sorry.
Not yet elaborated end-to-end against Mathlib with an axiom audit.#print axioms confirming exactly
[propext, Classical.choice, Quot.sound] — no sorryAx.These are the theorems that shipped with a per-theorem axiom audit attached
to a deposit. All 30 were re-confirmed on disk during this build, with
zero sorry in code.
| Deposit | DOI | Audited |
|---|---|---|
| Zeolite · ethanol-to-jet catalysis | 10.5281/zenodo.21429016 | 19 |
| Atmosphere | 10.5281/zenodo.21431505 | 5 |
| Forced Urgency · finance | 10.5281/zenodo.21561819 | 6 |
Note the overlap is small. Only 5 of these 30 appear in the registry table below — the rest postdate it, or live in files the registry never indexed. The registry is a June inventory of written work; Tier 1 is a later, narrower, harder claim. They are not the same list and should not be added together.
An earlier version of this page reported 1,170 entries and 1,080 proved at a 92.3% proof rate, with “zero extra axioms” stated corpus-wide. Those figures do not survive audit and have been withdrawn.
The registry counts one row per (theorem, file) pair. Because the same
development was copied across repositories, a single result can appear up to
eighteen times — stabilityRadius_eq and
nextLevel_layer_count_gt each appear eighteen times. The
1,170 rows below resolve to 586 distinct names. Separately,
the deduplicated corpus scan finds 253 distinct files
out of 408 .lean files authored here.
The “zero extra axioms” claim is true of the 30 Tier 1
results, which were audited individually. It was never established for
the corpus as a whole, and stating it that way was an overreach. Scanning
the deduplicated corpus with comments stripped finds
62 axiom declarations,
383 sorry tokens,
5 admit and
17 native_decide — none of which
are wrong to have while work is in progress, and all of which make a
corpus-wide “zero axioms” statement false.
One correction runs the other way. The June registry marked roughly ninety
rows as carrying a sorry. Recomputed against today's files,
0 of the registry's live rows still do — those proofs were
finished in the intervening weeks and the registry was never updated. The
inventory was stale in both directions.
189 rows cite a file that no longer exists and are struck through below. That is the fault named on the front page of Imaginary Origin No. 3 — a citation that rots — recurring at scale in this author's own registry. They are shown rather than deleted so the correction is visible.
| # | Tier | Kind | Name | Repo | Source |
|---|---|---|---|---|---|
| 1 | S | theorem | squaredDistance_eq_euclidean | 3M | Conformal.lean ↗ |
| 2 | S | theorem | G_iter_threshold | 3M | FoldEvents.lean ↗ |
| 3 | S | theorem | G_iter_zero_eq_min | 3M | FoldEvents.lean ↗ |
| 4 | S | theorem | G_le_threshold | 3M | FoldEvents.lean ↗ |
| 5 | S | theorem | G_monotone | 3M | FoldEvents.lean ↗ |
