{"id":3674,"job_id":7335,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Applicability screening of return #1927\n\nAdministrative, provisional relevance judgment for job #7335; no new scientific claim, verdict, experiment, proof rerun, artifact or route change. Source rung remains **measured**. The report's **heuristic** label describes possible relevance only.\n\n## Snapshot and authority\nThe current served source is trusted-accepted, measured, non-provisional, not superseded; its report SHA-256 is 52617c85dddfb8bb46714cb1d84cfb0f44dba3e58aa881482034611c0bc38989, matching the issued snapshot and a direct hash of its UTF-8 report. Review #1204's full text and scientific judgment match the assigned source context, including its spectrum corrections. All four artifact hash declarations match the issued set; their original bytes were not downloaded or independently rehashed in this screening. No typed source scopes or scope assessments exist. Every matrix scope_keys is therefore []; all positive relevance remains provisional and cannot transfer automatically.\n\nThe live research-applicability index reports bounded=true and lists 24 newer sources, omitting #1927. That omission is not evidence of withdrawal or staleness. Its seven target domains match the issued domains. Source currentness was checked directly through return #1927 and its current review. I did not reconstruct the server's private material-fingerprint algorithm; the issued input hash is preserved unchanged.\n\n## Source evidence and restrictions\nThe source evaluates q=x# at x=11,13,17,19, dimensions 1 and 2, using float64 full-period FFTs, Python half-even h=round(x^2*2^(j/2)), j=-10..12, 4<h<q, KMAX=64 and bandwidth 2/h. Review #1204 retains its finite certificate success: dim 2 h_true/h_m=144/204 at x=17 and 180/255 at x=19, with minorant k=15 in each; exponent penalties 0.12293698072505788 and 0.11829305913034073. They satisfy the source's prospective <=0.15 branch. Across eight cells the displayed penalty is 0-2 grid steps, maximum 0.273. These are historical observations, not new measurements.\n\nThe reviewer corrects 5,005/76,076 to rFFT counts including DC; full signed nonzero support slots are 10,008/152,150. These are support slots, not necessarily nonzero weighted coefficients. The centred strict band excludes d<=h/2, so the report's universal-denominator claim is false. Large denominators remain possible. Uncertified numerical error, truncated spatial checking, sampled grid, fixed KMAX and x<=19 prevent a verified/proven numerical or asymptotic extension.\n\n## Applicability matrix\n| Area | Decision | Scope keys | Evidence and limits |\n|---|---|---|---|\n| g2-exponent | applicable (provisional relevance only) | [] | Return #1927, Setup, Result and What this changes, with review #1204: the explicit signed Selberg minorant at bandwidth 2/h isolates the low-frequency weighted phase-cancellation quantity for every-window positivity. In dimension 2 the first sampled minorant certificates occur at h=204,k=15 for x=17 and h=255,k=15 for x=19, versus true-count grid certificates 144,k=11 and 180,k=13. Reviewed exponent penalties are 0.12293698072505788 and 0.11829305913034073, both below the prospective 0.15 threshold. This is relevant finite evidence for upper-gap mechanisms, not an improvement of the 4.26645028... asymptotic exponent. Route 143 revision 14 and accepted #2551/review #682 show the denominator-partition follow-up already progressed; do not treat the original next step as fresh work. A uniform-in-x worst-position cancellation/moment estimate, with all losses paid, would be required for an asymptotic upper bound. Review #1204 corrects the signed nonzero support counts to 10,008 and 152,150 and excludes d<=h/2 from the centred band; large d remains possible. #2551 retains conditional recorded upstream small/top inputs. |\n| adversarial | applicable (provisional relevance only) | [] | Return #1927, Gates and Result, and review #1204 identify concrete validation targets: minorant inequality, FFT normalization/conjugation, first-certifying grid cell/order and strict positivity margins. Historical worst gate values are 2.22e-16, 5.112e-7 and 6.217e-15 for pointwise excess, spatial-form discrepancy and direct-correlation error. At the true-count grid lengths the reviewed signed minorant minima are -0.1641 and -0.2049 for x=17,19, dimension 2, so increasing k cannot certify those particular counts. These finite observations and corrected spectrum assertions help specify adversarial falsifiers without rerunning them. Gates are floating-point observations, not interval proofs; the spatial comparison uses 201 period images and only q>=20h. A failed gate would concern its exact tested premise, not automatically refute the route, the accepted lower-bound theorem or twin-prime infinitude. No new counterexample search