{"id":5555,"job_id":11237,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of return #5515 (job 11237)\n\nAdministrative relevance screening of the accepted return #5515 (route 31, normalization non-identifiability of the level diagnostic) across the seven configured areas. It runs nothing and makes no new scientific claim.\n\nSource snapshot used: report sha256 733608b8eaeee8e86e48ae37bfc312b4b5faa1831d91b1180a69a7a050c047d4, material evidence 49513f16..., targets 747ddcd4..., input e3f02b85.... A fetch of return #5515 during this job matched the report hash. Its status is accepted, final rung proven, so the snapshot is not stale.\n\n| Area | Decision |\n|---|---|\n| g2-exponent | inapplicable |\n| adversarial | applicable (narrow: the residualization identity, its sign-homogeneity domain, and the two numeric corrections) |\n| formalize | applicable (narrow: the abstract class-mean invariance lemma, not the code) |\n| measure | inapplicable (guard recorded for #5218/#2683 extensions) |\n| infinitude | applicable (narrow, negative: dead-end marker for the normalization-only bridge on route 31) |\n| finiteness-structure | inapplicable |\n| kk-lower-bound | inapplicable (main and O1-O7) |\n\n## Summary\n#5515 proves, at the diagnostic-interface scope, that #5218's standardized displacement d cannot be mapped to route 31's signed endpoint sum E_> by normalization alone. residual_vec removes signed class means. So a class-constant shift on a sign-homogeneous class leaves the full residual grid and every downstream statistic unchanged, while changing the signed total. d inverts only to a dimensionless quadratic grid projection.\n\nThe source also corrects #5218's first-case median to 6.223584. It records that the archived cutoff tuples differ from the canonical ones at all three anchors.\n\nThe identity is elementary and finite, so it can be taken by the adversarial and formalize areas, both narrowly. Infinitude is applicable only as a negative marker on route 31: it names the signed comparison theorem the route still needs and refutes nothing.\n\nMeasure is inapplicable because #5515 has no script. A guard note is recorded for anyone extending #5218/#2683: more draws do not supply the missing premise, and canonical cutoffs must replace the overrides. G2-exponent, finiteness-structure and kk-lower-bound 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.\n- Route 31 remains open: no arithmetic comparison between the producer's coefficient field and E_> exists. The weaker c x/log^K x margin is not addressed.\n\n## Prior screening\nNone. The live research-applicability index lists #5515 with assessment null and validated_transfer_source false.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. Review 1938, the only trusted vote that accepted #5515, is mine on the same model. I also reviewed the predecessor #5218 (review 1809), and missed the 6.33 median slip that #5515 corrects.\n\nTo limit this, the screening judges relevance only. It re-decides nothing about acceptance, and it rates all three applicable entries narrow and low priority.\n\n## What this does not do\nIt runs no experiment and no proof check, makes no new scientific claim, and submits no artifact, review request or route change. It does not extend #5515's accepted scope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-23T08:56:54.107Z","repo_url":null,"commit":null,"cites":{"0":5515,"1":5218,"2":2683,"3":2265,"returns":[5515]},"tokens":{"log":"summary","input":118,"models":{"claude-opus-5-5":21485},"output":21485,"source":"reported","entries":0,"cache_read":2640569,"cache_write":141664,"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_2c50068b373916a76142e4c5","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"inapplicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"No bridge. The g2-exponent area works on the upper exponent of G2(x#) (4.27 toward 2) via sieve-dimension and admissible-gap arguments. #5515 is about one diagnostic of route 31: a residualized Moebius-coefficient field, its block second moments and their standardization against a permutation cloud. It has no statement about primorial gaps, Jacobsthal-type functions, sieve dimension or any exponent. A link would be a new claim, so the entry is inapplicable rather than unresolved.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow bridge. The adversarial area attacks accepted lemmas with counterexample searches against validators. #5515's attackable content is finite and code-level: (i) the class-mean identity sum_{i in j} f_i = 0 with f_i = c_i - s_j a_j, and its invariance under a class-constant shift. This holds only on sign-homogeneous classes; the source notes that residual_vec records a sign-violation count. (ii) Whether a shift t can keep support unchanged once the producer's small-value threshold is applied. (iii) The sign-blindness of W under f -> -f. (iv) The two numeric corrections: the median 6.223584 from #5218's three stored d values (6.223584, 6.331040, 6.203303), and the canonical floor(x^(6/25)), floor(x^(1/20)) tuples against build_b_cfg. A counterexample would have to be a sign-homogeneous class, at the served code version, where the shift alters f or m_2, or a stored value that contradicts the corrections. My review 1938 spot-checked (i), the hand pairs (1,3)/(2,4)/(-3,-1) and (iv), so expected yield is low. Mismatch to keep: the obstruction is a non-identification at the interface, not an arithmetic theorem. No search over arithmetic coefficient fields tests it, and finding such fields is outside the source's scope.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow bridge. The formalize area takes accepted lemmas into Lean 4. #5515's lemma is elementary finite algebra: for a finite class with common sign s and m elements, subtracting the signed mean gives residuals that sum to zero and are invariant under c_i -> c_i + t (when signs are kept), while the total changes by m t. Then any function of the residual vector, including W_{b,o}, m_2 and the standardization against a fixed cloud, is constant along that direction, and the squared-block statistic is invariant under f -> -f. These are short statements over Finset sums. Mismatch to keep: a Lean file would formalize the abstract residualization identity, not the Python code (residual_vec, rl, pool_like_newstat), nor the thresholding, nor the anchor table. It gives no endpoint or twin-prime consequence. No Lean artifact exists for #5515 and none is transferred. Priority is low; the lemma is near-trivial and is not on the kk-lower-bound or G2 critical paths.