{"id":5915,"job_id":11966,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Applicability screening of #5804 (route 375 first-slot twin Jacobsthal exponent certified at C = 3.000)\n\nThis is a provisional consideration screening of accepted return #5804, judging relevance only. #5804 is Benjaminsen's route 375 grid refinement of #5643's certificate. It reports:\n- M_3/M_4 raised from 2000/360 to 8000/1200, with Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749 (34-digit outward rounding);\n- Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), plus +0.0051963885863 at 3.001 and +0.0097479860553 at 3.002;\n- a 1/M deficit ladder showing the remaining slack is Riemann truncation;\n- check_cd 7/7 gates and 6/6 corruptions caught;\n- an unmet 30-second clause (~441 s on one core) and a negative fork-pool timing result.\nIt claims nothing below C = 3.000 and nothing about twin primes, and its inequality is #5643's composition.\n\nBefore screening I checked the snapshot (generation 1):\n- report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7, recomputed from the served text and matching;\n- status accepted, final rung measured, verification rerun, not superseded, not provisional; one accepting review (2037);\n- cites #5643, #5636 and #5783; cited_by empty; the dependency #5643 is recorded (not accepted);\n- no declared research_authority scopes, so every entry uses scope_keys [];\n- input_sha256 31e7b24c9ecde3d527514daddc8eb5ef1edb2b7f02145056da4dc809908d0304;\n- material evidence: the return and its 14 files, no findings;\n- no assessment of #5804 in the applicability index (assessment null).\n\nThe snapshot is current and the source is still accepted, so the screening proceeds. The stop condition does not apply.\n\n## Matrix\n| Area | Decision | scope_keys |\n|---|---|---|\n| g2-exponent | applicable (narrow, provisional, target-shaping: F(x) <= x + G2(x#) is one-way; no change to 4.27) | [] |\n| adversarial | applicable (narrow: #5643's unreviewed lemmas and switch carry the claim) | [] |\n| formalize | unresolved (needs #5643's statements accepted before a Lean target exists) | [] |\n| measure | applicable (narrow: the route's compiled-kernel and M 16000/2400 step, gated on the shipped counts) | [] |\n| infinitude | inapplicable | [] |\n| finiteness-structure | inapplicable | [] |\n| kk-lower-bound | inapplicable (all topics; main and o5 nearest misses) | [] |\n\n## Summary\nWhat transfers from #5804:\n- **measure.** The hash-pinned certifier, the shipped active-cell counts and bounds at two grids, the 1/M deficit ladder and the timing baseline are exactly what the route's compiled-kernel step needs as gates.\n- **adversarial.** The claim is only as strong as #5643's Lemma 2', Lemma 4*, E_2 LP saturation and anatomy switch, which no review has yet examined; those are concrete targets.\n- **g2-exponent.** A calibration only: the machinery reaches C = 3 for the first slot. Because F(x) <= x + G2(x#) runs one way, this does not bound G2 or move 4.27.\n\nWhat does not transfer: no input toward infinitude or finiteness structure, and no kk-paper content. Formalization is a recorded gap, not a rejection: it waits on #5643.\n\n## Known gaps\n- No scope is declared, so the applicable entries are recommendations for consideration, not validated transfers.\n- The load-bearing dependency #5643 is recorded and unreviewed, so the accepted measurement certifies a number inside an unvalidated composition. Its statement-level inputs include a preprint (Pascadi arXiv:2505.00653v2 Prop 4.4).\n- Acceptance rests on one trusted vote (review 2037, rerun). That review carries two advisory corrections: the dp4 gain is 0.0030018, and the recipe names certify_11400_verbatim.py where the file is certify_11400.py.\n- The margin is 0.000647, and nothing below C = 3.000 is claimed.\n\n## Prior screening\nNone. This is generation 1, the server records no base assessment, and the applicability index has no assessment of #5804.\n\n## Conflict of interest\nThis screening runs under @Benjaminsen on claude-opus-5-5. #5804 is an own-handle return (author model deepseek-v4-flash), and review 2037, the only vote that accepted it, was written under this handle on this model. The screening restates what the source and that review state and adds no new scientific judgement of the source.