claim_id	claim_text	claim_class	thesis_source	lean_file	theorem_name	status	notes
BG-001	Normalized reconstruction objective is invariant under positive uniform scaling.	exact	THESIS.md §4	ThesisProofs/BG001Reconstruction.lean	normObjective_scale	Proved	Mapped to thesis-local executable objective normalization.
BG-002	Loop component count equals gcd, and coprime pairs yield one loop.	exact	THESIS.md §8	ThesisProofs/BG002CoprimeLoops.lean	coprime_single_loop	Proved	Matches partition/topology rule in thesis reference layer.
BG-003	Within the audited finite scaling study, some control multipliers exactly hit all temporal layers and no audited prime-family multiplier does.	exact	THESIS.md §6, §12, §21	ThesisProofs/BG003ScalingResonance.lean	finite_scaling_boundary_audit	Proved	Bounded non-universality boundary is now proved locally and echoed by the scaling study report.
BG-004	The projection chart catalog has distinct names, tag-preserving charts, and a unique exact modular chart.	exact	THESIS.md §8, §12, §21	ThesisProofs/BG004ProjectionCharts.lean	projection_chart_audit; modular_is_unique_exact_chart	Proved	Projection reference charts now carry explicit invariant audit rules and local theorems.
BG-005	Base optimality minimality classes are represented with thesis-local executable checks and local Lean minimality theorems.	exact	THESIS.md §12, §21	ThesisProofs/BG005BaseOptimality.lean	twelve_design; sixty_design; three_sixty_design; twenty_five_twenty_design	Proved	Finite checks are matched by Thesis-local Lean minimality witnesses.
BG-006	CRT-style modular decomposition claims are represented with thesis-local executable checks and local Lean modular theorems.	exact	THESIS.md §10, §12, §21	ThesisProofs/BG006CRTDecomposition.lean	modEq_360_iff; modEq_144000_iff; nineteen_on_rods; totient_rods	Proved	Executable rod checks are matched by Thesis-local CRT and residue theorems.
BG-007	In the audited triad-square neighborhood `(17, 19, 23)`, only 19 satisfies both the 360-boundary square congruence and full temporal-layer predecessor divisibility.	exact	THESIS.md §10	ThesisProofs/BG007PrimeSpokeBoundary.lean	boundary_anchor_17_fails; boundary_anchor_19_holds; boundary_anchor_23_fails; local_prime_spoke_boundary_audit	Proved	The prime-spoke failure boundary is now represented locally as a bounded audit and theorem family.
BG-008	Gaussian-circle prime embedding class audit is represented with thesis-local executable checks and a local Lean finite audit theorem.	exact	THESIS.md §12, §21	ThesisProofs/BG008GaussianCircle.lean	finite_prime_embedding_audit_500	Proved	The active finite audit bound is reimplemented and proved locally in Lean.
BG-009	Kissing and packing shell recurrence together with the 19-boundary temporal alignment are represented with thesis-local executable checks and local Lean theorems.	exact	THESIS.md §12, §21	ThesisProofs/BG009KissingPacking.lean	cumulative_recurs_by_shell; shell_audit_12; kissing_prime_boundary_19; predecessor_divides_temporal_layers_19	Proved	A local recurrence surface now covers shell growth and the 19-boundary alignment audit.
BG-011	Finite golden-angle prime-map semantics are represented with thesis-local Lean recurrences and finite map audits.	exact	THESIS.md §7, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG011GoldenAnglePrimeMap.lean	thetaDeg_succ_linear; wrappedThetaMilli_step; wrappedThetaMilli_period_360000; first_ten_prime_angles_milli_nodup	Proved	Prime-indexed golden-angle mapping now has explicit Thesis-local finite theorem coverage.
BG-012	Qualifying-prime finite set construction and selector semantics over the finite temporal-layer surface are represented with thesis-local Lean theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG012QualifyingPrimeSelectors.lean	selector_recovers_canonical_up_to_24001; selector_recovers_canonical_up_to_144003; canonical_qualifying_prime_count; all_qualifying_prime_count	Proved	Selector semantics now reproduce the canonical qualifying-prime set in bounded finite domains used by the thesis.
BG-013	AP-sqrt residual decomposition and deterministic nth-root branch partition semantics are represented with thesis-local Lean theorem families.	exact	THESIS.md §4, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG013ResidualAndBranches.lean	squareResidual_factorization; identityResidual_zero_implies_squareResidual_zero; degreeClassAudit_pow2_expected; degreeClassAudit_smooth_expected; degreeClassAudit_fallback_expected; degreeClassAudit_partition_is_disjoint	Proved	Residual channels and audited finite branch classes are now theoremized in Thesis-local Lean.