was performed. |\n| formalize | applicable (provisional relevance only) | [] | Return #1927, Setup, and review #1204 isolate a conditional finite certificate implication: if the finite sum over N of (abs(X_m(N))/mean_m)^(2k) is strictly below 1, mean_m>0, t>=0 and m<=the window indicator, then every signed count S_m is positive and S_h>=S_m>0. The current reviewer accepts this implication conditional on the minorant premise and numerical bounds. This supplies a precise candidate lemma and statement restrictions for formalization, rather than an already formalized analytic theorem. An exact formal proof would separately need the definitions, periodisation, Fourier normalization, minorant premise and adequate numerical evidence; historical float64 values cannot be asserted as exact Lean premises. There is no Lean package or kernel receipt for #1927. This relevance judgment grants no proof rung and imports no accepted scope into Lean. |\n| measure | applicable (provisional relevance only) | [] | Return #1927 has four immutable artifacts, an eight-cell sampled-grid table and documented gates and controls; its report/recipe provide the finite reference experiment. Review #1204 reports an existing 127-check source/data audit over 174 rows and 159 shared baseline rows, not a new execution in this screening. At x=17,19 the dimension-2 minorant lengths are 204 and 255; exact least empty-free lengths recorded in the source are 108 and 150. #2551/review #682 and route 143 revision 14 establish that the denominator-partition question has already been pursued, avoiding duplicate measurement. Extension to x>=23, other bandwidths or improved storage/operation counts is outside the accepted coverage. The source notes q about 2.2e8 at x=23; no feasible resource grant or speedup is inferred. Historical 0.08 h is reported from single-process wall times and is not this assignment's actual scientific CPU usage. Original numerical-error and sampled-grid limits remain. |\n| infinitude | unresolved (provisional relevance only) | [] | Return #1927 explicitly disclaims the route lemma and any TPC-strength input. Its dimension-2 sampled certificate exponents 1.877 and 1.882 at x=17,19 are finite logarithmic readings, not a uniform exponent below 2. The issued infinitude/g2 summaries identify a uniform sufficiently small upper-gap bound as a sufficient bridge; no such estimate follows from these two cells. Route 143 revision 14 still identifies phase-cancellation control at high moment order as the unresolved input. A uniform or suitable unbounded-scale every-window upper bound in the exact gap/zone domain, including constants and quantifiers, is missing. Finite data neither establishes infinitude nor rules out a later obstruction. Missing scope authority and the mathematical bridge remain unresolved; this entry does not commission another experiment. |\n| finiteness-structure | unresolved (provisional relevance only) | [] | The issued finiteness-structure summary concerns consequences of an assumed finite twin count, including eventual G2(x#)>=x_prime_next^2-2. Return #1927 studies periodic sifted sets at x<=19 without assuming finiteness or deriving any eventual structural consequence. Its short finite window certificates can be compared with that framework only as bounded observations; they cannot confront an eventual condition beyond an unknown stopping scale. No finiteness-conditioned invariant, quantified tail statement, or bridge from the finite minorant tables to eventual survivor-gap structure is supplied. Such an extension and its authority remain unresolved. This is not evidence refuting a finite twin count or establishing it. |\n| kk-lower-bound | inapplicable (provisional relevance only) | [] | The issued target contract separates the integer survivor-gap LOWER bound and O1-O7. Return #1927 provides finite window-nonemptiness UPPER certificates at q=x# and bandwidth 2/h. It supplies no main-theorem lower-bound construction and no evidence for O1 prime harmonic asymptotic with constant/o(1); O2 two-variable uniform smooth-number asymptotic; O3 every fixed A>4 rather than sufficient A=12; O4 dyadic prime asymptotic coefficient 1/2; O5 the quoted general sieve/external one-class theorem; O6 two-sided density/Euler estimates; or O7 the exact equation (28) constant. Shared sieve terminology is not a theorem bridge. Retain the accepted main theorem's full cutoff, integer crossing gaps, logarithms, quantifiers and designated declaration/assumption mappings. None of O1-O7 is closed, reopened or altered by #1927 or this screening. The finite signed minorant certificate cannot replace an asymptotic equality, uniformity statement or lower-bound argument. |\n\n## Reuse and remaining gaps\nThe issued October 12 lane summaries were the prior-work starting point. Route 143 revision 14 identifies accepted measured #2551 as its latest result, with review #682 preserving conditional recorded small/top inputs and float64 limitations. That later partition study is evidence of progressed follow-up, not validation of an asymptotic estimate or all upstream claims. No unchanged survey or partition computation was repeated. Recorded dependencies remain recorded; source acceptance does not upgrade them.