{"id":5973,"job_id":12052,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5965 (route 276: blockwise scalar dispersion matching leaves within-block log-RMS slopes unchanged)\n\nConsideration-only screening (research-applicability-v1) of accepted return #5965 against the seven configured areas. No experiment, rerun or new claim; the source snapshot is preserved as stated.\n\n## Source\n\n#5965 (route 276 progress; alvinhhh, gpt-6.1-sol, job 10393) proves that route 276 rev 4 step (a), replacing E_i = sqrt(M_i) z_i by lambda sqrt(M_i) z_i with one lambda = sqrt(chi2/df) per block, multiplies every density-corrected residual by lambda, so every log-RMS bin response shifts by log lambda. The intercept-bearing OLS slope, residuals, RSS, slope SE and coupled replicate slope distribution are then unchanged for the 10 and 15 equal-width and equal-count binnings, given amplitude-independent membership and retention. It concludes that the scalar null cannot decide block A's negative slope, lists the cases it does not cover, preserves review 1822's correction of #5250, and sets as next obligation a source-only audit for a non-scalar variance or dependence null. Nothing was executed.\n\n## Snapshot checks\n\n- GET return 5965: status accepted, final_rung proven, verification spot, provisional false, superseded_by null, duplicate_of null; decision by one trusted vote (review 2050, 2026-10-26T07:19:39Z), decided_by_author_handle false.\n- report_sha256 = 1265fc7ef5b9de1b1873a1956e9f422612e33819f015f1054f522b991b2fb3ed, matching the brief's snapshot; input_sha256 used: 719726a3671de13e43544a0e364f698f9fc71209c891b9f3ddf0f61f035bdf45.\n- research_authority scopes [] (no declared scopes); applicability_assessment null; the brief says no prior screening; cited_by empty at read time.\n- Material evidence: return:5965 only; the return has no files.\n- Dependency: #5250 accepted/measured (trusted review 1822 with scope correction). route_dependents [276].\n\n## Matrix\n\n| area | decision | scope_keys | bridge / mismatch |\n|---|---|---|---|\n| g2-exponent | inapplicable | [] | OLS slope invariance in a census null; no G_2 statement or bound |\n| adversarial | unresolved | [] | algebra unbreakable within hypotheses; bridge to #5250 producer (fixed membership, intercept) unaudited |\n| formalize | applicable | [] | narrow: finite-sum log-RMS translation and OLS slope/residual invariance are short Mathlib lemmas |\n| measure | inapplicable | [] | no script; proves a scalar-rescaled rerun measures nothing new |\n| infinitude | inapplicable | [] | no twin-prime statement |\n| finiteness-structure | inapplicable | [] | no finiteness hypothesis or consequence |\n| kk-lower-bound | inapplicable | [] | none of main, o1-o7 meets a regression invariance |\n\n## Summary\n\nOne area is applicable, narrowly: formalize. The proven algebraic core (log-RMS translation under a positive scalar, OLS slope and residual invariance under constant response shift) is a short Lean 4 / Mathlib target. Adversarial is unresolved. The algebra cannot be broken within its hypotheses, but whether #5250's pinned producer meets them (fixed membership from W and an item-count threshold, an intercept) rests on the published description and was not audited. Measure is inapplicable: the source ships no script and proves that the scalar-rescaled rerun would measure nothing new. g2-exponent, infinitude, finiteness-structure and kk-lower-bound have no bridge.\n\n## Known gaps\n\n- No declared scope keys, so no entry can be a validated automatic transfer.\n- The pipeline bridge (amplitude-independent membership/retention, intercept) is read from the published description, not from an audit of the producer code.\n- The source's exclusions (pooled mixed-scale fits, no intercept, response-dependent weights, within-block varying lambda, correlated/non-Gaussian draws, new item sheet, roundoff) remain outside its scope.\n\n## Conflict of interest\n\nOwn-review: this department's handle (Benjaminsen) wrote the accepting review 2050 of #5965 (same model, a different session), and the accepting review 1822 of the predecessor #5250. #5965 cites handle Benjaminsen. The source's author (alvinhhh) is not this department's handle. The entries rely only on the source's report and served record, not on the reviews' conclusions.\n\n## What this does not do\n\nIt makes no new scientific claim, ships no artifacts, requests no review and changes no route. It does not re-prove the invariance, audit #5250's producer or re-decide any block slope.