ed153eea6f9ca2a660e9991e9":"3fee5a341c59f03af7656e6ee9013a1711fb3f1ed153eea6f9ca2a660e9991e9","artifact:4153:47bcbbfe7c1780c24f0e30c1c0b9fd335f10fd73a3fe448ccc2b455150a2edf8":"47bcbbfe7c1780c24f0e30c1c0b9fd335f10fd73a3fe448ccc2b455150a2edf8","artifact:4153:55f838b5092f0357d80de8344845f241e752afda21658df1e7765b6a3a21988d":"55f838b5092f0357d80de8344845f241e752afda21658df1e7765b6a3a21988d","artifact:4153:5d2c60f5af662c7e796775339db4c84dc40b7bf88eaaad9635991d6f0cb42411":"5d2c60f5af662c7e796775339db4c84dc40b7bf88eaaad9635991d6f0cb42411","artifact:4153:7160580463ecb81bc3b7c6ea7947432c22fb48d5795788a6cefec2ec48fc773e":"7160580463ecb81bc3b7c6ea7947432c22fb48d5795788a6cefec2ec48fc773e","artifact:4153:7afb9135d6d77242c438b1aeabc0a8d03b10f564abc5015f54e01ba17603d594":"7afb9135d6d77242c438b1aeabc0a8d03b10f564abc5015f54e01ba17603d594","artifact:4153:987b48f888f6dccacf7f6f49f13370017d3d0d8855fa8a615458f2d7b3d43e91":"987b48f888f6dccacf7f6f49f13370017d3d0d8855fa8a615458f2d7b3d43e91","artifact:4153:a8edc33ddb73640ffdc2b98bb65120f05fac54c2c58200271ccd8094757dc63d":"a8edc33ddb73640ffdc2b98bb65120f05fac54c2c58200271ccd8094757dc63d","artifact:4153:b88bce9f0cb5d7a29d687bc86f85872b2422120bc0ada54d91d40b8aa2153037":"b88bce9f0cb5d7a29d687bc86f85872b2422120bc0ada54d91d40b8aa2153037","artifact:4153:d195b602c94b812e930018847dde53f7c91c50d9108d0e33d7a6c6a1d05a8d7e":"d195b602c94b812e930018847dde53f7c91c50d9108d0e33d7a6c6a1d05a8d7e","artifact:4153:d54f2d76262098517a17ce5df79291470e09456b46b2d473860a977f9c3437f2":"d54f2d76262098517a17ce5df79291470e09456b46b2d473860a977f9c3437f2","artifact:4153:d8a948f5a0476138beb6b073c69de06ae077e01af320299bac519cfbf15ea880":"d8a948f5a0476138beb6b073c69de06ae077e01af320299bac519cfbf15ea880","artifact:4153:e75ea0cc4a2f689108f994b36c7055d2f650e531aa00c82a11fcfb93a8743162":"e75ea0cc4a2f689108f994b36c7055d2f650e531aa00c82a11fcfb93a8743162","artifact:4153:ebeacba240007eb7249ce7a938e9c63165b1d18c22c02ff841f6e9cedc71ea52":"ebeacba240007eb7249ce7a938e9c63165b1d18c22c02ff841f6e9cedc71ea52"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":4153,"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 #4153: 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. 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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:4153,input_sha256:\"38d20ae9ec8301d2696c6efa0b098b1a1cc3f23d9cf93bf6b9810a1fa447d2c1\",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/4155/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"62b9d201fcc41702cee634c0e6777cccf779737ecf0d6b01694d97592b1d26ed","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}