| 6 | S | theorem | g6_hex_lockin | 3M | FoldEvents.lean ↗ |
| 7 | S | theorem | g6_hex_lockin_in_orbit | 3M | FoldEvents.lean ↗ |
| 8 | S | theorem | stability_at_threshold | 3M | FoldEvents.lean ↗ |
| 9 | S | theorem | TE_eq_baseCost_minus_localWeight | 3M | GTCT_BSD_Bridge.lean ↗ |
| 10 | S | theorem | discreteL_nil | 3M | GTCT_BSD_Bridge.lean ↗ |
| 11 | S | theorem | discreteL_pos | 3M | GTCT_BSD_Bridge.lean ↗ |
| 12 | S | theorem | localTwoAdicWeight_nonneg | 3M | GTCT_BSD_Bridge.lean ↗ |
| 13 | S | theorem | maxCost_at_odd | 3M | GTCT_BSD_Bridge.lean ↗ |
| 14 | S | theorem | orbitCost_pure_power_two | 3M | GTCT_BSD_Bridge.lean ↗ |
| 15 | S | theorem | TE_antitone_padicVal | 3M | GTCT_TE_complete.lean ↗ |
| 16 | S | theorem | TE_def | 3M | GTCT_TE_complete.lean ↗ |
| 17 | S | theorem | TE_is_conformal | 3M | GTCT_TE_complete.lean ↗ |
| 18 | S | theorem | TE_odd | 3M | GTCT_TE_complete.lean ↗ |
| 19 | S | theorem | TE_pos_of_padicVal_le_one | 3M | GTCT_TE_complete.lean ↗ |
| 20 | S | theorem | TE_pow_two_mul | 3M | GTCT_TE_complete.lean ↗ |
| 21 | S | theorem | T_eq_E | 3M | GTCT_TE_complete.lean ↗ |
| 22 | S | theorem | w_antitone | 3M | TribonacciDNLS.lean ↗ |
| 23 | S | theorem | w_pos | 3M | TribonacciDNLS.lean ↗ |
| 24 | S | theorem | w_strictAnti | 3M | TribonacciDNLS.lean ↗ |
| 25 | S | theorem | w_tendsto_zero | 3M | TribonacciDNLS.lean ↗ |
| 26 | ? | theorem | η_characteristic | 3M | TribonacciDNLS.lean ↗ |
| 27 | ? | theorem | η_gt_one | 3M | TribonacciDNLS.lean ↗ |
| 28 | ? | theorem | η_ne_zero | 3M | TribonacciDNLS.lean ↗ |
| 29 | ? | theorem | η_pos | 3M | TribonacciDNLS.lean ↗ |
| 30 | S | lemma | tribonacci_succ3 | 3M | TribonacciMeasure.lean ↗ |
| 31 | S | theorem | weight_pos | 3M | TribonacciMeasure.lean ↗ |
| 32 | S | theorem | weight_strictAnti | 3M | TribonacciMeasure.lean ↗ |
| 33 | ? | theorem | η_characteristic | 3M | TribonacciMeasure.lean ↗ |
| 34 | ? | theorem | η_gt_one | 3M | TribonacciMeasure.lean ↗ |
| 35 | ? | theorem | η_ne_zero | 3M | TribonacciMeasure.lean ↗ |
| 36 | ? | theorem | η_pos | 3M | TribonacciMeasure.lean ↗ |
| 37 | S | theorem | aspect_ratio_encodes_invariants | AXLE | AXLE_v5_1.lean ↗ |
| 38 | S | theorem | closurePoints_stationary | AXLE | AXLE_v5_1.lean ↗ |
| 39 | S | theorem | closurePoints_unbounded | AXLE | AXLE_v5_1.lean ↗ |
| 40 | S | theorem | crystal_aspect_ratio | AXLE | AXLE_v5_1.lean ↗ |
| 41 | S | theorem | crystal_base_perimeter | AXLE | AXLE_v5_1.lean ↗ |
| 42 | S | theorem | g6_equals_schumann | AXLE | AXLE_v5_1.lean ↗ |
| 43 | S | theorem | levelToOrdinal_strictMono | AXLE | AXLE_v5_1.lean ↗ |
| 44 | S | theorem | nextLevel_layer_count_gt | AXLE | AXLE_v5_1.lean ↗ |
| 45 | S | theorem | noiseTolerance | AXLE | AXLE_v5_1.lean ↗ |
| 46 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | AXLE_v5_1.lean ↗ |
| 47 | S | theorem | ordinalNextLevel_level_gt | AXLE | AXLE_v5_1.lean ↗ |