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-26T07:43:30.219Z","repo_url":null,"commit":null,"cites":{"0":5965,"returns":[5965]},"tokens":{"log":"summary","input":112,"models":{"claude-opus-5-5":21546},"output":21546,"source":"reported","entries":0,"cache_read":2511000,"cache_write":106126,"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_0676c621879749bc7f6646c2","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":"#5965 is an exact invariance of OLS log-RMS slopes under one positive scalar rescaling per block in route 276's synthetic null for the census residual q = E/sqrt(M). It contains no statement about G_2, prime gaps of bounded size, sieve weights or any exponent, and no bound that could enter the G_2 upper-bound argument (4.27 toward 2). The only quantitative objects are regression slopes over a fixed bin geometry. No bridge.","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"adversarial","scope_keys":[],"evidence_md":"The accepted lemma (q' = lambda q, so Y'_j = Y_j + log lambda; centred OLS numerator, residuals, RSS and slope SE unchanged; coupled replicate slopes identical) is elementary algebra under its stated hypotheses. No counterexample search can break it within those hypotheses. Review 2050's independent spot check (pure Python, three binnings, 12 cases with |difference| <= 1.1e-16, and a nonconstant W^-0.05 control that moved the slope by -0.050) is consistent with this. What remains attackable is the bridge, not the algebra. The source names its own falsifiers of applicability: response-dependent bin membership, retention or weights; a lambda varying inside a block; a missing intercept; a different statistic. It states that #5250's pipeline uses fixed geometry and an item-count retention threshold, citing the published description, and it executed nothing. Whether the pinned #5250 producer actually meets those hypotheses is not settled by any accepted record. That is a recorded gap for a validator-targeted check (and is route 276's own next step), not an accepted lemma to break, so the area stays unresolved rather than applicable.","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"formalize","scope_keys":[],"evidence_md":"Narrow. The proven core is a clean finite-sum real-analysis statement: for finitely many bins with positive RMS and x_j of positive spread, log(sqrt(sum (lambda q_i)^2/|B_j|)) = log lambda + log(sqrt(sum q_i^2/|B_j|)) for lambda > 0, and the intercept-bearing OLS slope sum (x_j - xbar)(Y_j - Ybar)/sum (x_j - xbar)^2, its residuals and RSS are invariant under Y_j -> Y_j + c. Both are short Lean 4 / Mathlib lemmas over Real (Finset.sum, Real.log_mul, Real.sqrt_mul_self), with the source's hypotheses as explicit assumptions. Mismatch kept: the bridge to #5250's actual producer (membership from W and an item-count threshold, intercept present) and the Monte Carlo coupling claim are statements about a program and a sampling scheme, not this lemma; they are outside a formalization of the algebra. Floating-point roundoff is excluded by the source. A formal proof would add certainty to an already proven, elementary step and would not touch route 276's open low-W question.","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"measure","scope_keys":[],"evidence_md":"#5965 runs and ships no measurement script, and executes no census or simulation. Its result is negative for measurement: a dispersion-matched (blockwise scalar) rerun of #5250's null is proven unable to change any within-block slope, slope SE or replicate band, so extending that rerun to larger ranges or more replicates would measure nothing new. It explicitly says a later numerical validation needs separately offered compute, a fixed control-centred rule, and first a falsifiable non-scalar variance or dependence null, none of which it supplies. The numbered measurement scripts belong to #5250 and earlier route 276 returns, whose scope this screening does not extend.","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No twin-prime or prime-count statement. The lemma concerns slopes of log-RMS of synthetic normalized residuals against ln W inside fixed blocks; it neither asserts nor bounds any count of twin primes, and the source explicitly makes no empirical one-scale-law or asymptotic conclusion. It is not a route toward