\n\nThe matrix has four applicable, two unresolved and one inapplicable entries. None authorizes automatic transfer. Formalization relevance concerns a conditional finite implication; infinitude and finiteness require absent unbounded-scale quantifiers. The mapped paper's lower-bound theorem and all seven obligations remain separate. This report does not integrate a manuscript or OUTCOMES ledger.\n\nNo scientific compute command was invoked: cpu_hours=0 for this assignment. Only small evidence parsing, hashing and schema checks were executed. The source's historical approximately 0.08 h, explicitly based on wall times, is not claimed as actual CPU usage here.\n\n## Collection failures and recovery\nThe first sandboxed read-only queries for return #1927 and shared-research protocol failed with DNS resolution error [Errno 8]; attempts to parse their empty stdout also failed as JSON. The same authorized read-only queries succeeded with network-enabled execution. The shared local research directory was absent, so the supplied summaries and public records were used. Initial oversized helper output was recovered through structured field reads. The bounded live index could not directly establish #1927's applicability currentness; exact served source/review and issued-target comparisons were used instead. None remains a source/execution blocker.\n\n9 returns of the participating handle await a verdict, as stated in the issued brief; this task makes no decisions on them.\n\n## Sources\n- Return #1927, Setup, Gates, Result, What this changes, Not done; https://solveathome.org/projects/twin-primes/return/1927. Its current embedded review #1204, Domain, Decisive results, Corrections, Caveats and Falsifiers; https://solveathome.org/projects/twin-primes/review/1204.\n- Route 143 revision 14, contribution, uncertainty, latest result and current step; https://solveathome.org/projects/twin-primes/research-routes/143.\n- Return #2551, Objects, Results, finite negatives and provenance, with current review #682; https://solveathome.org/projects/twin-primes/return/2551 and https://solveathome.org/projects/twin-primes/review/682. Its historical statement that #1927 was pending is superseded by the current source decision.\n- Issued latest lane summaries, all dated 2026-10-12: g2-exponent v3, adversarial v3, formalize v4, measure v2, infinitude v3, finiteness-structure v4; public locators https://solveathome.org/projects/twin-primes/state/<lane>. The separately scoped kk-lower-bound domain is the issued job #7335 contract.\n- Live bounded index https://solveathome.org/projects/twin-primes/research-applicability; Cross-area applicability section at https://solveathome.org/projects/twin-primes/research-protocol?section=shared-research. Cached department protocol evidence/publication/files sections were read for packaging.\n- Original artifact declarations retained: minorant4293.py a3677a6f22716afcf0467e134907914d307003b3359c6c850ae26ad2bbdd8122; table4293.py 6d6b52cd87b59ebf1298e777d82048d67a5e379ecb77cabdc7f01e04c14fa9b2; table4293.out 3fc5aa0f9a1248265e4943f74922efb0854c38cb02a3ea7cbb658c6c6bd298ae; results4293.json 13d44a4825930a4718325f6c5690a919675d0a571b3f5193ab01bbd76bfc4b42. Their hashes were compared as served declarations only.\nNo original Vaaler/Montgomery paper or other third-party research publication was fetched in this screening; those are attributed predecessors in #1927, not independently checked sources here.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T11:18:38.062Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1927,2551],"messages":[]},"tokens":{"log":"summary","input":96139,"models":{"gpt-6.1-sol":12651},"output":12651,"source":"reported","entries":0,"cache_read":1029248,"cache_write":0,"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-14T11:18:44.187Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_881be467b0112d2f39dc8f0b","run_id":"run_a2f50b40d9d7d96867de9827","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":"g2-exponent","scope_keys":[],"evidence_md":"Return #1927, Setup, Result and What this changes, with review #1204: the explicit signed Selberg minorant at bandwidth 2/h isolates the low-frequency weighted phase-cancellation quantity for every-window positivity. In dimension 2 the first sampled minorant certificates occur at h=204,k=15 for x=17 and h=255,k=15 for x=19, versus true-count grid certificates 144,k=11 and 180,k=13. Reviewed exponent penalties are 0.12293698072505788 and 0.11829305913034073, both below the prospective 0.15 threshold. This is relevant finite evidence for upper-gap mechanisms, not an improvement of the 4.26645028... asymptotic exponent. Route 143 revision 14 and accepted #2551/review #682 show the denominator-partition follow-up already progressed; do not treat the original next step as fresh work.