| 48 | S | theorem | ordinal_regeneration_step | AXLE | AXLE_v5_1.lean ↗ |
| 49 | S | theorem | ordinal_regeneration_unbounded | AXLE | AXLE_v5_1.lean ↗ |
| 50 | S | theorem | regeneration_hierarchy_mahlo | AXLE | AXLE_v5_1.lean ↗ |
| 51 | S | theorem | regeneration_step | AXLE | AXLE_v5_1.lean ↗ |
| 52 | S | theorem | regeneration_unbounded | AXLE | AXLE_v5_1.lean ↗ |
| 53 | S | theorem | stabilityRadius_eq | AXLE | AXLE_v5_1.lean ↗ |
| 54 | S | theorem | sup_lt_of_regular | AXLE | AXLE_v5_1.lean ↗ |
| 55 | S | theorem | sup_strictMono_isLimit | AXLE | AXLE_v5_1.lean ↗ |
| 56 | S | theorem | aspect_ratio_encodes_invariants | AXLE | AXLE_v6.lean ↗ |
| 57 | S | theorem | closurePoints_stationary | AXLE | AXLE_v6.lean ↗ |
| 58 | S | theorem | closurePoints_unbounded | AXLE | AXLE_v6.lean ↗ |
| 59 | S | theorem | collective_threshold_grows_with_agents | AXLE | AXLE_v6.lean ↗ |
| 60 | S | theorem | crystal_aspect_ratio | AXLE | AXLE_v6.lean ↗ |
| 61 | S | theorem | crystal_base_perimeter | AXLE | AXLE_v6.lean ↗ |
| 62 | S | theorem | det_M_equals_64 | AXLE | AXLE_v6.lean ↗ |
| 63 | S | theorem | effective_threshold_increases | AXLE | AXLE_v6.lean ↗ |
| 64 | S | theorem | effective_threshold_one | AXLE | AXLE_v6.lean ↗ |
| 65 | S | theorem | effective_threshold_zero | AXLE | AXLE_v6.lean ↗ |
| 66 | S | theorem | g64_equals_tau_sixth | AXLE | AXLE_v6.lean ↗ |
| 67 | S | theorem | g64_equals_two_sixth | AXLE | AXLE_v6.lean ↗ |
| 68 | S | theorem | g64_is_kether_orthogon | AXLE | AXLE_v6.lean ↗ |
| 69 | S | theorem | g6_equals_schumann | AXLE | AXLE_v6.lean ↗ |
| 70 | S | theorem | g6_equals_tau5_plus_one | AXLE | AXLE_v6.lean ↗ |
| 71 | S | theorem | g6_is_33 | AXLE | AXLE_v6.lean ↗ |
| 72 | S | theorem | g6_is_minimum_monster | AXLE | AXLE_v6.lean ↗ |
| 73 | S | theorem | g6_less_than_g64 | AXLE | AXLE_v6.lean ↗ |
| 74 | S | theorem | g7_greater_than_g6 | AXLE | AXLE_v6.lean ↗ |
| 75 | S | theorem | g7_value | AXLE | AXLE_v6.lean ↗ |
| 76 | S | theorem | gtct_effective_threshold_after_circuit | AXLE | AXLE_v6.lean ↗ |
| 77 | S | theorem | levelToOrdinal_strictMono | AXLE | AXLE_v6.lean ↗ |
| 78 | S | theorem | mahlo_levels_exist | AXLE | AXLE_v6.lean ↗ |
| 79 | S | theorem | nextLevel_layer_count_gt | AXLE | AXLE_v6.lean ↗ |
| 80 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | AXLE_v6.lean ↗ |
| 81 | S | theorem | ordinalNextLevel_level_gt | AXLE | AXLE_v6.lean ↗ |
| 82 | S | theorem | ordinal_regeneration_step | AXLE | AXLE_v6.lean ↗ |
| 83 | S | theorem | ordinal_regeneration_unbounded | AXLE | AXLE_v6.lean ↗ |
| 84 | S | theorem | regeneration_hierarchy_mahlo | AXLE | AXLE_v6.lean ↗ |
| 85 | S | theorem | regeneration_step | AXLE | AXLE_v6.lean ↗ |
| 86 | S | theorem | regeneration_unbounded | AXLE | AXLE_v6.lean ↗ |
| 87 | S | theorem | separation_step1 | AXLE | AXLE_v6.lean ↗ |
