# Phase B Bulk Import Log

Automated merge of the five Phase-B brief-catalog skeleton files
(areas D, E, F, G, H) into `knowledge_graph.json`.

## Per-area skeletons ingested

- Area **D** (brief_catalog_skeletons_area_D.md): **41**
- Area **E** (brief_catalog_skeletons_area_E.md): **69**
- Area **F** (brief_catalog_skeletons_area_F.md): **27**
- Area **G** (brief_catalog_skeletons_area_G.md): **54**
- Area **H** (brief_catalog_skeletons_area_H.md): **40**
- **Total:** **231**

## Counts

- Baseline nodes: **501**
- Baseline edges: **696**
- New theorem nodes added: **229**
- New axiom nodes added:   **21**
- New state nodes added:   **0**
- New edges added:         **562**
- Final nodes: **751**
- Final edges: **1258**

## New theorems

- `s_compactness_theorem_fol` — Compactness theorem
- `s_lowenheim_skolem` — Löwenheim–Skolem theorem
- `s_church_rosser` — Church–Rosser theorem
- `s_deduction_theorem` — Deduction theorem
- `s_los_theorem` — Łoś's theorem
- `s_craig_interpolation` — Craig's interpolation theorem
- `s_beth_definability` — Beth's definability theorem
- `s_lindstrom_theorem` — Lindström's theorem
- `s_morley_categoricity` — Morley's categoricity theorem
- `s_martin_borel_determinacy` — Martin's Borel determinacy theorem
- `s_cohen_forcing` — Cohen's forcing theorems
- `s_mrdp_theorem` — Matiyasevich's theorem (MRDP)
- `s_paris_harrington` — Paris–Harrington theorem
- `s_gentzen_consistency` — Gentzen's consistency proof
- `s_ac_equivalents` — Axiom of choice equivalents
- `s_schroder_bernstein` — Schröder–Bernstein theorem
- `s_hartogs_theorem` — Hartogs's theorem
- `s_konig_cardinal_theorem` — König's theorem (cardinal)
- `s_reflection_principle` — Reflection principle
- `s_silver_theorem` — Silver's theorem
- `s_hall_marriage` — Hall's marriage theorem
- `s_konig_lemma` — König's lemma
- `s_konig_bipartite` — Kőnig's theorem (bipartite)
- `s_dilworth_theorem` — Dilworth's theorem
- `s_mirsky_theorem` — Mirsky's theorem
- `s_turan_theorem` — Turán's theorem
- `s_erdos_ko_rado` — Erdős–Ko–Rado theorem
- `s_menger_theorem` — Menger's theorem
- `s_maxflow_mincut` — Max-flow min-cut theorem
- `s_kuratowski_planarity` — Kuratowski's theorem
- `s_wagner_planarity` — Wagner's theorem
- `s_schur_ramsey` — Schur's theorem (Ramsey)
- `s_van_der_waerden` — Van der Waerden's theorem
- `s_hales_jewett` — Hales–Jewett theorem
- `s_hindman_theorem` — Hindman's theorem
- `s_cayley_formula` — Cayley's formula
- `s_matrix_tree` — Matrix-tree theorem
- `s_best_theorem` — BEST theorem
- `s_burnside_lemma` — Burnside's lemma
- `s_polya_enumeration` — Pólya enumeration theorem
- `s_pigeonhole_principle` — Pigeonhole principle
- `s_fermat_two_square_theorem` — Fermat's two-square theorem
- `s_lagrange_four_square_theorem` — Lagrange's four-square theorem
- `s_legendre_three_square_theorem` — Legendre's three-square theorem
- `s_bertrand_postulate` — Bertrand's postulate
- `s_dirichlet_primes_in_ap` — Dirichlet's theorem on primes in arithmetic progressions
- `s_dirichlet_unit_theorem` — Dirichlet's unit theorem
- `s_minkowski_convex_body_theorem` — Minkowski's theorem on convex bodies
- `s_hilbert_waring_theorem` — Hilbert–Waring theorem
