claim_id	source_project	claim_family	claim_text	claim_class	validation_kind	thesis_disposition	source_paths	executable_artifacts	notes
XP-SQ-001	squares	bridge-geometry	Circle-square bridge ratio is s/r = sqrt(pi).	exact	direct_formula	formalize	Thesis/reference/bridge.py	Thesis/support/generate_bridge_metrics.py; Thesis/support/generated/bridge_metrics.json	Canonical bridge identity already thesis-central; imported here as source claim witness.
XP-SQ-002	squares	bridge-geometry	Square diagonal ratio is diag/s = sqrt(2).	exact	direct_formula	formalize	Thesis/reference/bridge.py	Thesis/support/generate_bridge_metrics.py; Thesis/support/generated/bridge_metrics.json	Canonical exact ratio.
XP-SQ-003	squares	bridge-geometry	Composite bridge ratio diag/r = sqrt(2*pi).	exact	derived_formula	formalize	Thesis/reference/bridge.py	Thesis/support/generate_bridge_metrics.py; Thesis/support/generated/bridge_metrics.json	Useful exact composite relation not previously surfaced explicitly.
XP-SQ-004	squares	bridge-geometry	Normalized kissing-gap relation is kissing_gap/draw_side = 1/sqrt(2) - 2/sqrt(pi).	exact	direct_formula	formalize	Thesis/reference/bridge.py	Thesis/support/generate_bridge_metrics.py; Thesis/support/generated/bridge_metrics.json	Exact draw-space bridge derivative.
XP-SQ-005	squares	bridge-geometry	Inner-offset normalization is inner_offset/(draw_side/2) = sqrt(4/pi - 1).	exact	direct_formula	formalize	Thesis/reference/bridge.py	Thesis/support/generate_bridge_metrics.py; Thesis/support/generated/bridge_metrics.json	Exact offset identity.
XP-SQ-006	squares	reconstruction	Center-shift side reconstruction uses s_from_center_shift = (dx + dy) / scale.	exact	direct_formula	formalize	Thesis/reference/reconstruction.py	Thesis/support/reconstruction_metrics.py; Thesis/support/generated/reconstruction_metrics.json	Current best solver candidate in squares explorer.
XP-SQ-007	squares	reconstruction	Center-distance side reconstruction uses s_from_center_distance = sqrt(2) * ||O2 - O1|| / scale.	exact	direct_formula	formalize	Thesis/reference/reconstruction.py	Thesis/support/reconstruction_metrics.py; Thesis/support/generated/reconstruction_metrics.json	Secondary exact reconstruction route.
XP-SQ-008	squares	reconstruction	Inner-offset side reconstruction uses s_from_inner_offset = 2 * inner_offset / (sqrt(4/pi - 1) * scale).	exact	direct_formula	formalize	Thesis/reference/reconstruction.py	Thesis/support/reconstruction_metrics.py; Thesis/support/generated/reconstruction_metrics.json	Diagnostic exact reconstruction route.
XP-SQ-009	squares	boundary-primes	Boundary prime closure claim: 19^2 = 361 and 19^2 - 1 = 360.	exact	finite_arithmetic	formalize	Thesis/reference/squares_local.py	Thesis/support/prime_spoke_failure_boundaries.py; Thesis/support/generated/prime_spoke_failure_boundaries.json	Central annulus closure surface.
XP-SQ-010	squares	temporal-divisibility	Temporal-hit function maps a prime p to layers divisible by p-1.	exact	finite_audit	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/prime_coprime_symbols.py; Thesis/support/generated/prime_coprime_symbols.json	Source surface for bounded layer-hit audits.
XP-SQ-011	squares	harmonic-anchors	Harmonic square anchor triad is (17, 19, 23) with 19 as the central deterministic boundary anchor.	structural_proxy	finite_audit	bounded-audit	Thesis/reference/squares_local.py	Thesis/support/prime_spoke_failure_boundaries.py; Thesis/support/generated/prime_spoke_failure_boundaries.json	Keep deterministic status distinct from symbolic anchor language.
XP-SQ-012	squares	nth-root-branches	Nth-root degrees partition into pow2_chain, smooth_235, and fallback classes.	exact	finite_audit	formalize	Thesis/reference/scaling.py	Thesis/support/generated/lean_proof_audit_report.md	Already partially theoremized; imported as source claim surface.
XP-SQ-013	squares	nth-root-branches	Layer amplification route computes cumulative_scale_and_inv_sqrt for deterministic scaling experiments.	empirical	deterministic_algorithm	projection-chart	Thesis/reference/scaling.py	Thesis/support/nth_root_branches_audit.py; Thesis/support/generated/nth_root_branches_audit.json	Useful algorithmic surface but not theorem language by itself.