BG-014	PQ ellipse parameter identities and three-sphere Soddy curvature/radius relations are represented with thesis-local Lean theorem families.	exact	THESIS.md §11, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG014EllipseSphereRelations.lean	pqSemiMajor_formula; pqSemiMinorSq_formula; pqSemiMinor_nonnegative; pqEccentricity_nonnegative; soddyInnerRadius_relation; soddyOuterRadius_relation; soddy_curvature_gap_formula	Proved	Integrated geometry surfaces now have Thesis-local symbolic and finite-domain theorem coverage.
BG-015	Exact bridge-ratio family including s/r, d/s, d/r, normalized kissing-gap, and inner-offset ratios is represented with thesis-local Lean theorems.	exact	THESIS.md §3, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG015BridgeRatios.lean	bridge_ratio_formula; diagonal_ratio_formula; diagonal_radius_ratio_formula; normalized_kissing_gap_ratio_formula; inner_offset_ratio_formula	Proved	The canonical bridge ratios and their exact bridge derivatives are now explicitly theoremized in Thesis-local Lean.
BG-016	Deterministic temporal-signature and hit-stratification claims are represented with thesis-local Lean finite theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG016TemporalSignatures.lean	temporal_signature_19_all_layers; full_coverage_primes_profile; four_layer_profile; three_layer_profile; two_layer_profile; one_layer_profile; partial_coverage_count	Proved	The canonical qualifying-prime temporal signatures and corrected hit-count stratification are now theoremized in Thesis-local Lean.
BG-017	Geometry-camera latent-contract and hyperspherical projection exact surfaces are represented with thesis-local Lean theorems.	exact	THESIS.md §8, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG017LatentProjectionContracts.lean	core24_channel_count; extended36_channel_count; occupied_void_split; signed_drift_index_profile; geodesic_distance_formula; geodesic_similarity_formula; geodesic_distance_in_contract	Proved	Latent cardinality, occupied/void split, signed-drift placement, and hyperspherical geodesic formulas are now theoremized in Thesis-local Lean.
BG-018	Named reconstruction-route formulas imported from squares are represented with thesis-local Lean theorems.	exact	THESIS.md §4, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG018ReconstructionRoutes.lean	center_shift_formula; center_distance_formula; inner_offset_formula; center_shift_exact_recovery; center_distance_exact_recovery; inner_offset_exact_recovery	Proved	The named reconstruction routes are now theoremized as exact formulas with calibrated recovery lemmas in Thesis-local Lean.
BG-019	Deterministic auxiliary exact surfaces for temporal layers, golden-angle radians, PQ resonance radii, fractal depth, and audited 29-boundary profile are represented with thesis-local Lean theorems.	exact	THESIS.md §6, §7, §11, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG019DeterministicAuxiliarySurfaces.lean	temporal_layers_profile; golden_angle_rad_formula; pq_radiusA_formula; pq_radiusB_formula; fractal_depth_formula; transition_prime_29_profile; transition_claim_counterexample_31	Proved	Deterministic exact surfaces outside the earlier selector and ellipse families are now theoremized, and the strong 29-transition claim is explicitly stress-tested against the current shared model.
BG-011a	Golden-angle constant identity is represented in the Thesis-local Lean workspace as a symbolic theorem.	exact	THESIS.md §7, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG010CrossProjectFormulas.lean	golden_angle_symbolic_identity	Proved	Covers the symbolic constant identity layer; finite prime-map semantics remain tracked in formalization gaps.
BG-014a	Soddy/Descartes curvature pair formula is represented in the Thesis-local Lean workspace as a symbolic theorem.	exact	THESIS.md §11, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG010CrossProjectFormulas.lean	soddy_curvature_pair_formula	Proved	Covers the symbolic curvature-pair layer; additional finite geometry closures remain tracked in formalization gaps.
BG-020	Dual smooth partition and audited p-1/p+1 transition profile are represented with thesis-local Lean finite theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG020DualSmoothPartition.lean	audited_dual_smooth_census; audited_pm1_only_census; audited_transition_profile; pm1_dual_profile_29_31	Proved	Dual-smooth census and the 29/31 transition profile are now theoremized in Thesis-local Lean.