- `s_thue_theorem` — Thue's theorem
- `s_roth_approximation_theorem` — Roth's theorem
- `s_siegel_integral_points_theorem` — Siegel's theorem on integral points
- `s_mordell_weil_theorem` — Mordell–Weil theorem
- `s_hasse_minkowski_theorem` — Hasse–Minkowski theorem
- `s_hasse_elliptic_bound` — Hasse's theorem on elliptic curves
- `s_weil_conjectures_deligne` — Weil conjectures (Deligne's theorem)
- `s_chebotarev_density_theorem` — Chebotarev density theorem
- `s_class_field_theory_main` — Main theorem of class field theory
- `s_artin_reciprocity_law` — Artin reciprocity law
- `s_erdos_ginzburg_ziv_theorem` — Erdős–Ginzburg–Ziv theorem
- `s_chen_theorem` — Chen's theorem
- `s_vinogradov_three_primes_theorem` — Vinogradov's theorem
- `s_eisenstein_criterion` — Eisenstein's criterion
- `s_gauss_lemma_polynomials` — Gauss's lemma (polynomials)
- `s_primitive_element_theorem` — Primitive element theorem
- `s_artin_schreier_theorem` — Artin–Schreier theorem
- `s_hilbert_theorem_90` — Hilbert's theorem 90
- `s_luroth_theorem` — Lüroth's theorem
- `s_nakayama_lemma` — Nakayama's lemma
- `s_krull_hauptidealsatz` — Krull's principal ideal theorem (Hauptidealsatz)
- `s_krull_intersection_theorem` — Krull intersection theorem
- `s_krull_akizuki_theorem` — Krull–Akizuki theorem
- `s_cohen_structure_theorem` — Cohen structure theorem
- `s_hilbert_syzygy_theorem` — Hilbert's syzygy theorem
- `s_auslander_buchsbaum_formula` — Auslander–Buchsbaum formula
- `s_going_up_going_down_theorem` — Going-up and going-down theorems
- `s_bezout_theorem` — Bézout's theorem
- `s_chow_theorem` — Chow's theorem
- `s_hironaka_resolution` — Hironaka's resolution of singularities
- `s_serre_duality` — Serre duality
- `s_grothendieck_riemann_roch` — Grothendieck–Riemann–Roch
- `s_zariski_main_theorem` — Zariski's main theorem
- `s_kodaira_vanishing_theorem` — Kodaira vanishing theorem
- `s_lefschetz_hyperplane_theorem` — Lefschetz hyperplane theorem
- `s_rank_nullity_theorem` — Rank–nullity theorem
- `s_spectral_theorem_finite_dim` — Spectral theorem (finite dim)
- `s_schur_decomposition` — Schur decomposition
- `s_jordan_normal_form` — Jordan normal form
- `s_singular_value_decomposition` — Singular value decomposition
- `s_perron_frobenius_theorem` — Perron–Frobenius theorem
- `s_gershgorin_circle_theorem` — Gershgorin circle theorem
- `s_sylvester_law_of_inertia` — Sylvester's law of inertia
- `s_gram_schmidt_process` — Gram–Schmidt process
- `s_cramer_rule` — Cramer's rule
- `s_cauchy_group_theorem` — Cauchy's theorem (group theory)
- `s_jordan_holder_theorem` — Jordan–Hölder theorem
- `s_krull_schmidt_theorem` — Krull–Schmidt theorem
- `s_feit_thompson_theorem` — Feit–Thompson theorem
- `s_schur_zassenhaus_theorem` — Schur–Zassenhaus theorem
- `s_fg_abelian_structure_theorem` — Structure theorem for finitely generated abelian groups
- `s_frattini_argument` — Frattini's argument
- `s_jordan_finite_linear_theorem` — Jordan's theorem on finite linear groups
- `s_burnside_paqb_theorem` — Burnside's p^a q^b theorem
- `s_hnn_theorem` — Higman–Neumann–Neumann theorem
- `s_maschke_theorem` — Maschke's theorem
- `s_schur_lemma` — Schur's lemma