XP-DT-001	deterministic	modulus-layers	Base modulus is 144000 = 2^7 * 3^2 * 5^3.	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/generated/lean_proof_audit_report.md	Canonical deterministic modulus.
XP-DT-002	deterministic	modulus-layers	Temporal layer family is (7200, 14400, 28800, 36000, 72000, 144000).	exact	finite_family	formalize	Thesis/reference/deterministic_local.py	Thesis/support/prime_coprime_symbols.py; Thesis/support/generated/prime_coprime_symbols.json	Canonical bounded layer family.
XP-DT-003	deterministic	qualifying-primes	Prime p qualifies iff p >= 7 and p-1 is 2,3,5-smooth and divides at least one temporal layer.	exact	finite_selector	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/generated/lean_proof_audit_report.md	Canonical selector rule.
XP-DT-004	deterministic	qualifying-primes	Canonical qualifying-prime set contains exactly 35 primes >= 7.	exact	finite_enumeration	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/generated/lean_proof_audit_report.md	Finite exact set already partially theoremized.
XP-DT-005	deterministic	qualifying-primes	All qualifying primes list extends the 35-prime set by degenerate cases 2 and 3.	exact	finite_family	bounded-audit	Thesis/reference/prime_temporal_local.py	Thesis/support/qualifying_primes_audit.py; Thesis/support/generated/qualifying_primes_audit.json	Inventory claim for deterministic base cases.
XP-DT-006	deterministic	golden-angle	Golden angle in radians is pi * (3 - sqrt(5)).	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/generated/lean_proof_audit_report.md	Canonical irrational projection constant.
XP-DT-007	deterministic	golden-angle	Golden angle in degrees is degrees(pi * (3 - sqrt(5))).	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/generated/lean_proof_audit_report.md	Degree-form projection constant.
XP-DT-008	deterministic	golden-angle	Twin angular spacing is exactly 2 * golden_angle.	exact	direct_formula	bounded-audit	Thesis/reference/deterministic_local.py	Thesis/support/golden_angle_audit.py; Thesis/support/generated/golden_angle_audit.json	Deterministic twin-prime chart constant.
XP-DT-009	deterministic	twin-pairs	Double smooth twin-pair family is ((3,5), (5,7), (17,19)).	exact	finite_family	bounded-audit	Thesis/reference/partitions.py	Thesis/support/twin_pairs_audit.py; Thesis/support/generated/twin_pairs_audit.json	Bounded symbolic/deterministic pair inventory.
XP-DT-010	deterministic	kissing-radii	Kissing radii equal RADIUS_UNIT * [1,2,4,5,10,20] = (7200, 14400, 28800, 36000, 72000, 144000).	exact	direct_formula	formalize	Thesis/reference/partitions.py	Thesis/support/generated/lean_proof_audit_report.md	Finite shell-radius family.
XP-DT-011	deterministic	temporal-alignment	Daily-cycle alignment is 10 * SECONDS_IN_DAY = 6 * BASE_MODULUS = 864000.	exact	direct_formula	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/generated/lean_proof_audit_report.md	Finite exact alignment.
XP-DT-012	deterministic	boundary-primes	Transition around 29 and 31 is treated as a bounded dual-channel profile rather than a singleton onset theorem.	empirical	finite_audit	bounded-audit	Thesis/reference/squares_local.py	Thesis/support/dual_prime_partition_audit.py; Thesis/support/generated/dual_prime_partition_audit.json	Retires the over-strong singleton wording and keeps the corrected transition profile as bounded audit evidence.
XP-DT-013	deterministic	boundary-primes	Pre-stabilization boundary is 31; primes below it form a distinct pre-stabilization phase.	interpretive	finite_boundary	projection-chart	Thesis/reference/squares_local.py	Thesis/support/bounded_family_audits.py; Thesis/support/generated/bounded_family_audits.json	Keep separated from exact number-theoretic claims unless formalized.
XP-DT-014	deterministic	pq-ellipse	Geometric-mean PQ resonance ellipse uses Ra = BASE_MODULUS * p/sqrt(pq) and Rb = BASE_MODULUS * q/sqrt(pq).	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/pq_ellipse_audit.py; Thesis/support/generated/pq_ellipse_audit.json	Second PQ chart distinct from direct semi-major/semi-minor chart.
XP-DT-015	deterministic	pq-ellipse	PQ resonance chart classifies pairs by ratio bands into circularelliptic, near-circular, rectangular, and highly-elliptic.	empirical	finite_audit	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Classification thresholds are policy bands, not theorem identities.
