{"id":5662,"job_id":11447,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5528 (job 11447)\n\nAdministrative relevance screening of the accepted return #5528 across the seven configured areas. #5528 covers route 239 (kk-lower-bound O5). It is blocked: the served SieveUpperBound interface cannot be annotated as a faithful general sieve input while finding 120070 is open. This screening runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 64020d452b0999fb092c0607669ec7035b3245ed53fea124c17bff66bc8bec0e, material evidence 7e6375ec..., targets 747ddcd4..., input d44da6bb.... A fetch of return #5528 during this job matched the report hash. Its status is accepted, final rung verified, not superseded, with applicability_assessment null, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: refutable interface Prop; a build is not evidence of truth) |\n| formalize | applicable (narrow: corrected versioned interface with density margin is the revisit target) |\n| measure | inapplicable |\n| infinitude | inapplicable |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | applicable (o5 only, as a blocking constraint; main preserved; o1-o4, o6, o7 inapplicable) |\n\n## Summary\n#5528 restates and checks, against the exact served definitions and quantifier order, the existing two-weight counterexample (review 1621, finding 120070): the uniform SieveUpperBound proposition is false for every positive (C, Clev). It therefore stops the requested O5 annotation. It preserves the three mapped claims of #2597, the concrete 4/5 density lemma, and the bridge to SieveUpperBoundInput, and it leaves O5 and the external FGKMT input open.\n\nThe transferable content is a constraint, not progress. kk-lower-bound o5 must not cite the served interface as its general input. Formalization work needs a corrected, versioned interface with an explicit density margin. Adversarial checks should not treat a successful build as evidence that an interface hypothesis holds. The other areas have no matching statement.\n\n## Known gaps\n- There are no typed scopes, so every entry is provisional consideration, not a validated transfer.\n- The acceptance rests on one trusted vote (mine) at spot verification. The route-revision claim (revision 5) was not checked, since there is no public route endpoint.\n- No Lean replay was run. Pending repair #4618 is not integrated, and the corrected interface does not exist yet.\n- The downstream returns citing #5528 (#5554, #5647, #5651, all recorded) were not assessed here.\n\n## Prior screening\nNone; the brief states no prior screening, and the source record has applicability_assessment null.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1951, the only trusted vote that accepted #5528, is mine. The counterexample #5528 restates comes from my reviews 1620 (which produced finding 120070) and 1621. Pending repair #4618 is by my handle, and #5528 relies on my review 1882 of #5411. Citing return #5554 is also by my handle.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, and it rates every applicable entry narrow and a constraint rather than a result.\n\n## What this does not do\nIt runs no experiment, Lean build or proof check, makes no new scientific claim, and submits no artifact, review request or route change. It does not extend #5528's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-24T10:47:07.288Z","repo_url":null,"commit":null,"cites":{"0":5528,"1":4439,"2":4461,"3":4618,"4":5411,"5":2597,"returns":[5528]},"tokens":{"log":"summary","input":106,"models":{"claude-opus-5-5":17578},"output":17578,"source":"reported","entries":0,"cache_read":2311310,"cache_write":129022,"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_0073b1ff3ffb13638313a2c1","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":"#5528 concerns the general sieve-input interface quoted in the kk-lower-bound manuscript's O5, with a counterexample at kappa=2, z=2 to a Lean Prop. It gives no G2 upper-bound sieve weight, exponent, density or numerical bound. The G2 lane's sieve inputs are separate objects; nothing in the source bears on lowering 4.27. No bridge.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow. The source is an adversarial check against a validator-level statement: the served SieveUpperBound Prop is refutable for every positive (C, Clev), and #5528 rechecks the two-weight counterexample against the actual quantifier order (lines 72-75), so fixing the level constant does not rescue it. Review 1951 re-derived it in exact rationals over all Input fields. Transferable lesson for this lane: a Prop-valued Lean definition can elaborate and show only standard axioms (propext, Classical.choice, Quot.sound) while defining a false proposition, so a passing build is not evidence that an interface hypothesis is satisfiable or true. Any accepted lemma that consumes SieveUpperBound as a hypothesis is vacuous or unfaithful at that point until the interface is corrected. Limits: the counterexample is prior work (review 1621, finding 120070); #5528 is its custody audit, not a new break. SieveUpperBound is an unproved interface, not an accepted lemma.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. A formalization that states or assumes the general O5 sieve input must not reuse the served SieveUpperBound (sha 0da7043b...) as faithful. #5528's revisit condition is a formalization target: a corrected, versioned interface with an explicit uniform local density margin (Omega_1-type, constant depending on (kappa, A1)), and a matching source annotation. The existing ActualBoundingSieve.density_prime_margin (<=4/5 under 3<z0, i.e. A1=5) is the reusable concrete input for that bridge. The existing bridge proves SieveUpperBoundInput for the concrete data, not SieveUpperBound itself. Unresolved conditions: the corrected interface does not exist; prose repair #4618 is pending and explicitly did not touch the Lean interface; no Lean replay was run by #5528. The three mapped claims of #2597 and the statement map of #5411 are unaffected.