- `s_wedderburn_finite_division_ring` — Wedderburn's theorem (finite division rings)
- `s_artin_wedderburn_theorem` — Artin–Wedderburn theorem
- `s_peter_weyl_theorem` — Peter–Weyl theorem
- `s_frobenius_reciprocity` — Frobenius reciprocity
- `s_heine_borel` — Heine–Borel theorem
- `s_urysohn_lemma` — Urysohn's lemma
- `s_tietze_extension` — Tietze extension theorem
- `s_urysohn_metrization` — Urysohn metrization theorem
- `s_alexandroff_compactification` — Alexandroff compactification (one-point)
- `s_borsuk_ulam` — Borsuk–Ulam theorem
- `s_ham_sandwich` — Ham sandwich theorem
- `s_jordan_curve_theorem` — Jordan curve theorem
- `s_hairy_ball` — Hairy ball theorem
- `s_poincare_hopf` — Poincaré–Hopf theorem
- `s_invariance_of_domain` — Brouwer's invariance of domain
- `s_de_rham_theorem` — de Rham's theorem
- `s_whitney_embedding` — Whitney embedding theorem
- `s_nash_embedding` — Nash embedding theorem
- `s_mostow_rigidity` — Mostow rigidity theorem
- `s_h_cobordism` — Smale's h-cobordism theorem
- `s_freedman_theorem` — Freedman's theorem
- `s_donaldson_theorem` — Donaldson's theorem
- `s_alexander_duality` — Alexander duality
- `s_poincare_duality` — Poincaré duality
- `s_hopf_rinow` — Hopf–Rinow theorem
- `s_cartan_hadamard` — Cartan–Hadamard theorem
- `s_myers_theorem` — Myers's theorem
- `s_hodge_theorem` — Hodge theorem
- `s_chern_gauss_bonnet` — Chern–Gauss–Bonnet theorem
- `s_uniformization_theorem` — Uniformization theorem
- `s_monotone_convergence_theorem` — Monotone convergence theorem
- `s_fatou_lemma` — Fatou's lemma
- `s_dominated_convergence_theorem` — Dominated convergence theorem
- `s_fubini_theorem` — Fubini's theorem
- `s_tonelli_theorem` — Tonelli's theorem
- `s_radon_nikodym_theorem` — Radon–Nikodym theorem
- `s_lebesgue_differentiation_theorem` — Lebesgue differentiation theorem
- `s_vitali_covering_lemma` — Vitali covering lemma
- `s_egorov_theorem` — Egorov's theorem
- `s_lusin_theorem` — Lusin's theorem
- `s_rademacher_theorem` — Rademacher's theorem
- `s_sard_theorem` — Sard's theorem
- `s_baire_category_theorem` — Baire category theorem
- `s_arzela_ascoli_theorem` — Arzelà–Ascoli theorem
- `s_picard_little_theorem` — Picard's little theorem
- `s_picard_great_theorem` — Picard's great theorem
- `s_casorati_weierstrass_theorem` — Casorati–Weierstrass theorem
- `s_residue_theorem` — Residue theorem
- `s_argument_principle` — Argument principle
- `s_rouche_theorem` — Rouché's theorem
- `s_morera_theorem` — Morera's theorem
- `s_schwarz_lemma` — Schwarz lemma
- `s_phragmen_lindelof_principle` — Phragmén–Lindelöf principle
- `s_mittag_leffler_theorem` — Mittag-Leffler theorem
- `s_weierstrass_factorization_theorem` — Weierstrass factorization theorem
- `s_montel_theorem` — Montel's theorem
- `s_hurwitz_theorem` — Hurwitz's theorem
- `s_bloch_theorem` — Bloch's theorem
- `s_gauss_lucas_theorem` — Gauss–Lucas theorem
- `s_banach_steinhaus_theorem` — Banach–Steinhaus theorem
- `s_open_mapping_theorem` — Open mapping theorem
- `s_closed_graph_theorem` — Closed graph theorem
- `s_banach_alaoglu_theorem` — Banach–Alaoglu theorem
- `s_krein_milman_theorem` — Kreĭn–Milman theorem
- `s_riesz_representation_theorems` — Riesz representation theorems