XP-DT-016	deterministic	pq-ellipse	Direct PQ ellipse chart uses semi_major=(q+1)/2, semi_minor=sqrt((q^2-p^2)/4), and derived eccentricity.	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/generated/lean_proof_audit_report.md	Distinct PQ geometry surface already partially theoremized.
XP-DT-017	deterministic	soddy-geometry	Two-sphere Soddy curvature pair uses b_inner,b_outer = b1 + b2 +/- 2*sqrt(b1*b2).	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/generated/lean_proof_audit_report.md	Exact Descartes curvature identity.
XP-DT-018	deterministic	soddy-geometry	Three-sphere Soddy radii use k_i = 1/r_i and return 1/(k1+k2+k3 +/- 2*sqrt(k1k2+k2k3+k3k1)).	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/generated/lean_proof_audit_report.md	Three-sphere curvature/radius surface.
XP-DT-019	deterministic	projection-space	Quadrant-of-prime chart assigns Q1..Q4 from golden-angle degree placement modulo 360.	structural_proxy	finite_chart	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Projection chart, not standalone theorem.
XP-DT-020	deterministic	temporal-stratification	Qualifying primes stratify by temporal hit counts rather than all hitting all six layers; observed multiplicities are 6, 4, 3, 2, and 1.	empirical	finite_audit	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/temporal_signature_audit.py; Thesis/support/generated/temporal_signature_audit.json	This corrects the overstated constant-hit narrative and is a strong bounded-theorem candidate.
XP-DT-021	deterministic	temporal-signatures	Temporal alignment matrix records each qualifying prime's exact layer-divisibility signature together with full-coverage and coverage-distribution summaries.	exact	finite_audit	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/temporal_signature_audit.py; Thesis/support/generated/temporal_signature_audit.json	Finite signature inventory surface directly supports bounded temporal-stratification proofs.
XP-DT-022	deterministic	temporal-signatures	Shared temporal groups partition primes by identical temporal signatures.	exact	finite_audit	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/temporal_signature_audit.py; Thesis/support/generated/temporal_signature_audit.json	Natural refinement of temporal-hit structure.
XP-DT-023	deterministic	temporal-signatures	Temporal cross-correlation between primes is computed as Jaccard similarity of temporal signatures.	exact	direct_formula	projection-chart	Thesis/reference/prime_temporal_local.py	Thesis/support/temporal_signature_audit.py; Thesis/support/generated/temporal_signature_audit.json	Exact metric on bounded signature sets, but better treated as chart metric unless theoremized.
XP-DT-024	deterministic	lattice-object	Fractal depth of a prime node is the sum of the exponent tuple of p-1 over the 2,3,5 smoothness basis.	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/lattice_object_audit.py; Thesis/support/generated/lattice_object_audit.json	Strong candidate for exact depth-spectrum formalization. Coverage hardening track: CH-008.
XP-DT-025	deterministic	lattice-object	Prime-lattice node radius is normalized as log10(|p|)/log10(BASE_MODULUS) for |p| > 1.	exact	direct_formula	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/lattice_object_audit.py; Thesis/support/generated/lattice_object_audit.json	Deterministic radial chart coordinate, not core theorem language by default.
XP-DT-026	deterministic	lattice-object	Narrative layer classification bins primes into six named radial layers by magnitude intervals.	structural_proxy	finite_family	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Useful chart-language surface but intentionally not exact number-theoretic theorem language.
XP-DT-027	deterministic	multi-dimensional-projection	Multi-dimensional prime projection uses normalized golden-angle phase, ring index, p-1 exponent coordinates, and temporal-layer phase extensions.	exact	deterministic_projection	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/multi_dimensional_projection_audit.py; Thesis/support/generated/multi_dimensional_projection_audit.json	Deterministic projection constructor for higher-dimensional chart studies.
XP-DT-028	deterministic	dual-smooth-partition	Dual-smooth prime family where both p-1 and p+1 are {2,3,5}-smooth is a finite exact set within the audited bound.	exact	finite_audit	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/dual_prime_partition_audit.py; Thesis/support/generated/dual_prime_partition_audit.json	Captures the user's p-1/p+1 dual theory as a finite audited exact family.
XP-DT-029	deterministic	boundary-primes-dual	Primes 29 and 31 form a dual transition profile: 29 has p+1 smoothness without p-1 smoothness, while 31 is dual-smooth and inaugurates the post-boundary ring.	empirical	finite_audit	bounded-audit	Thesis/reference/prime_temporal_local.py	Thesis/support/dual_prime_partition_audit.py; Thesis/support/generated/dual_prime_partition_audit.json	Reframes the earlier over-strong singleton claim as a dual transition profile rather than a failure. Coverage hardening track: CH-005.