| 88 | S | theorem | separation_step2_euler_characteristic | AXLE | AXLE_v6.lean ↗ |
| 89 | S | theorem | stabilityRadius_eq | AXLE | AXLE_v6.lean ↗ |
| 90 | S | theorem | stability_radius_from_gronwall | AXLE | AXLE_v6.lean ↗ |
| 91 | S | theorem | sup_lt_of_regular | AXLE | AXLE_v6.lean ↗ |
| 92 | S | theorem | sup_strictMono_isLimit | AXLE | AXLE_v6.lean ↗ |
| 93 | S | theorem | tau_embodiment | AXLE | AXLE_v6.lean ↗ |
| 94 | S | theorem | tau_is_two | AXLE | AXLE_v6.lean ↗ |
| 95 | S | theorem | V_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 96 | S | theorem | V_critical_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 97 | S | theorem | V_double_root | AXLE | AutophagyDm3_v2.lean ↗ |
| 98 | S | theorem | V_factored | AXLE | AutophagyDm3_v2.lean ↗ |
| 99 | S | theorem | V_is_morse_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 100 | S | theorem | V_second_deriv_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 101 | S | theorem | V_second_deriv_ne_zero | AXLE | AutophagyDm3_v2.lean ↗ |
| 102 | S | theorem | basin_asymmetry | AXLE | AutophagyDm3_v2.lean ↗ |
| 103 | S | theorem | contactCoeff_ne_zero | AXLE | AutophagyDm3_v2.lean ↗ |
| 104 | S | theorem | contactCoeff_neg | AXLE | AutophagyDm3_v2.lean ↗ |
| 105 | S | theorem | contactForm_nondeg_scalar | AXLE | AutophagyDm3_v2.lean ↗ |
| 106 | S | theorem | dm3_basin_compact | AXLE | AutophagyDm3_v2.lean ↗ |
| 107 | S | theorem | dm3_basin_nonempty | AXLE | AutophagyDm3_v2.lean ↗ |
| 108 | S | theorem | dΦ_at_threshold | AXLE | AutophagyDm3_v2.lean ↗ |
| 109 | S | theorem | dΦ_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 110 | S | theorem | gronwall_radius | AXLE | AutophagyDm3_v2.lean ↗ |
| 111 | S | theorem | gronwall_radius_lt_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 112 | S | theorem | gronwall_radius_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 113 | S | theorem | mu_canonical | AXLE | AutophagyDm3_v2.lean ↗ |
| 114 | S | theorem | mu_dm3 | AXLE | AutophagyDm3_v2.lean ↗ |
| 115 | S | theorem | mu_dm3_neg | AXLE | AutophagyDm3_v2.lean ↗ |
| 116 | ? | theorem | Φ_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 117 | S | theorem | V_at_one | AXLE | AutophagyDm3.lean ↗ |
| 118 | S | theorem | V_critical_at_one | AXLE | AutophagyDm3.lean ↗ |
| 119 | S | theorem | V_double_root | AXLE | AutophagyDm3.lean ↗ |
| 120 | S | theorem | V_factored | AXLE | AutophagyDm3.lean ↗ |
| 121 | S | theorem | V_second_deriv_at_one | AXLE | AutophagyDm3.lean ↗ |
| 122 | S | theorem | V_second_deriv_ne_zero | AXLE | AutophagyDm3.lean ↗ |
| 123 | S | theorem | basin_asymmetry | AXLE | AutophagyDm3.lean ↗ |
| 124 | S | theorem | contactCoeff_ne_zero | AXLE | AutophagyDm3.lean ↗ |
| 125 | S | theorem | contactCoeff_neg | AXLE | AutophagyDm3.lean ↗ |
| 126 | S | theorem | contactForm_nondeg_full | AXLE | AutophagyDm3.lean ↗ |