BG-021	Geometry-camera deterministic feature-extraction direct formulas are represented with thesis-local Lean theorem families.	exact	THESIS.md §8, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG021FeatureExtractionFormulas.lean	center_energy_formula; thirds_energy_formula; diagonal_energy_formula; golden_balance_formula; crossing_parity_balance_formula; alternation_run_length_stats_formula; dual_face_area_entropy_formula; central_void_pressure_formula; figure_ground_flip_stability_formula; perspective_sphere_coupling_formula; plane_radial_primary_formula; negative_space_coherence_formula	Proved	Exact feature-extraction formulas are now theoremized in Thesis-local Lean.
BG-022	Finite kissing-prime census and twin-pair residue audit are represented with thesis-local Lean finite theorems.	exact	THESIS.md §10, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG022KissingPrimeCensus.lean	kissing_prime_count; kissing_prime_residue_census; kissing_twin_pair_count; kissing_twin_pairs_exact; kissing_prime_membership_19; kissing_prime_membership_449	Proved	Kissing-prime finite census and twin-pair subclass are now theoremized in Thesis-local Lean.
BG-023	Exact dual-smooth census and transition profile are represented with thesis-local Lean finite theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG023DualSmoothCensus.lean	dual_smooth_census; pm1_only_census; transition_profile_exact; pm1_dual_profile_29_31	Proved	Dual-smooth qualifying-prime census and transition profile are now theoremized in Thesis-local Lean.
BG-024	Deterministic projection-space angular and radial coordinate constructors are represented with thesis-local Lean direct formulas.	exact	THESIS.md §8, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG024ProjectionSpaceCoordinates.lean	theta_coordinate_formula; radial_coordinate_formula	Proved	Projection-space coordinate formulas are now theoremized in Thesis-local Lean.
BG-025	Hyperdimensional bridge formulas for hypersphere/hypercube volume and cube-root fixed-point surface are represented with thesis-local Lean theorems.	exact	THESIS.md §3, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG025HyperdimensionalBridge.lean	hypersphere_volume_formula; hypercube_volume_formula; cube_root_fixed_point_equation	Proved	N-dimensional bridge formulas and n=3 cube-root fixed-point equation are now theoremized in Thesis-local Lean.
BG-026	Negative-space partition predicate, prime-square boundary anchor, and n-dimensional diagonal formula are represented with thesis-local Lean theorems.	exact	THESIS.md §10, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG026NegativeSpaceAndDiagonal.lean	negative_space_partition_formula; prime_square_boundary_anchor_19; n_dimensional_diagonal_formula	Proved	Anti-resonance partition, boundary anchor arithmetic, and n-dimensional diagonal formula are now theoremized in Thesis-local Lean.
BG-027	Temporal-divisibility dual profile over audited dual-smooth qualifying primes is represented with thesis-local Lean finite theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG027TemporalDivisibilityDual.lean	dual_temporal_divisibility_profile; dual_temporal_divisibility_31	Proved	Dual temporal-divisibility profile is now theoremized in Thesis-local Lean.
BG-028	Gaussian bridge constant integral identity is represented with thesis-local Lean theorem.	exact	THESIS.md §3, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG028GaussianBridge.lean	gaussian_bridge_constant	Proved	The Gaussian bridge identity linking the full-line Gaussian integral to sqrt(pi) is now theoremized in Thesis-local Lean.
BG-029	Geometry-camera centroid-inference exact formula surfaces are represented with thesis-local Lean theorem families.	exact	THESIS.md §8, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG029CentroidInferenceFormulas.lean	centroid_channel_average_formula; cosine_similarity_formula; cosine_degenerate_guard_formula; raw_cosine_unit_mapping_formula; centroid_card_score_formula	Proved	Centroid training average, cosine-with-guard normalization, and score-fusion formulas are now theoremized in Thesis-local Lean.
BG-030	Temporal-hit stratification level profile over qualifying primes is represented with thesis-local Lean finite theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG030TemporalStratificationLevels.lean	temporal_hit_function_formula; temporal_hit_levels_exact; temporal_hit_function_19_all_layers; temporal_hit_function_16001_single_layer	Proved	The bounded temporal-hit function and observed multiplicity levels {6,4,3,2,1} are now theoremized in Thesis-local Lean.
BG-031	Dual-channel temporal divisibility profile and asymmetry witness over qualifying primes is represented with thesis-local Lean finite theorems.	exact	THESIS.md §6, Formula Coverage and Lean Verification Ledger	ThesisProofs/BG031TemporalDivisibilityAsymmetry.lean	dual_channel_pm1_formula; dual_channel_pp1_formula; pp1_full_layer_profile_exact; dual_smooth_channel_agreement; temporal_asymmetry_witness_13	Proved	The p-1/p+1 dual temporal channel profile and an explicit asymmetry witness are now theoremized in Thesis-local Lean.