XP-DT-030	deterministic	temporal-divisibility-dual	Temporal divisibility should be audited on both p-1 and p+1 channels to expose dual layer-hit partitions and asymmetry spectra.	empirical	finite_audit	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/dual_prime_partition_audit.py; Thesis/support/generated/dual_prime_partition_audit.json	Extends the current p-1-only audit to the user's dual theory.
XP-GC-001	geometry-camera-android	latent-contract	On-device latent contract uses 36 deterministic channels with exactly one signed channel and the rest constrained to [0,1].	exact	finite_contract	formalize	Thesis/reference/geometry_camera_local.py	Thesis/support/geometry_camera_contract_audit.py; Thesis/support/generated/geometry_camera_contract_audit.json	Deterministic bounded projection-manifold contract.
XP-GC-002	geometry-camera-android	centroid-inference	Centroid training averages labeled feature vectors channelwise and stores positive and rejected-label negative centroids.	exact	deterministic_algorithm	projection-chart	Thesis/reference/geometry_camera_local.py	Thesis/support/centroid_inference_audit.py; Thesis/support/generated/centroid_inference_audit.json	Deterministic inference path, not number-theoretic theorem.
XP-GC-003	geometry-camera-android	centroid-inference	Cosine similarity is dot(a,b)/(||a||*||b||) with finite guards and zero-return for degenerate norms.	exact	direct_formula	projection-chart	Thesis/reference/geometry_camera_local.py	Thesis/support/centroid_inference_audit.py; Thesis/support/generated/centroid_inference_audit.json	Exact bounded scoring primitive.
XP-GC-004	geometry-camera-android	centroid-inference	Card score is positive_similarity - 0.42 * negative_similarity after mapping raw cosine scores into [0,1].	exact	deterministic_scoring	projection-chart	Thesis/reference/geometry_camera_local.py	Thesis/support/centroid_inference_audit.py; Thesis/support/generated/centroid_inference_audit.json	Exact app-scoring rule.
XP-GC-005	geometry-camera-android	hyperspherical-projection	CORE_24 latent projection concatenates 12 occupied-space and 12 void-space channels then L2-normalizes.	exact	deterministic_projection	formalize	Thesis/reference/geometry_camera_local.py	Thesis/support/hyperspherical_projection_audit.py; Thesis/support/generated/hyperspherical_projection_audit.json	Strong occupied/void dual-space witness for Thesis projection philosophy.
XP-GC-006	geometry-camera-android	hyperspherical-projection	EXTENDED_36 projection appends 12 meta or temporal channels to CORE_24 before normalization.	exact	deterministic_projection	projection-chart	Thesis/reference/geometry_camera_local.py	Thesis/support/hyperspherical_projection_audit.py; Thesis/support/generated/hyperspherical_projection_audit.json	Bounded latent extension chart.
XP-GC-007	geometry-camera-android	hyperspherical-projection	Geodesic distance on the latent sphere is acos(clamp(dot(u,v), -1, 1)).	exact	direct_formula	formalize	Thesis/reference/geometry_camera_local.py	Thesis/support/hyperspherical_projection_audit.py; Thesis/support/generated/hyperspherical_projection_audit.json	Exact unit-sphere distance primitive.
XP-GC-008	geometry-camera-android	hyperspherical-projection	Geodesic similarity is normalized as 1 - distance/pi on the hypersphere.	exact	direct_formula	projection-chart	Thesis/reference/geometry_camera_local.py	Thesis/support/hyperspherical_projection_audit.py; Thesis/support/generated/hyperspherical_projection_audit.json	Exact bounded similarity chart.
XP-GC-009	geometry-camera-android	graph-resonance	Recursive resonance uses a bounded depth and fanout graph walk with pathScore*0.84 + bridgeScore*0.16.	empirical	finite_audit	projection-chart	Thesis/reference/projection.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Deterministic but weighted policy surface; not theorem language. Coverage hardening track: CH-001.
XP-GC-010	geometry-camera-android	graph-resonance	Emergent bridge cards are cross-family related cards above threshold score and capped to six results.	empirical	finite_audit	projection-chart	Thesis/reference/projection.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Bounded audit chart for relation bridges. Coverage hardening track: CH-001.
XP-GC-011	geometry-camera-android	perspective-audit	Perspective audit requires vanishing point coordinates in [0,1], at least 3 plane hypotheses, finite 9-value homographies, and bounded homography confidence.	exact	finite_contract	bounded-audit	Thesis/reference/geometry_camera_local.py	Thesis/support/geometry_camera_contract_audit.py; Thesis/support/generated/geometry_camera_contract_audit.json	Strong test-defined contract surface.