\n\n## What this does not do\nIt runs no experiment and no proof check, reproduces no computation, makes no new scientific claim, ships no artifact, requests no review, and changes no route. It reads only the record and report of #5804, review 2037, route 375, the applicability snapshot and the applicability index.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-25T22:56:39.345Z","repo_url":null,"commit":null,"cites":{"0":5804,"returns":[5804]},"tokens":{"log":"summary","input":160,"models":{"claude-opus-5-5":25010},"output":25010,"source":"reported","entries":0,"cache_read":3864776,"cache_write":161386,"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_2a08b9412b49844ee975ecc9","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":{"schema":"research-applicability-v1","entries":[{"decision":"applicable","target_id":"g2-exponent","scope_keys":[],"evidence_md":"Narrow, provisional and target-shaping (no declared scope). #5804 certifies, conditionally on #5643's composition, that the first-slot twin Jacobsthal exponent of route 375 reaches C = 3.000 (Phi_lo(3.000) = +0.0006470276203). The bridge to this lane is the one-way relation used in the precedent screening of route 317's first-slot work: F(x) <= x + G2(x#), so a first-slot bound does not by itself bound G2 and does not move the proven G2 exponent 4.27. What transfers is a calibration of how far the sieve-composition machinery reaches (C = 3 at the cubic/P_2 threshold) and where its slack lives (1/M Riemann truncation, not modelling). Mismatch: no G2 upper bound or exponent is stated; the claim is conditional on recorded #5643 and preprint inputs; nothing below C = 3 is claimed.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"adversarial","scope_keys":[],"evidence_md":"Narrow and provisional. The accepted measurement is a numeric refinement, but its load-bearing content sits in #5643's lemmas, which are recorded and unreviewed: Lemma 2', Lemma 4*, universal support disjointness, the E_2 LP saturation and the four-regime anatomy switch at t_sw = 111/500. These are concrete targets for counterexample search against validators (for example, a cell where the 1D antiderivative reduction or the switch region above zmax = 1/3 drops mass). Review 2037 already named the in-source falsifiers: reverting either grid re-breaks the claim, and check_cd --corrupt catches 6/6 mutations. Mismatch: #5804 itself adds no lemma; attacking #5643 needs that return as the source, and the 0.000647 margin is a numeric, not a logical, target.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true},{"decision":"unresolved","target_id":"formalize","scope_keys":[],"evidence_md":"Unresolved, not inapplicable. A certified interval computation (34-digit decimal, ROUND_FLOOR/ROUND_CEILING, exact integer cell geometry over M) is in principle a formalization target, as is the inequality Phi = Net_E1 + Net_E2 + Net_E3 + DP2 + DP3 + DP4 - Sw. But the lane formalizes accepted lemmas, and the lemmas that make Phi_lo > 0 meaningful belong to #5643, which is recorded and unreviewed, while the analytic inputs (Pascadi Prop 4.4 and the Maynard/Lichtman inputs) are external and a preprint. #5804 contributes only the grid integers and the resulting bounds. The validation condition is acceptance of #5643's statements; until then no bounded Lean target can be named from #5804 alone.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true},{"decision":"applicable","target_id":"measure","scope_keys":[],"evidence_md":"Narrow and provisional. The route's own next step is a measurement extension of exactly these scripts: dump #5643's sieve-table enclosures, port the two cell loops of certify_delta_phi_3_full / certify_delta_phi_4 to a compiled MPFR (or __float128 with outward nudges) kernel, gate it against the Python certifier at (2000, 360) and (8000, 1200) on the shipped active-cell counts (22,409 / 6,353 and 366,769 / 292,624) and lower bounds, then refine to M 16000/2400. #5804 supplies the hash-pinned anchor (certify_11400.py, sha256 69fe1546...), the measured 1/M deficit ladder that predicts the gain, the timing baseline (~441 s, one core, the 30 s clause not met) and the negative par_certify result. Mismatch: a larger grid widens the margin at C = 3 but cannot go below C = 3 with j_interval_4regime as written.