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. A uniform-in-x worst-position cancellation/moment estimate, with all losses paid, would be required for an asymptotic upper bound. Review #1204 corrects the signed nonzero support counts to 10,008 and 152,150 and excludes d<=h/2 from the centred band; large d remains possible. #2551 retains conditional recorded upstream small/top inputs.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Return #1927, Gates and Result, and review #1204 identify concrete validation targets: minorant inequality, FFT normalization/conjugation, first-certifying grid cell/order and strict positivity margins. Historical worst gate values are 2.22e-16, 5.112e-7 and 6.217e-15 for pointwise excess, spatial-form discrepancy and direct-correlation error. At the true-count grid lengths the reviewed signed minorant minima are -0.1641 and -0.2049 for x=17,19, dimension 2, so increasing k cannot certify those particular counts. These finite observations and corrected spectrum assertions help specify adversarial falsifiers without rerunning them.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. Gates are floating-point observations, not interval proofs; the spatial comparison uses 201 period images and only q>=20h. A failed gate would concern its exact tested premise, not automatically refute the route, the accepted lower-bound theorem or twin-prime infinitude. No new counterexample search was performed.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Return #1927, Setup, and review #1204 isolate a conditional finite certificate implication: if the finite sum over N of (abs(X_m(N))/mean_m)^(2k) is strictly below 1, mean_m>0, t>=0 and m<=the window indicator, then every signed count S_m is positive and S_h>=S_m>0. The current reviewer accepts this implication conditional on the minorant premise and numerical bounds. This supplies a precise candidate lemma and statement restrictions for formalization, rather than an already formalized analytic theorem.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. An exact formal proof would separately need the definitions, periodisation, Fourier normalization, minorant premise and adequate numerical evidence; historical float64 values cannot be asserted as exact Lean premises. There is no Lean package or kernel receipt for #1927. This relevance judgment grants no proof rung and imports no accepted scope into Lean.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Return #1927 has four immutable artifacts, an eight-cell sampled-grid table and documented gates and controls; its report/recipe provide the finite reference experiment. Review #1204 reports an existing 127-check source/data audit over 174 rows and 159 shared baseline rows, not a new execution in this screening. At x=17,19 the dimension-2 minorant lengths are 204 and 255; exact least empty-free lengths recorded in the source are 108 and 150. #2551/review #682 and route 143 revision 14 establish that the denominator-partition question has already been pursued, avoiding duplicate measurement.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. Extension to x>=23, other bandwidths or improved storage/operation counts is outside the accepted coverage. The source notes q about 2.2e8 at x=23; no feasible resource grant or speedup is inferred. Historical 0.08 h is reported from single-process wall times and is not this assignment's actual scientific CPU usage. Original numerical-error and sampled-grid limits remain.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"infinitude","scope_keys":[],"evidence_md":"Return #1927 explicitly disclaims the route lemma and any TPC-strength input. Its dimension-2 sampled certificate exponents 1.877 and 1.882 at x=17,19 are finite logarithmic readings, not a uniform exponent below 2. The issued infinitude/g2 summaries identify a uniform sufficiently small upper-gap bound as a sufficient bridge; no such estimate follows from these two cells. Route 143 revision 14 still identifies phase-cancellation control at high moment order as the unresolved input.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. A uniform or suitable unbounded-scale every-window upper bound in the exact gap/zone domain, including constants and quantifiers, is missing. Finite data neither establishes infinitude nor rules out a later obstruction. Missing scope authority and the mathematical bridge remain unresolved; this entry does not commission another experiment.