XP-GC-012	geometry-camera-android	negative-space-proxies	Occupied-space and void-space channels are deliberately co-modeled as one projection object in CORE_24 rather than separate classifiers.	structural_proxy	deterministic_projection	formalize	Thesis/reference/projection.py	Thesis/support/negative_space_proxies_audit.py; Thesis/support/generated/negative_space_proxies_audit.json	Strong cross-repo witness for negative-space thesis language. Coverage hardening track: CH-012.
XP-GC-013	geometry-camera-android	feature-extraction	Cymatic wave resonance is a bounded weighted fusion of ring regularity, sector regularity, alternation balance, crossing parity, and cycle-basis density.	empirical	deterministic_scoring	projection-chart	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Empirical score surface, not theorem language.
XP-GC-014	geometry-camera-android	feature-extraction	Dodecahedral face coherence is a bounded weighted fusion of node-ring occupancy, chord orbit coverage, cycle-basis density, dual-face entropy, and inverse ring drift.	empirical	deterministic_scoring	projection-chart	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Structural proxy for platonic alignment, not literal polyhedron theorem.
XP-GC-015	geometry-camera-android	feature-extraction	Icosahedral vertex coherence is a bounded weighted fusion of chord orbit coverage, node-degree entropy, perspective coupling, self-similarity, and inverse angle variance.	empirical	deterministic_scoring	projection-chart	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Structural proxy score surface.
XP-SQ-014	squares	negative-space-partition	Negative space or anti-resonance partition is defined by gcd(A,360) > 1 over the audited area family.	exact	finite_audit	formalize	Thesis/reference/squares_local.py	Thesis/support/squares_duality_audit.py; Thesis/support/generated/squares_duality_audit.json	Complements resonance-window logic with an explicit anti-resonance partition.
XP-SQ-015	squares	prime-anchor-duality	Prime-anchor neighborhoods form six mirrored bands [p, p^2, 360k-p^2, 360k-p, 360k+p, 360k+p^2].	exact	finite_family	projection-chart	Thesis/reference/squares_local.py	Thesis/support/prime_anchor_duality_audit.py; Thesis/support/generated/prime_anchor_duality_audit.json	Explicit mirrored-band order for p and p^2 around the 360k midline.
XP-SQ-016	squares	prime-square-boundary	The color-wheel center and kissing-boundary surface use p^2-1 as the circular center anchor, exemplified by 19^2-1=360.	exact	finite_arithmetic	formalize	Thesis/reference/squares_local.py	Thesis/support/squares_duality_audit.py; Thesis/support/generated/squares_duality_audit.json	Directly connects p^2-1 to negative-space and square-circle boundary research.
XP-SQ-017	squares	gaussian-bridge	Gaussian bridge constant satisfies integral exp(-x^2) dx over the full real line equals sqrt(pi).	exact	direct_formula	formalize	Thesis/reference/squares_local.py	Thesis/support/gaussian_bridge_audit.py; Thesis/support/generated/gaussian_bridge_audit.json	Analytic bridge constant underlying the circle-square identity.
XP-SQ-018	squares	hyperdimensional-bridge	N-dimensional hypersphere volume uses V_n(r)=pi^(n/2) * r^n / Gamma(n/2+1).	exact	direct_formula	formalize	Thesis/reference/squares_local.py	Thesis/support/hyperdimensional_bridge_audit.py; Thesis/support/generated/hyperdimensional_bridge_audit.json	Generalized hypersphere bridge formula for higher-dimensional root research.
XP-SQ-019	squares	hyperdimensional-bridge	N-dimensional hypercube volume uses V_n(s)=s^n as the cube-family side measure dual to hypersphere volume.	exact	direct_formula	formalize	Thesis/reference/squares_local.py	Thesis/support/hyperdimensional_bridge_audit.py; Thesis/support/generated/hyperdimensional_bridge_audit.json	Pairs with hypersphere volume for generalized bridge reasoning.
XP-SQ-020	squares	hyperdimensional-bridge	Cube-root solver recovers side length from volume using multiplication-only bisection on s^3=V.	exact	deterministic_algorithm	formalize	Thesis/reference/squares_local.py	Thesis/support/hyperdimensional_bridge_audit.py; Thesis/support/generated/hyperdimensional_bridge_audit.json	N-dimensional bridge operationalization for the n=3 case.
XP-SQ-021	squares	kissing-spheres-3d	3D kissing sphere visualization preserves the 2D kissing-circle boundary language as a higher-dimensional projection chart.	structural_proxy	finite_chart	projection-chart	Thesis/reference/duality.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Projection claim rather than exact theorem.