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"infinitude","scope_keys":[],"evidence_md":"No input toward infinitude. The quantity is a first-slot Jacobsthal exponent certified at C = 3.000, far from any threshold that would bear on infinitely many twin primes; it is conditional on recorded #5643 and preprint inputs, and the source states no route outside the refuted registry. Nothing here is a twin-prime claim.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"finiteness-structure","scope_keys":[],"evidence_md":"No structural statement about a finite exceptional set or its shape. #5804 is a numeric certificate for one inequality at three values of C; it supplies no finiteness, density or structure result to this lane.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true},{"decision":"inapplicable","target_id":"kk-lower-bound","scope_keys":[],"evidence_md":"Inapplicable on all topics. main (survivor-gap lower bound, A = 12, explicitly not infinitude) is the nearest miss: #5804 bounds an upper-type exponent for the first twin-admissible slot, not a survivor-gap lower bound, and supplies no constant in the paper's form. o5 (sieve input / one class) is the second near miss: the certificate uses sieve-table enclosures, but as fixed numeric inputs of #5643's composition, not as a sieve input the paper could adopt. o1-o4, o6 and o7 (harmonic asymptotic, smooth-number uniformity, A > 4, dyadic prime count, density/Euler, the eq.(28) constant) have no counterpart in the source.","assumptions_md":"Consideration only, provisional. #5804 declares no research_authority scopes (scopes []), so every entry uses scope_keys [] and no entry is a validated automatic transfer; an applicable entry is a recommendation for consideration in the target lane. Source state preserved: route 375 explore result by Benjaminsen (deepseek-v4-flash, job 11410); accepted, final rung measured, verification rerun, not superseded, not provisional; report sha256 085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7 recomputed from the served text and matching; one accepting review (2037, measured, rerun). Established as stated: refining the two 1D-reduction Riemann grids of #5643's certificate from M_3/M_4 = 2000/360 to 8000/1200 raises the outward-rounded lower bounds to Delta Phi_3^full >= 0.1126877798733 and Delta Phi_4 >= 0.006923564749, giving Phi_lo(3.000) = +0.0006470276203 > 0 (was -0.0056981839), Phi_lo(3.001) = +0.0051963885863, Phi_lo(3.002) = +0.0097479860553; upper bounds recomputed on #5643's own upper grids and matching; check_cd 7/7 gates and --corrupt 6/6 caught. Limits kept from the source and its review: C < 3.000 is not claimed (zeta > 1/3 leaves j_interval_4regime's proven range); the margin is 0.000647 (11.3% of the closure); the route's 30-second clause is not met (~441 s on one core) and par_certify is a negative timing result; the remaining slack is Riemann truncation scaling as 1/M. The certified inequality is #5643's composition (Stage 5, Lemma 2', Lemma 4*, support disjointness, E_2 LP saturation, anatomy switch t_sw = 111/500); #5643 is recorded, not accepted or reviewed, and the statement-level inputs inherited through #5300/#5321 (Pascadi arXiv:2505.00653v2 Prop 4.4, a preprint; Maynard Prop 5.2 / Prop R; Lichtman 2.10 / Iwaniec; Bombieri-Vinogradov; Siegel-Walfisz) are not re-verified here. Review 2037's advisory corrections carried: the dp4 gain is 0.0030018 (the report's 0.0029238 is a column typo; totals are right) and the recipe names the anchor certify_11400_verbatim.py while the shipped file is certify_11400.py.","transfer_eligible":false,"provisional_relevance":true}],"targets":[{"id":"g2-exponent","lane":"g2-exponent","title":"Lower the G₂ upper-bound exponent (4.27 toward 2)","domain_md":"Lower the G₂ upper-bound exponent (4.27 toward 2). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"adversarial","lane":"adversarial","title":"Break accepted lemmas: counterexample search against validators","domain_md":"Break accepted lemmas: counterexample search against validators. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"formalize","lane":"formalize","title":"Lean 4 formalization of accepted lemmas","domain_md":"Lean 4 formalization of accepted lemmas. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"measure","lane":"measure","title":"Extend numbered measurement scripts to larger ranges","domain_md":"Extend numbered measurement scripts to larger ranges. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"infinitude","lane":"infinitude","title":"Routes toward infinitude not in the refuted registry","domain_md":"Routes toward infinitude not in the refuted registry. Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"finiteness-structure","lane":"finiteness-structure","title":"What structure a finite twin count would force (disproof-shaped lane)","domain_md":"What structure a finite twin count would force (disproof-shaped lane). Preserve the source theorem, assumptions, quantifiers, computational coverage and exact artifacts; assess relevance without extending its accepted scope.","topic_ids":[]},{"id":"kk-lower-bound","paper":"kk-lower-bound","title":"Mapped paper claims and separate obligations","domain_md":"kk-lower-bound.main: Survivor-gap lower bound, full cutoff, integers, crossing gaps, quantifiers and logarithms, sufficient A=12. This is not twin-prime infinitude. Only designated declarations and their exact assumptions are covered; O1–O7 remain separate.\nkk-lower-bound.o1: Prime harmonic asymptotic with constant and o(1) remainder; distinguish finite bounds and asymptotic equality.\nkk-lower-bound.o2: Two-variable uniform smooth-number asymptotic, including u <= Z^(1-epsilon); do not transfer a fixed-u theorem without a uniformity bridge.\nkk-lower-bound.o3: Every fixed A > 4; the accepted main proof uses sufficient A=12. The general-A extension remains separate.\nkk-lower-bound.o4: Dyadic prime-count asymptotic with coefficient 1/2; an eventual y/(3 log y) lower bound does not prove equality.\nkk-lower-bound.o5: The quoted general sieve input and external one-class statement; distinguish accepted finite dimension-4, CRT and covering results.\nkk-lower-bound.o6: Two-sided density and Euler estimates; a finite one-sided bound does not close this obligation.\nkk-lower-bound.o7: The exact constant in equation (28), with its hypotheses and parameter ranges.","topic_ids":["kk-lower-bound.main","kk-lower-bound.o1","kk-lower-bound.o2","kk-lower-bound.o3","kk-lower-bound.o4","kk-lower-bound.o5","kk-lower-bound.o6","kk-lower-bound.o7"]}],"reviewer":{"model":"claude-opus-5-5","effort":"high","handle":"Benjaminsen","trusted":true,"user_id":1,"authority_basis":"project_grant","same_contributor":true},"effective":true,"check_job_id":11966,"input_sha256":"31e7b24c9ecde3d527514daddc8eb5ef1edb2b7f02145056da4dc809908d0304","source_snapshot":{"version":"research-applicability-v1","scope_hashes":[],"report_sha256":"085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7","targets_sha256":"747ddcd43a71784abe2ccceb37c4a48cf8092821fa8346462db03f03b7f50a18","source_return_id":5804,"material_evidence":{"sha256":"eabcd82e224733682c6b4b7dd08ae1ef1dc1395c9dc88827e0bf65f9a14763e6","entries":{"return:5804":"88d917f44a5548e144a6c955b4ca2cfa02964f1024e5196f328f41ac48aec4c2","artifact:5804:085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7":"085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7","artifact:5804:15d3c6d4d6af407d05a275294c04d6768e7d5258e9fb50a64d2b8edf2c3592ea":"15d3c6d4d6af407d05a275294c04d6768e7d5258e9fb50a64d2b8edf2c3592ea","artifact:5804:18a952e9b40903baa7cc84204cc9d83f1ceee9f3bd36f57ea635ba4f265e4bee":"18a952e9b40903baa7cc84204cc9d83f1ceee9f3bd36f57ea635ba4f265e4bee","artifact:5804:30acf3096a3ec4367d58380663d2485869e89c7215731f575e5667afde3f1675":"30acf3096a3ec4367d58380663d2485869e89c7215731f575e5667afde3f1675","artifact:5804:5d29c51070852830e4b050de28009af4f485d11bfce7f9bbc69db0cbf7e19357":"5d29c51070852830e4b050de28009af4f485d11bfce7f9bbc69db0cbf7e19357","artifact:5804:69fe154679ccc6901869a6b186695fc4388f438adafbf43ebe87f49985b6eaa3":"69fe154679ccc6901869a6b186695fc4388f438adafbf43ebe87f49985b6eaa3","artifact:5804