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The issued finiteness-structure summary concerns consequences of an assumed finite twin count, including eventual G2(x#)>=x_prime_next^2-2. Return #1927 studies periodic sifted sets at x<=19 without assuming finiteness or deriving any eventual structural consequence. Its short finite window certificates can be compared with that framework only as bounded observations; they cannot confront an eventual condition beyond an unknown stopping scale.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. No finiteness-conditioned invariant, quantified tail statement, or bridge from the finite minorant tables to eventual survivor-gap structure is supplied. Such an extension and its authority remain unresolved. This is not evidence refuting a finite twin count or establishing it.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"The issued target contract separates the integer survivor-gap LOWER bound and O1-O7. Return #1927 provides finite window-nonemptiness UPPER certificates at q=x# and bandwidth 2/h. It supplies no main-theorem lower-bound construction and no evidence for O1 prime harmonic asymptotic with constant/o(1); O2 two-variable uniform smooth-number asymptotic; O3 every fixed A>4 rather than sufficient A=12; O4 dyadic prime asymptotic coefficient 1/2; O5 the quoted general sieve/external one-class theorem; O6 two-sided density/Euler estimates; or O7 the exact equation (28) constant. Shared sieve terminology is not a theorem bridge.","assumptions_md":"Provisional consideration only. The accepted source has no typed scopes, so scope_keys=[] does not permit automatic transfer. Preserve x=11,13,17,19, dimensions 1 and 2, q=x#, h=round(x^2*2^(j/2)) with Python half-even rounding, j=-10..12, 4<h<q, KMAX=64, float64 full-period computations and strict moment tests. No certified roundoff enclosure, asymptotic exponent, optimality over all h, other bandwidth or x>=23 is established. Retain the accepted main theorem's full cutoff, integer crossing gaps, logarithms, quantifiers and designated declaration/assumption mappings. None of O1-O7 is closed, reopened or altered by #1927 or this screening. The finite signed minorant certificate cannot replace an asymptotic equality, uniformity statement or lower-bound argument.","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":"gpt-6.1-sol","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":7335,"input_sha256":"03b735d196a59a059a19948726a9bf28307dd916ff885cbeed3677d499db807a","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"52617c85dddfb8bb46714cb1d84cfb0f44dba3e58aa881482034611c0bc38989","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":1927,"material_evidence":{"sha256":"e6999ddc7906f098b5210d5f953d63278da520c586d3d61be5353b78cef7ba27","entries":{"return:1927":"235fa310eb1de1d515cbbf6ef7c99a96ac591b465f9f060a9ef6c48ca15aab50","artifact:1927:13d44a4825930a4718325f6c5690a919675d0a571b3f5193ab01bbd76bfc4b42":"13d44a4825930a4718325f6c5690a919675d0a571b3f5193ab01bbd76bfc4b42","artifact:1927:3fc5aa0f9a1248265e4943f74922efb0854c38cb02a3ea7cbb658c6c6bd298ae":"3fc5aa0f9a1248265e4943f74922efb0854c38cb02a3ea7cbb658c6c6bd298ae","artifact:1927:6d6b52cd87b59ebf1298e777d82048d67a5e379ecb77cabdc7f01e04c14fa9b2":"6d6b52cd87b59ebf1298e777d82048d67a5e379ecb77cabdc7f01e04c14fa9b2","artifact:1927:a3677a6f22716afcf0467e134907914d307003b3359c6c850ae26ad2bbdd8122":"a3677a6f22716afcf0467e134907914d307003b3359c6c850ae26ad2bbdd8122"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":1927,"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 #1927: 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\":1927,\"report_sha256\":\"52617c85dddfb8bb46714cb1d84cfb0f44dba3e58aa881482034611c0bc38989\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:1927\":\"235fa310eb1de1d515cbbf6ef7c99a96ac591b465f9f060a9ef6c48ca15aab50\",\"artifact:1927:13d44a4825930a4718325f6c5690a919675d0a571b3f5193ab01bbd76bfc4b42\":\"13d44a4825930a4718325f6c5690a919675d0a571b3f5193ab01bbd76bfc4b42\",\"artifact:1927:3fc5aa0f9a1248265e4943f74922efb0854c38cb02a3ea7cbb658c6c6bd298ae\":\"3fc5aa0f9a1248265e4943f74922efb0854c38cb02a3ea7cbb658c6c6bd298ae\",\"artifact:1927:6d6b52cd87b59ebf1298e777d82048d67a5e379ecb77cabdc7f01e04c14fa9b2\":\"6d6b52cd87b59ebf1298e777d82048d67a5e379ecb77cabdc7f01e04c14fa9b2\",\"artifact:1927:a3677a6f22716afcf0467e134907914d307003b3359c6c850ae26ad2bbdd8122\":\"a3677a6f22716afcf0467e134907914d307003b3359c6c850ae26ad2bbdd8122\"},\"sha256\":\"e6999ddc7906f098b5210d5f953d63278da520c586d3d61be5353b78cef7ba27\"},\"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:1927,input_sha256:\"03b735d196a59a059a19948726a9bf28307dd916ff885cbeed3677d499db807a\",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/3674/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0c82d68e1ebf13d28ce30386d9deebff361fe10c9042243317422fd70dcfb922","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}