XP-GC-016	geometry-camera-android	prime-anchor-duality	Feature channel primeContactResonance measures normalized contact strength between observed geometry and prime-anchor neighborhoods.	empirical	deterministic_projection	projection-chart	Thesis/reference/squares_local.py	Thesis/support/prime_anchor_duality_audit.py; Thesis/support/generated/prime_anchor_duality_audit.json	Cross-project analogue to squares prime-anchor error bands.
XP-GC-017	geometry-camera-android	temporal-divisibility	Feature channel temporalResonance encodes weighted compatibility with nested temporal-layer structure rather than a single time scale.	empirical	deterministic_projection	projection-chart	Thesis/reference/prime_temporal_local.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Cross-project analogue to deterministic temporal-layer signatures. Coverage hardening track: CH-002.
XP-GC-018	geometry-camera-android	negative-space-partition	Void-space metrics voidCorridorContinuity and centralVoidPressure implement an on-device negative-space partition complementary to occupied structure.	structural_proxy	deterministic_projection	formalize	Thesis/reference/squares_local.py	Thesis/support/negative_space_partition_audit.py; Thesis/support/generated/negative_space_partition_audit.json	Connects geometry-camera void channels to squares negative-space research. Coverage hardening track: CH-012.
XP-GC-019	geometry-camera-android	modulus-layers	Temporal replay and decan framing use 360 as a cycle anchor, matching the 360k modulus shell used in squares and deterministic boundary language.	empirical	finite_audit	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/modulus_layers_audit.py; Thesis/support/generated/modulus_layers_audit.json	Cross-project analogue for 360-based cyclical framing. Coverage hardening track: CH-002.
XP-GC-020	geometry-camera-android	multi-dimensional-projection	Latent projection onto a 36D unit hypersphere with geodesic distance instantiates an n-dimensional bridge generalization across projects.	exact	deterministic_projection	formalize	Thesis/reference/deterministic_local.py	Thesis/support/multi_dimensional_projection_audit.py; Thesis/support/generated/multi_dimensional_projection_audit.json	Cross-project bridge between squares hyperdimensional language and geometry-camera latent manifolds.
XP-GC-021	geometry-camera-android	feature-extraction	Center energy sums edge magnitude inside a central box of width and height one tenth of the image extent.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact compositional-focus measurement.
XP-GC-022	geometry-camera-android	feature-extraction	Thirds energy sums edge magnitude near vertical and horizontal thirds with two-pixel tolerance.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact rule-of-thirds energy measurement.
XP-GC-023	geometry-camera-android	feature-extraction	Diagonal energy measures support near the two image diagonals with 0.03 normalized tolerance.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact diagonal composition measurement.
XP-GC-024	geometry-camera-android	feature-extraction	Golden ratio guide points are placed at w/phi^2, w/phi, h/phi^2, and h/phi.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact phi-grid extraction surface.
XP-GC-025	geometry-camera-android	feature-extraction	Crossing parity balance computes sign symmetry between gx*gy positive and negative crossings above joint gradient threshold.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact weave-style parity metric.
XP-GC-026	geometry-camera-android	feature-extraction	Alternation run-length statistic computes normalized even-odd sector energy balance.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact sector alternation measurement.
XP-GC-027	geometry-camera-android	feature-extraction	Dual face area entropy uses a 6x6 cell dark-ratio Shannon-style entropy normalized by ln(2).	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact void-distribution metric.
XP-DT-031	deterministic	projection-space	Prime-lattice angular position is theta(p)=(p*GOLDEN_ANGLE) mod 2pi.	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/projection_space_audit.py; Thesis/support/generated/projection_space_audit.json	Exact node-angle constructor shared by lattice-object and geometry charts.
XP-DT-032	deterministic	projection-space	Prime-lattice radial coordinate is log10(|p|)/log10(BASE_MODULUS) for |p|>1 and 0 otherwise.	exact	direct_formula	formalize	Thesis/reference/deterministic_local.py	Thesis/support/projection_space_audit.py; Thesis/support/generated/projection_space_audit.json	Exact logarithmic depth coordinate.
XP-DT-033	deterministic	lattice-object	Lattice edges carry PQ product, ellipse ratio, angular separation, and temporal divisibility as deterministic edge metadata.	exact	deterministic_projection	projection-chart	Thesis/reference/deterministic_local.py	Thesis/support/lattice_object_audit.py; Thesis/support/generated/lattice_object_audit.json	Deterministic graph-edge chart for the prime lattice.
