{ "schema_version": "1.0", "rh_status": "OPEN", "as_of": "2026-10-01", "editorial_aggregation": true, "source_states_modified": false, "author_display": "@ykbballer91", "version": "0.1.0", "publication_status": "PUBLIC", "public_release_date": "2026-09-30", "original_phase1_track_count": 17, "subsequent_updates": [ "Even-L2 cyclicity / full-ground capture Priority 1", "Finite even Fourier head spanning / Priority 2", "Existing-theorem import audit and Direct CMP / ES: CASE D; public update 2026-10-01" ], "source_repository_head": "c4b6fc587ebb6ad2cec37b9a24c38a3a7e823423", "claims": { "fixed_finite_m_support_selection": { "value": true, "source_path": "research/hierarchical_selection_state.json", "source_key": "support_all_fixed_finite_m_selection_proved", "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294", "public_source": "source-records/research/hierarchical_selection_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "restricted_projection_selection_scope": { "value": "Only the lowest direction restricted to P_N R_a span{k,k'',...,k^(2m)}, for each fixed finite m. Not the full finite Weil ground.", "source_path": "research/hierarchical_selection_state.json", "source_key": "resolved_full_selector_scope", "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294", "public_source": "source-records/research/hierarchical_selection_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "sufficient_resolution": { "value": "liminf N/(a*Y)>4/pi^2; in particular N/(a*Y)->infinity", "source_path": "research/hierarchical_selection_state.json", "source_key": "sufficient_path_condition", "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294", "public_source": "source-records/research/hierarchical_selection_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "cyclicity": { "value": "PROVED", "source_path": "research/full_ground_capture/state.json", "source_key": "cyclicity_status", "source_sha256": "8905c11ad1eaa7dd83f1ef89714c8dae133ed3b13cfb9d798a9845967df5d4e9", "public_source": "source-records/research/full_ground_capture/state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "cyclicity_scope": { "value": "K IS CYCLIC IN EVEN L2: PROVED", "source_path": "research/full_ground_capture/state.json", "source_key": "conclusion", "source_sha256": "8905c11ad1eaa7dd83f1ef89714c8dae133ed3b13cfb9d798a9845967df5d4e9", "public_source": "source-records/research/full_ground_capture/state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "cyclicity_RH_used": { "value": false, "source_path": "research/full_ground_capture/state.json", "source_key": "RH_used", "source_sha256": "8905c11ad1eaa7dd83f1ef89714c8dae133ed3b13cfb9d798a9845967df5d4e9", "public_source": "source-records/research/full_ground_capture/state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "growing_dimension_control": { "value": false, "source_path": "research/hierarchical_selection_state.json", "source_key": "uniform_m_to_infinity_control_proved", "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294", "public_source": "source-records/research/hierarchical_selection_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "full_ground_comparison": { "value": false, "source_path": "research/hierarchical_selection_state.json", "source_key": "actual_full_ground_to_k_comparison_proved", "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294", "public_source": "source-records/research/hierarchical_selection_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "ES_on_required_sequence": { "value": false, "source_path": "research/local_global_state.json", "source_key": "finite_prime_ES_for_required_cofinal_sequence_proved", "source_sha256": "4ba6b5027bf8aec5b923ef60f86fd42f9cd3b756285bc8ec2c1a7c5c875b38e0", "public_source": "source-records/research/local_global_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "G_star": { "value": false, "source_path": "research/hierarchical_selection_state.json", "source_key": "G_star_proved", "source_sha256": "b4f57fe270afe210ad4ed3883bd3dbe4bdd3aa5d3778c5e8aad155c608b51294", "public_source": "source-records/research/hierarchical_selection_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "exact_break": { "value": "G*: There exists an ES-admissible sequence (lambda_j,N_j), lambda_j -> infinity, such that for every compact K