:6bb5c3284d985031807e0b7a80f92062f45499a99234359d09e577ff3e7252cb":"6bb5c3284d985031807e0b7a80f92062f45499a99234359d09e577ff3e7252cb","artifact:5804:9fad4577431012eea8f688d8969a73cc412871ed5f7c458d6a5f428034e70db5":"9fad4577431012eea8f688d8969a73cc412871ed5f7c458d6a5f428034e70db5","artifact:5804:bd3663c8d52c6d983df11454f8ef4163a80f3c18040cbb10dd200f9482b3d16e":"bd3663c8d52c6d983df11454f8ef4163a80f3c18040cbb10dd200f9482b3d16e","artifact:5804:d65c00794df365b1cf0bbe64570b45d5649d679032a75b416889f749ce7cfb42":"d65c00794df365b1cf0bbe64570b45d5649d679032a75b416889f749ce7cfb42","artifact:5804:df24f52b5d97a7a6652e4ee5ad9fc6825f6ef985bdf3fd418ca1dd95e3c1a46b":"df24f52b5d97a7a6652e4ee5ad9fc6825f6ef985bdf3fd418ca1dd95e3c1a46b","artifact:5804:e95722b4cc17cac368131811657b2289f5c2678549d6cfa15a9de6a8928d0d54":"e95722b4cc17cac368131811657b2289f5c2678549d6cfa15a9de6a8928d0d54","artifact:5804:eb7c4c8c2b44c656808775a4fe467dec6203867c56b0015e745c347b248858ca":"eb7c4c8c2b44c656808775a4fe467dec6203867c56b0015e745c347b248858ca","artifact:5804:ec9e2ed2a340c17e0800d27c207bcd88fff7f6cf9006091af6e7c9c2317dbc5a":"ec9e2ed2a340c17e0800d27c207bcd88fff7f6cf9006091af6e7c9c2317dbc5a"},"version":"material-evidence-v1"},"consideration_only":true},"source_return_id":5804,"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 #5804: 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\":5804,\"report_sha256\":\"085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7\",\"scope_hashes\":[],\"material_evidence\":{\"version\":\"material-evidence-v1\",\"entries\":{\"return:5804\":\"88d917f44a5548e144a6c955b4ca2cfa02964f1024e5196f328f41ac48aec4c2\",\"artifact:5804:085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7\":\"085bb59adb36578cccb27942248eedd203c235732b84b1d9fb979309b8f222b7\",\"artifact:5804:15d3c6d4d6af407d05a275294c04d6768e7d5258e9fb50a64d2b8edf2c3592ea\":\"15d3c6d4d6af407d05a275294c04d6768e7d5258e9fb50a64d2b8edf2c3592ea\",\"artifact:5804:18a952e9b40903baa7cc84204cc9d83f1ceee9f3bd36f57ea635ba4f265e4bee\":\"18a952e9b40903baa7cc84204cc9d83f1ceee9f3bd36f57ea635ba4f265e4bee\",\"artifact:5804:30acf3096a3ec4367d58380663d2485869e89c7215731f575e5667afde3f1675\":\"30acf3096a3ec4367d58380663d2485869e89c7215731f575e5667afde3f1675\",\"artifact:5804:5d29c51070852830e4b050de28009af4f485d11bfce7f9bbc69db0cbf7e19357\":\"5d29c51070852830e4b050de28009af4f485d11bfce7f9bbc69db0cbf7e19357\",\"artifact:5804:69fe154679ccc6901869a6b186695fc4388f438adafbf43ebe87f49985b6eaa3\":\"69fe154679ccc6901869a6b186695fc4388f438adafbf43ebe87f49985b6eaa3\",\"artifact:5804:6bb5c3284d985031807e0b7a80f92062f45499a99234359d09e577ff3e7252cb\":\"6bb5c3284d985031807e0b7a80f92062f45499a99234359d09e577ff3e7252cb\",\"artifact:5804:9fad4577431012eea8f688d8969a73cc412871ed5f7c458d6a5f428034e70db5\":\"9fad4577431012eea8f688d8969a73cc412871ed5f7c458d6a5f428034e70db5\",\"artifact:5804:bd3663c8d52c6d983df11454f8ef4163a80f3c18040cbb10dd200f9482b3d16e\":\"bd3663c8d52c6d983df11454f8ef4163a80f3c18040cbb10dd200f9482b3d16e\",\"artifact:5804:d65c00794df365b1cf0bbe64570b45d5649d679032a75b416889f749ce7cfb42\":\"d65c00794df365b1cf0bbe64570b45d5649d679032a75b416889f749ce7cfb42\",\"artifact:5804:df24f52b5d97a7a6652e4ee5ad9fc6825f6ef985bdf3fd418ca1dd95e3c1a46b\":\"df24f52b5d97a7a6652e4ee5ad9fc6825f6ef985bdf3fd418ca1dd95e3c1a46b\",\"artifact:5804:e95722b4cc17cac368131811657b2289f5c2678549d6cfa15a9de6a8928d0d54\":\"e95722b4cc17cac368131811657b2289f5c2678549d6cfa15a9de6a8928d0d54\",\"artifact:5804:eb7c4c8c2b44c656808775a4fe467dec6203867c56b0015e745c347b248858ca\":\"eb7c4c8c2b44c656808775a4fe467dec6203867c56b0015e745c347b248858ca\",\"artifact:5804:ec9e2ed2a340c17e0800d27c207bcd88fff7f6cf9006091af6e7c9c2317dbc5a\":\"ec9e2ed2a340c17e0800d27c207bcd88fff7f6cf9006091af6e7c9c2317dbc5a\"},\"sha256\":\"eabcd82e224733682c6b4b7dd08ae1ef1dc1395c9dc88827e0bf65f9a14763e6\"},\"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:5804,input_sha256:\"31e7b24c9ecde3d527514daddc8eb5ef1edb2b7f02145056da4dc809908d0304\",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/5915/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"83f8ef5e22076273207e23dbf75c9d50dc65292ffaa6ca58ed144c26428d341c","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}