- `s_spectral_theorem_self_adjoint` — Spectral theorem for self-adjoint operators
- `s_gelfand_naimark_theorem` — Gelfand–Naimark theorem
- `s_lax_milgram_lemma` — Lax–Milgram lemma
- `s_sobolev_embedding_theorem` — Sobolev embedding theorem
- `s_rellich_kondrachov_theorem` — Rellich–Kondrachov theorem
- `s_stone_one_parameter_unitary_theorem` — Stone's theorem on one-parameter unitary groups
- `s_riesz_fischer_theorem` — Riesz–Fischer theorem
- `s_plancherel_theorem` — Plancherel theorem
- `s_riesz_thorin_interpolation_theorem` — Riesz–Thorin interpolation theorem
- `s_marcinkiewicz_interpolation_theorem` — Marcinkiewicz interpolation theorem
- `s_carleson_theorem` — Carleson's theorem
- `s_hardy_littlewood_maximal_inequality` — Hardy–Littlewood maximal inequality
- `s_picard_lindelof_theorem` — Picard–Lindelöf theorem
- `s_peano_existence_theorem` — Peano existence theorem
- `s_cauchy_kovalevskaya_theorem` — Cauchy–Kovalevskaya theorem
- `s_frobenius_theorem_distributions` — Frobenius theorem (DE / distributions)
- `s_poincare_bendixson_theorem` — Poincaré–Bendixson theorem
- `s_hartman_grobman_theorem` — Hartman–Grobman theorem
- `s_kam_theorem` — KAM theorem
- `s_kolmogorov_zero_one_law` — Kolmogorov's 0–1 law
- `s_kolmogorov_extension_theorem` — Kolmogorov's extension theorem
- `s_borel_cantelli_lemma` — Borel–Cantelli lemma
- `s_doob_martingale_convergence` — Doob's martingale convergence theorem
- `s_doob_optional_stopping` — Doob's optional stopping theorem
- `s_ito_lemma` — Itô's lemma
- `s_feynman_kac_formula` — Feynman–Kac formula
- `s_girsanov_theorem` — Girsanov's theorem
- `s_glivenko_cantelli` — Glivenko–Cantelli theorem
- `s_donsker_theorem` — Donsker's theorem
- `s_lindeberg_feller_clt` — Lindeberg–Feller central limit theorem
- `s_sharkovskii_theorem` — Sharkovskii's theorem
- `s_oseledets_multiplicative_ergodic` — Oseledets multiplicative ergodic theorem
- `s_yoneda_lemma` — Yoneda lemma
- `s_adjoint_functor_theorem` — Adjoint functor theorem
- `s_rice_theorem` — Rice's theorem
- `s_cook_levin_theorem` — Cook–Levin theorem
- `s_time_hierarchy_theorem` — Time hierarchy theorem
- `s_space_hierarchy_theorem` — Space hierarchy theorem
- `s_ladner_theorem` — Ladner's theorem
- `s_immerman_szelepcsenyi` — Immerman–Szelepcsényi theorem
- `s_pcp_theorem` — PCP theorem
- `s_godel_speed_up_theorem` — Gödel speed-up theorem
- `s_savitch_theorem` — Savitch's theorem
- `s_shannon_source_coding` — Shannon's source coding theorem
- `s_shannon_noisy_channel` — Shannon's noisy-channel coding theorem
- `s_shannon_hartley_theorem` — Shannon–Hartley theorem
- `s_kraft_inequality` — Kraft's inequality
- `s_cpt_theorem` — CPT theorem
- `s_spin_statistics_theorem` — Spin-statistics theorem
- `s_haag_theorem` — Haag's theorem
- `s_noether_second_theorem` — Noether's second theorem
- `s_reeh_schlieder_theorem` — Reeh–Schlieder theorem
- `s_bell_theorem` — Bell's theorem
- `s_kochen_specker_theorem` — Kochen–Specker theorem
- `s_von_neumann_minimax` — Von Neumann's minimax theorem
- `s_nash_existence_theorem` — Nash's existence theorem
- `s_arrow_impossibility` — Arrow's impossibility theorem
- `s_gibbard_satterthwaite` — Gibbard–Satterthwaite theorem