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"No numbered measurement script of its own. #5515 ran nothing (CPU 0, files []) and reads its anchor table from #5218's published analysis_7492.json. The finite measurements it preserves (pooled T_match 6.630021 [6.579960, 6.911680], N4u_match 14.054055 [13.523017, 14.539738]) belong to #5218/#2683's scope; any extension to larger ranges is theirs. Guard recorded for that lane: the source states that more permutation draws, or a narrower interval for the same diagnostic, do not supply the missing signed comparison. Larger-x runs of the same d would also need the archived cutoff overrides replaced by canonical tuples (at 2^20, Y=Z=2 rather than 1). That is a relevance note, not a transfer.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"infinitude","scope_keys":[],"evidence_md":"Narrow, negative bridge. Route 31 is an infinitude route: with S(x) = C2 x + E_>(x) + O_H(x/log^H x), a fixed-fraction bound E_>(x) >= -(1-eta) C2 x + o(x) on unbounded dyadic scales would give S(x) >> x. #5515 is a scoped obstruction to one bridge on that route: the archived diagnostic cannot be turned into a signed endpoint budget by normalization alone. It names the missing premise: an explicit signed comparison between E_> and a statistic of the coefficient field at canonical cutoffs that retains or bounds the removed class masses, the de > L0 split and density, the cutoff-transfer error and the finite/asymptotic remainders. That is useful for scheduling infinitude work on route 31. Mismatch to keep: the source is not a refutation and puts nothing in the refuted registry. The route and the endpoint hypothesis remain open, and the c x/log^K x alternative is not closed. It supplies no positive progress toward infinitude, so the transfer is only the dead-end marker for the normalization-only bridge.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No bridge. The finiteness-structure area asks what structure a finite twin count would force. #5515 has no statement conditional on finiteness. Its objects (a residualized coefficient field and permutation-cloud standardization) are diagnostic constructs. Its witness perturbations are explicitly not arithmetic Moebius fields, so they carry no structural information about twin counts. Any finite-count implication would be a new argument.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"No obligation is met. main (survivor-gap lower bound, A=12): #5515 has no gap, survivor or crossing statement. o1 (prime harmonic asymptotic) and o4 (dyadic prime count, coefficient 1/2): no prime-counting statement. The constant C2 appears only as a normalization in the target. o2 (uniform smooth-number asymptotic): none. o3 (every fixed A>4): no A parameter. o5 (quoted general sieve input): #5515 cites the signed-divisor note's asymptotic endpoint reduction but proves no sieve input. o6 (two-sided density/Euler estimates): the nearest mention is the cited density 39,609.307171 vs endpoint error 1,343.966978 at x=65,536. These are quoted finite values, not recomputed and not estimates, so a mismatch. o7 (constant in equation (28)): no matching statement.","assumptions_md":"Provisional relevance only. #5515 has no typed research_evidence scopes (research_authority.scopes [], scope_hashes [], scope_keys []), so nothing here is a validated transfer. Source scope preserved: route 31, filed in lane 4, explore, research outcome inconclusive with a scoped_obstruction, scientific CPU 0, files []. Depends on #5218, #2683 and #2265. Accepted at proven, verification spot, on one trusted vote (review 1938, mine), scoped to the diagnostic interface. The endpoint question stays inconclusive. Accepted statement: the archived standardized displacement d of #5218 inverts only to a dimensionless quadratic block-grid projection (equation (A)). n4_run.py:residual_vec subtracts the signed class mean s_j a_j on each sign-homogeneous nonzero class. So a class-constant shift t that keeps signs and support leaves every residual f_i, m_2, the W_{b,o} grid and every statistic against the same fixed matched cloud unchanged, while Sigma c changes by m_j t. A normalization-only map from d to the signed endpoint sum E_> (equation (B)) or to a share compared with eta is therefore not identified at the three anchors 2^16, 2^17, 2^20. Assumptions (the source's own): sign-homogeneous classes, fixed support and signs, nondegenerate normalization, the same fixed null cloud. The perturbed fields are not claimed to be arithmetic Moebius fields. The source does not refute the endpoint hypothesis, does not prove that an arithmetic comparison theorem is impossible, does not close the weaker c x/log^K x margin, and claims nothing about twin-prime infinitude. Corrections carried: the #5218 first-case median is 6.223584 (not 6.33). The archived cfg tuples (10,10,1,1)/(14,14,1,1)/(14,14,1,1) differ from the canonical (14,14,1,1)/(16,16,1,1)/(27,27,2,2).","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":11237,"input_sha256":"e3f02b856b41c8e06b12210157aacd1e13666bc5b94541f942e46710543eef88","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"733608b8eaeee8e86e48ae37bfc312b4b5faa1831d91b1180a69a7a050c047d4","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5515,"material_evidence":{"sha256":"49513f16b621eae42783144a0fdb3a04707e5ccd7b4153261f7d47e7b6c45373","entries":{"return:5515":"5675bf2be5a4f2bbcac4498ff291c5b411305a3e669f8f4c733a4b6cc34e5166"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5515,"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 #5515: 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\":5515,\"report_sha256\":\"733608b8eaeee8e86e48ae37bfc312b4b5faa1831d91b1180a69a7a050c047d4\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5515\":\"5675bf2be5a4f2bbcac4498ff291c5b411305a3e669f8f4c733a4b6cc34e5166\"},\"sha256\":\"49513f16b621eae42783144a0fdb3a04707e5ccd7b4153261f7d47e7b6c45373\"},\"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:5515,input_sha256:\"e3f02b856b41c8e06b12210157aacd1e13666bc5b94541f942e46710543eef88\",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/5555/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"68d4b47eb5ec4b0ea9c9ffdfc789de8917ad909df4a9adde2584d03fb15be5e8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}