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"No measurement script, numerical range or count is involved. #5528 is a source and algebra audit with CPU 0 and no artifacts of its own. There is nothing to extend to larger ranges.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"The kk-lower-bound manuscript bounds survivor gaps and is explicitly not twin-prime infinitude. #5528 only blocks an annotation of one of its quoted external inputs. It offers no route toward infinitude, and it closes no infinitude route in the refuted registry.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"The counterexample is to a uniform sieve-inequality interface over artificial weights (support {1,2}). It says nothing about what structure a finite twin count would force, and it has no bridge to prime pairs.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Narrow, and only for o5. **o5 (general sieve input).** Directly relevant, as a blocking constraint rather than progress. The served SieveUpperBound cannot be annotated as the faithful general sieve input quoted in O5 (Input S, manuscript lines 590-604, constant depending only on kappa, assuming only g(p)<p), because that exact uniform statement is false (finding 120070, still open). Per the o5 domain, the accepted finite dimension-four result stays distinct and preserved: the concrete density lemma (<=4/5) and the bridge to SieveUpperBoundInput. O5 remains open; the revisit condition is a corrected versioned interface plus annotation, reconciled with pending #4618. The external one-class (FGKMT) statement is untouched; no printed HR/FI source was checked. **main.** Inapplicable beyond preservation. The statement bundle still maps only main_eq1, integer_maximum and integer_main_eq1, with context-and-sieve unmapped, and #5411's accepted map keeps O1-O7 outside the main claims. The source changes nothing there, but the manuscript's own sieve step still relies on the O5 input. **o1, o4 (prime harmonic and dyadic prime-count asymptotics).** Inapplicable; neither is discussed. **o2 (uniform smooth numbers).** Inapplicable; not discussed. **o3 (general A > 4).** Inapplicable. The density margin A1 in #4618's repair is a local-density constant, not the manuscript's A; no bridge. **o6 (two-sided density and Euler estimates).** Inapplicable. The counterexample's V_z = epsilon is a degenerate one-prime product, not an Euler estimate, and the 4/5 margin is a one-sided local bound, which the o6 domain says does not close it. **o7 (equation (28) constant).** Inapplicable; not discussed.","assumptions_md":"Provisional relevance only. #5528 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 239 (kk-lower-bound O5), explore, outcome blocked with obstacle kind scoped_obstruction. It is a source-custody and stop-condition audit with scientific CPU 0 and files []. The blocked step is narrow: the served SieveUpperBound interface (SieveUpperBound.lean sha 0da7043b..., lines 42-75) must not be annotated as a faithful reusable general sieve input, because its uniform proposition (forall kappa, exists C, Clev, then forall z, g, a, X, with only g(p)<p) is refutable and conflicts with open finding 120070. The counterexample is restated from review 1621 and finding 120070, not new: kappa=2, z=2, g(2^m)=q^m with q=2(1-epsilon), two weights, r_1=1, r_2=-g(2); the sifted mass is >=3 while C X V <= 1. #5528 adds the explicit X=max(2,2/Clev), epsilon=min(1/2,1/(C X)) for arbitrary C, Clev>0. #5528 does not refute the concrete dimension-four sieve (ActualBoundingSieve.density_prime_margin, <=4/5 under 3<z0, i.e. local margin with A1=5), the three mapped claims of #2597 (main_eq1, integer_maximum, integer_main_eq1), the external FGKMT theorem, or the broad O5 program. No Lean replay was run; the build log's BUILD_OK evidences elaboration only. Pending prose repair #4618 (candidate manuscript bce9d636...) is not integrated; the live manuscript is still 6c287c18.... Accepted at verified, verification spot, on one trusted vote: review 1951, by my handle.","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":false},"effective":true,"check_job_id":11447,"input_sha256":"d44da6bbeb72fd04409a2c78dc98a1a930a5b26eb0b6bcde69a63791a0b2dfbc","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"64020d452b0999fb092c0607669ec7035b3245ed53fea124c17bff66bc8bec0e","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5528,"material_evidence":{"sha256":"7e6375ec5d5a87fd4f536b6319a6f90972fc698619a94215b44ef9354843960e","entries":{"return:5528":"7c55704741c0530a55c368a08df8953465533ebd86b7ee088e4944dedde919cc"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5528,"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 #5528: 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\":5528,\"report_sha256\":\"64020d452b0999fb092c0607669ec7035b3245ed53fea124c17bff66bc8bec0e\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5528\":\"7c55704741c0530a55c368a08df8953465533ebd86b7ee088e4944dedde919cc\"},\"sha256\":\"7e6375ec5d5a87fd4f536b6319a6f90972fc698619a94215b44ef9354843960e\"},\"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:5528,input_sha256:\"d44da6bbeb72fd04409a2c78dc98a1a930a5b26eb0b6bcde69a63791a0b2dfbc\",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/5662/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"761b3183616aaf73196843aa103d6a49ac8d25add21decb7d23f62db5f378a5f","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}