XP-DT-034	deterministic	angular-clusters	Angular clustering groups primes within a bounded golden-angle tolerance into deterministic clusters.	empirical	finite_audit	projection-chart	Thesis/reference/projection.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Bounded symmetry/cluster chart surface. Coverage hardening track: CH-011.
XP-DT-035	deterministic	reverse-mapping	Reverse mapping attempts to reconstruct pq candidates from temporal quantities by divisibility and alignment ranking.	empirical	deterministic_algorithm	projection-chart	Thesis/reference/projection.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Algorithmic inverse chart rather than exact theorem. Coverage hardening track: CH-011.
XP-DT-036	deterministic	dual-smooth-census	Ambient dual-smooth prime census inside the audited bound is exactly {2,3,5,7,11,17,19,31}.	exact	finite_enumeration	formalize	Thesis/reference/prime_temporal_local.py	Thesis/support/dual_prime_partition_audit.py; Thesis/support/generated/dual_prime_partition_audit.json	Distinguishes the full ambient dual-smooth family from the qualifying-set-restricted one.
XP-DT-037	deterministic	phase-boundary	Pre-stabilization ring and post-stabilization ring language around 29/31 constitute a bounded phase-boundary chart rather than a one-line exact theorem.	empirical	finite_audit	projection-chart	Thesis/reference/prime_temporal_local.py	Thesis/support/dual_prime_partition_audit.py; Thesis/support/generated/dual_prime_partition_audit.json	Captures the ring-language interpretation without overclaiming exactness. Coverage hardening track: CH-005.
XP-DT-038	deterministic	angular-clusters	Quadratic mirror and angular-fold claims should be audited with explicit tolerance bands rather than informal symmetry language.	empirical	finite_audit	projection-chart	Thesis/reference/projection.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Explicitly records tolerance-driven symmetry detection as a chart claim. Coverage hardening track: CH-011.
XP-SQ-026	squares	kissing-prime-census	Kissing primes below 500 satisfying p^2 ≡ 1 (mod 360) form a finite exact census of 14 primes.	exact	finite_enumeration	formalize	Thesis/reference/squares_local.py	Thesis/support/kissing_prime_census_audit.py; Thesis/support/generated/kissing_prime_census_audit.json	Exact bounded census deserving Thesis-owned finite audit and theoremization.
XP-SQ-027	squares	kissing-prime-census	Twin kissing prime pairs below 500 are exactly (179,181) and (269,271).	exact	finite_enumeration	formalize	Thesis/reference/squares_local.py	Thesis/support/kissing_prime_census_audit.py; Thesis/support/generated/kissing_prime_census_audit.json	Rare bounded combinatorial subclass of the kissing-prime census.
XP-SQ-028	squares	scale-invariance	Bridge measurement remains exact under arbitrary positive scaling beyond the temporal-layer family in audited fixed-scale runs.	empirical	finite_audit	bounded-audit	Thesis/reference/scaling.py	Thesis/support/scale_invariance_audit.py; Thesis/support/generated/scale_invariance_audit.json	Extends temporal-layer invariance language to broader positive scales. Coverage hardening tracks: CH-006, CH-013.
XP-SQ-029	squares	direct-benchmark	Direct geometric solver benchmark over 10000 areas ranks center_shift first, center_distance second, inner_offset third by absolute error against bisection.	empirical	finite_audit	bounded-audit	Thesis/reference/reconstruction.py	Thesis/support/direct_solver_benchmark.py; Thesis/support/generated/direct_solver_benchmark.json	Strong empirical reconstruction ordering surface beyond exact route formulas.
XP-SQ-030	squares	dodecahedron-anchor	Canonical dodecahedron and icosahedron projections are exported together with center-surplus-cell semantics as a recursive comparison anchor.	structural_proxy	finite_chart	projection-chart	Thesis/reference/duality.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Useful direct dodecahedron anchor for cross-project recursive comparison. Coverage hardening track: CH-007.
XP-SQ-031	squares	harmonic-ratios	Triad nucleus ratios V=1/1, Y=5/4, G=3/2 define a stable harmonic bridge between color, pitch, and knot charts.	exact	finite_family	projection-chart	Thesis/reference/triad.py	Thesis/support/harmonic_ratios_audit.py; Thesis/support/generated/harmonic_ratios_audit.json	Cross-media chart family that should stay distinguished from theorem language unless formalized further.
XP-SQ-032	squares	n-dimensional-diagonal	Higher-dimensional diagonal and bridge constants are documented as extensions of the 2D bridge family.	exact	direct_formula	formalize	Thesis/reference/lattice_counting.py	Thesis/support/n_dimensional_diagonal_audit.py; Thesis/support/generated/n_dimensional_diagonal_audit.json	Extends exact bridge vocabulary beyond 2D.