## New axioms

- `s_normal_hausdorff_space` — normal hausdorff space
- `s_second_countable_regular_hausdorff_space` — second countable regular hausdorff space
- `s_locally_compact_hausdorff_space` — locally compact hausdorff space
- `s_continuous_map_Sn_to_Rn` — continuous map Sn to Rn
- `s_n_measurable_bodies_in_Rn` — n measurable bodies in Rn
- `s_simple_closed_curve_in_plane` — simple closed curve in plane
- `s_continuous_tangent_vector_field` — continuous tangent vector field
- `s_continuous_injection_between_Rn_opens` — continuous injection between Rn opens
- `s_closed_hyperbolic_manifold_dim_ge_3` — closed hyperbolic manifold dim ge 3
- `s_simply_connected_manifold_dim_ge_5` — simply connected manifold dim ge 5
- `s_h_cobordism_between_manifolds` — h cobordism between manifolds
- `s_topological_4_manifold` — topological 4 manifold
- `s_smooth_4_manifold` — smooth 4 manifold
- `s_subspace_of_Sn` — subspace of Sn
- `s_closed_oriented_n_manifold` — closed oriented n manifold
- `s_connected_riemannian_manifold` — connected riemannian manifold
- `s_complete_simply_connected_nonpositive_curvature_manifold` — complete simply connected nonpositive curvature manifold
- `s_ricci_curvature_positive_lower_bound` — ricci curvature positive lower bound
- `s_compact_riemannian_manifold` — compact riemannian manifold
- `s_simply_connected_riemann_surface` — simply connected riemann surface
- `s_diagram_in_C` — diagram in C

## New states

_None. (Pure one-step skeletons expected to add only theorems + axioms.)_

## Unknown technique references (skipped steps)

_None — every referenced technique id exists in the graph._

## Dedup / near-duplicate flags

- (theorem_name_near_dup) `s_luroth_theorem` "Lüroth's theorem"  ⇔  `s_roth_approximation_theorem` "Roth's theorem"  (area E)
- (theorem_name_near_dup) `s_serre_duality` "Serre duality"  ⇔  `t_duality` "Duality"  (area E)
- (axiom_name_near_dup) `s_locally_compact_hausdorff_space` "locally compact hausdorff space"  ⇔  `s_compact_hausdorff_space` "compact hausdorff space"  (area F)
- (theorem_name_near_dup) `s_alexander_duality` "Alexander duality"  ⇔  `t_duality` "Duality"  (area F)
- (theorem_name_near_dup) `s_poincare_duality` "Poincaré duality"  ⇔  `t_duality` "Duality"  (area F)
- (theorem_name_near_dup) `s_chern_gauss_bonnet` "Chern–Gauss–Bonnet theorem"  ⇔  `s_gauss_bonnet_theorem` "Gauss–Bonnet theorem"  (area F)
- (theorem_name_near_dup) `s_lindeberg_feller_clt` "Lindeberg–Feller central limit theorem"  ⇔  `s_central_limit_theorem` "Central limit theorem"  (area H)

## Integrity checks

- New theorems with zero incoming edges: **0**
- New state/axiom nodes with zero incident edges: **0**
- New theorems unreachable from any axiom (reverse BFS): **0**

## Fan-in audit (top 10 techniques by incoming edge count) — pure fan-in

| technique | before | after | Δ |
| --- | ---: | ---: | ---: |
| `t_reduce_to_canonical_form` | 38 | 61 | +23 |
| `t_compose_with_identity` | 52 | 52 | +0 |
| `t_compactness_argument` | 16 | 48 | +32 |
| `t_axiomatize_from_instances` | 29 | 47 | +18 |
| `t_auxiliary_construction` | 41 | 41 | +0 |
| `t_structural_isomorphism` | 15 | 40 | +25 |
| `t_conserved_quantity` | 23 | 40 | +17 |
| `t_obstruction_class` | 0 | 38 | +38 |
| `t_symmetry_reduction` | 21 | 33 | +12 |
| `t_duality` | 0 | 28 | +28 |

## Fan-in audit — total incident edges (in + out) on each technique

| technique | before | after | Δ |
| --- | ---: | ---: | ---: |
| `t_reduce_to_canonical_form` | 61 | 97 | +36 |
| `t_compactness_argument` | 31 | 91 | +60 |
| `t_compose_with_identity` | 88 | 88 | +0 |
| `t_axiomatize_from_instances` | 44 | 75 | +31 |
| `t_conserved_quantity` | 41 | 71 | +30 |
| `t_structural_isomorphism` | 28 | 70 | +42 |
| `t_auxiliary_construction` | 64 | 64 | +0 |
| `t_obstruction_class` | 0 | 64 | +64 |
| `t_symmetry_reduction` | 34 | 53 | +19 |
| `t_duality` | 0 | 50 | +50 |