contained in Omega, sup_K |vhat(lambda_j,N_j;z)/vhat(lambda_j,N_j;z_star) - khat_lambda_j(z)/khat_lambda_j(z_star)| -> 0. ES and the comparison estimate are both unproved obligations.", "source_path": "research/local_global_state.json", "source_key": "exact_break_proposition", "source_sha256": "4ba6b5027bf8aec5b923ef60f86fd42f9cd3b756285bc8ec2c1a7c5c875b38e0", "public_source": "source-records/research/local_global_state.json", "source_commit": null, "source_commit_note": "Uncommitted research document at snapshot; historical repository HEAD is recorded separately." }, "finite_head_fixed_exact_spanning": { "value": true, "source_path": "research/full_ground_capture/priority2/state.json", "source_key": "actual_finite_prefix_spanning_for_each_fixed_head", "source_sha256": "788e093efb38c5dda549cd027893e40c7464fd0a1c2615627ae8565f1109d81c", "public_source": "source-records/research/full_ground_capture/priority2/state.json", "source_commit": null, "scope": "Fixed head exact span is not uniform capture, Weil-form control or RH." }, "finite_head_explicit_all_parameter_minimal_order": { "value": false, "source_path": "research/full_ground_capture/priority2/state.json", "source_key": "explicit_minimal_m_for_all_parameters", "source_sha256": "788e093efb38c5dda549cd027893e40c7464fd0a1c2615627ae8565f1109d81c", "public_source": "source-records/research/full_ground_capture/priority2/state.json", "source_commit": null, "scope": "Fixed head exact span is not uniform capture, Weil-form control or RH." }, "finite_head_interval_certificates": { "value": "Two finite parameter intervals; raw rank/singular-value bounds only", "source_path": "research/full_ground_capture/priority2/state.json", "source_key": "interval_certified_ranges", "source_sha256": "788e093efb38c5dda549cd027893e40c7464fd0a1c2615627ae8565f1109d81c", "public_source": "source-records/research/full_ground_capture/priority2/state.json", "source_commit": null, "scope": "Fixed head exact span is not uniform capture, Weil-form control or RH." }, "uniform_moving_head_capture": { "value": false, "source_path": "research/full_ground_capture/priority2/state.json", "source_key": "full_ground_capture_started", "source_sha256": "788e093efb38c5dda549cd027893e40c7464fd0a1c2615627ae8565f1109d81c", "public_source": "source-records/research/full_ground_capture/priority2/state.json", "source_commit": null, "scope": "Fixed head exact span is not uniform capture, Weil-form control or RH." } }, "rh_closed": false, "evidence_scope": "Written auxiliary proofs with scoped internal independent AI audits; not external peer review or full formal verification.", "historical_claims_snapshot_date": "2026-09-30", "source_repository_head_scope": "Original archived snapshot; later editorial updates do not rewrite its claims or source records.", "latest_update": { "public_update_date": "2026-10-01", "research_as_of": "2026-09-30", "public_summary": "../docs/updates/2026-10-01-cmp-es.md", "provenance": "Editorial summary of completed import/CMP/ES work, confirmed by the creator for this publication update.", "new_research_performed_for_publication": false, "import_audit": { "items_reviewed": 19, "generic_or_fixed_scope_items_delegated": 12, "new_actual_moving_weil_asymptotic_obligations_discharged": 0 }, "combined_case": "CASE D — CMP OPEN + ES OPEN", "CMP": { "status": "OPEN", "scope": "Value-normalized transforms converge uniformly on every compact subset of |Im z|<1/2; anchor z_star=i/4.", "sufficient_condition": "lambda^r D_{lambda,N}->0 for every 00.", "D_definition": "L2 norm of (I-P_v) P_N R_a k_lambda, where k_lambda is the raw prolate proxy and P_v projects onto the selected unit actual finite ground.", "sufficient_condition_proved": false, "equivalence_to_CMP_claimed": false, "ordinary_L2_convergence_sufficient": false }, "ES": { "status": "OPEN", "eventual_conditions": [ "e_minus(a,N)>e_plus(a,N)", "Delta_plus(a,N)>0" ], "finite_certification": { "c": 13, "N": 4, "scope": "Simple even ground at this one fixed endpoint only; not eventual ES." } }, "same_cofinal_sequence_required": true, "same_cofinal_sequence_established": false, "full_even_ground_capture_proved": false, "rh_closed": false, "next_action": "Investigate CMP and ES independently on the same admissible cofinal sequence; no automatic third route." } }