XP-MA-001	math	apml-boundary	APML runtime adapter and wrapper surfaces are integration-boundary layers and must stay separated from AP-domain exact theorem surfaces.	structural_proxy	boundary_audit	bounded-audit	Thesis/artifacts/apml_boundary_local_spec.md	Thesis/archive/EXTREME_CROSS_PROJECT_TOPIC_COVERAGE_AUDIT_2026-09-27.md	Boundary separator for exact-vs-wrapper claim-class governance. Coverage hardening track: CH-010.
GT-001	thesis	global-theory-track	Knot-theoretic invariants are tracked as an open finite-domain formalization program and remain non-promoted until closure gates pass.	interpretive/proxy	formalization_track	open-track	Thesis/THESIS.md; Thesis/THESIS_FORMALIZATION_GAP_MATRIX.md	Thesis/support/generated/knot_invariant_audit.json	Target theorem surface: proofs/ThesisProofs/ThesisProofs/GT001KnotInvariants.lean; promotion gate: executable invariant audit plus finite correspondence theorems.
GT-002	thesis	global-theory-track	Category-theoretic morphism and functor claims are tracked as an open finite-domain formalization program and remain non-promoted until closure gates pass.	interpretive/proxy	formalization_track	open-track	Thesis/THESIS.md; Thesis/THESIS_FORMALIZATION_GAP_MATRIX.md	Thesis/artifacts/category_composition_audit.md	Target theorem surface: proofs/ThesisProofs/ThesisProofs/GT002CategoryFunctors.lean; promotion gate: identity and associativity plus functoriality proofs on finite domains.
GT-003	thesis	global-theory-track	Cymatic PDE claims are tracked as an open bounded physical-model program and remain non-promoted until closure gates pass.	interpretive/proxy	boundary_reproducibility_track	open-track	Thesis/THESIS.md; Thesis/THESIS_FORMALIZATION_GAP_MATRIX.md	Thesis/artifacts/cymatic_pde_spec.md	Target theorem surface: proofs/ThesisProofs/ThesisProofs/GT003CymaticPDE.lean; promotion gate: reproducible solver-vs-measurement report with analytic/empirical separation.
GT-004	thesis	global-theory-track	Universal single-object algebraic unification is tracked as an open finite-domain formalization program and remains non-promoted until closure gates pass.	interpretive/proxy	formalization_track	open-track	Thesis/THESIS.md; Thesis/THESIS_FORMALIZATION_GAP_MATRIX.md	Thesis/artifacts/universal_object_spec.md	Target theorem surface: proofs/ThesisProofs/ThesisProofs/GT004UniversalObject.lean; promotion gate: finite-domain universality and reconstruction-map proofs.
XP-GC-028	geometry-camera-android	feature-extraction	Perspective sphere coupling is an exact weighted blend of convergence, ring resonance, spoke resonance, and node-degree entropy.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact feature formula theoremized in the Thesis BG-021 surface.
XP-GC-029	geometry-camera-android	feature-extraction	Plane radial slice scoring is an exact weighted blend of sweep support and object-radial support with rank boosts from selected plane and polar sweep bins.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact plane-scoring surface for perspective decomposition.
XP-GC-030	geometry-camera-android	negative-space-partition	Negative-space coherence is an exact weighted blend of dual-face entropy, void corridor continuity, vesica coherence, ring integrity, central void pressure, and figure-ground stability.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/negative_space_partition_audit.py; Thesis/support/generated/negative_space_partition_audit.json	Exact void-coherence surface complementing occupied geometry metrics.
XP-GC-031	geometry-camera-android	feature-extraction	Central void pressure equals centerVoidDark divided by centerVoidTotal inside the central sample window when defined.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Simple exact void-density primitive.
XP-GC-032	geometry-camera-android	feature-extraction	Figure-ground flip stability is an exact weighted blend of dark-bright balance and dual-face entropy.	exact	direct_formula	formalize	Thesis/reference/geometry_camera_feature_formulas_local.py	Thesis/support/formalize_backfill_audit.py; Thesis/support/generated/formalize_backfill_audit.json	Exact occupied/void balance primitive.
XP-GC-033	geometry-camera-android	dodecahedron-anchor	Platonic dodecahedral and icosahedral coherence channels serve as explicit recursive comparison anchors inside the latent and projection stack.	structural_proxy	deterministic_projection	projection-chart	Thesis/reference/duality.py	Thesis/support/projection_chart_backfill_audit.py; Thesis/support/generated/projection_chart_backfill_audit.json	Best geometry-camera analogue of the dodecahedron comparison model.