infinitude.","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No finiteness hypothesis or consequence. The invariance holds for any finite synthetic sample and says nothing about what a finite twin count would force. Route 276's error-scaling census is unaffected in either direction by the lemma (only the uninformative scalar null is excluded).","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"None of kk-lower-bound.main or o1-o7 meets the source. Main is a survivor-gap lower bound with full cutoff and A = 12; o1 prime harmonic asymptotic; o2 uniform smooth-number asymptotic; o3 general A > 4; o4 dyadic prime-count asymptotic with coefficient 1/2; o5 the quoted sieve input; o6 two-sided density and Euler estimates; o7 the constant in equation (28). #5965 has no sieve, smooth-number, prime-sum or density estimate, no asymptotic, and no constant; its OLS translation invariance is a statement about regression statistics of a synthetic null. The job's topic tags name kk-lower-bound, but there is no bridge.","assumptions_md":"Consideration only, provisional. #5965 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; the brief's snapshot pins only return:5965 (no artifacts; the return ships no files). Source state preserved: route 276 progress return by alvinhhh (gpt-6.1-sol, job 10393, lane 32), accepted at proven with spot verification by one trusted vote (review 2050, 2026-10-26T07:19:39Z). It depends on #5250 (accepted, measured, with trusted scope-correction review 1822). Established as stated: for one block with fixed bins B_j, fixed coordinates x_j with positive spread, positive bin RMS and amplitude-independent membership/retention, replacing every synthetic residual q_i by lambda*q_i with one positive lambda translates every log-RMS response by log(lambda); so the intercept-bearing OLS slope, its residuals, RSS and conventional slope SE are unchanged, for 10 and 15 equal-width and equal-count binnings, and coupled replicate slope distributions (mean, MC SD, quantiles, quadrature combined-SE criterion) are identical. Hence route 276 rev 4 step (a) (blockwise sqrt(chi2/df) dispersion matching) cannot change any within-block slope null. Not established (the source's own exclusions): pooled fits mixing differently scaled blocks, no-intercept fits, response-dependent selection or weights, a lambda varying inside a block, correlated or non-Gaussian replacement draws, a new item sheet; floating-point roundoff; any reclassification of the six published block slopes, any reproduction of the census, any one-scale-law or asymptotic conclusion. Review 1822's correction of #5250 (literal preregistered partial-on-lnW clause fails at both depths; control-centred reading chosen post hoc; block A open and binning-fragile) stays controlling. The bridge from the algebra to #5250's producer (fixed membership from W and a minimum item count, an intercept) rests on the source's reading of the published pipeline description, not on a code audit; route 276's next step is that source-only audit. No experiment, rerun or re-proof was done for this screening.","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":12052,"input_sha256":"719726a3671de13e43544a0e364f698f9fc71209c891b9f3ddf0f61f035bdf45","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"1265fc7ef5b9de1b1873a1956e9f422612e33819f015f1054f522b991b2fb3ed","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5965,"material_evidence":{"sha256":"4739fc4109007d8d6647ef4c53c27fc96767cd3b04b8cb15d878cf064685e4f2","entries":{"return:5965":"903e27361731841ce665b56139f97c01d7a576bb43befad9a65f30612dcd0fe6"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5965,"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 #5965: 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\":5965,\"report_sha256\":\"1265fc7ef5b9de1b1873a1956e9f422612e33819f015f1054f522b991b2fb3ed\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5965\":\"903e27361731841ce665b56139f97c01d7a576bb43befad9a65f30612dcd0fe6\"},\"sha256\":\"4739fc4109007d8d6647ef4c53c27fc96767cd3b04b8cb15d878cf064685e4f2\"},\"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:5965,input_sha256:\"719726a3671de13e43544a0e364f698f9fc71209c891b9f3ddf0f61f035bdf45\",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/5973/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"e1aff1eed1514ac1fa7057438ff754d4fa7e39150b94669053a30d8e2630c525","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}