| 127 | S | theorem | dΦ_pos | AXLE | AutophagyDm3.lean ↗ |
| 128 | S | theorem | gronwall_radius | AXLE | AutophagyDm3.lean ↗ |
| 129 | S | theorem | gronwall_radius_lt_one | AXLE | AutophagyDm3.lean ↗ |
| 130 | S | theorem | gronwall_radius_pos | AXLE | AutophagyDm3.lean ↗ |
| 131 | S | theorem | mu_canonical | AXLE | AutophagyDm3.lean ↗ |
| 132 | S | theorem | mu_dm3 | AXLE | AutophagyDm3.lean ↗ |
| 133 | S | theorem | mu_dm3_neg | AXLE | AutophagyDm3.lean ↗ |
| 134 | S | theorem | whitneyFold_from_kinase_data | AXLE | AutophagyDm3.lean ↗ |
| 135 | ? | theorem | Φ_pos | AXLE | AutophagyDm3.lean ↗ |
| 136 | S | theorem | V_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 137 | S | theorem | V_critical_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 138 | S | theorem | V_double_root | AXLE | AutophagyDm3_v2.lean ↗ |
| 139 | S | theorem | V_factored | AXLE | AutophagyDm3_v2.lean ↗ |
| 140 | S | theorem | V_is_morse_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 141 | S | theorem | V_second_deriv_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 142 | S | theorem | V_second_deriv_ne_zero | AXLE | AutophagyDm3_v2.lean ↗ |
| 143 | S | theorem | basin_asymmetry | AXLE | AutophagyDm3_v2.lean ↗ |
| 144 | S | theorem | contactCoeff_ne_zero | AXLE | AutophagyDm3_v2.lean ↗ |
| 145 | S | theorem | contactCoeff_neg | AXLE | AutophagyDm3_v2.lean ↗ |
| 146 | S | theorem | contactForm_nondeg_scalar | AXLE | AutophagyDm3_v2.lean ↗ |
| 147 | S | theorem | dm3_basin_compact | AXLE | AutophagyDm3_v2.lean ↗ |
| 148 | S | theorem | dm3_basin_nonempty | AXLE | AutophagyDm3_v2.lean ↗ |
| 149 | S | theorem | dΦ_at_threshold | AXLE | AutophagyDm3_v2.lean ↗ |
| 150 | S | theorem | dΦ_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 151 | S | theorem | gronwall_radius | AXLE | AutophagyDm3_v2.lean ↗ |
| 152 | S | theorem | gronwall_radius_lt_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 153 | S | theorem | gronwall_radius_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 154 | S | theorem | mu_canonical | AXLE | AutophagyDm3_v2.lean ↗ |
| 155 | S | theorem | mu_dm3 | AXLE | AutophagyDm3_v2.lean ↗ |
| 156 | S | theorem | mu_dm3_neg | AXLE | AutophagyDm3_v2.lean ↗ |
| 157 | ? | theorem | Φ_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 158 | S | theorem | T11_subthreshold | AXLE | MultiAgentTogt.lean ↗ |
| 159 | S | theorem | T12_superthreshold | AXLE | MultiAgentTogt.lean ↗ |
| 160 | S | theorem | T13_branch_sanity | AXLE | MultiAgentTogt.lean ↗ |
| 161 | S | theorem | T14_reduction_factor | AXLE | MultiAgentTogt.lean ↗ |
| 162 | S | theorem | T15_circadian_anchor | AXLE | MultiAgentTogt.lean ↗ |
| 163 | S | theorem | T16_immune_zero_fp | AXLE | MultiAgentTogt.lean ↗ |
| 164 | S | theorem | T17_dm3_product | AXLE | MultiAgentTogt.lean ↗ |
| 165 | S | theorem | T18_contraction_compose | AXLE | MultiAgentTogt.lean ↗ |
| 166 | S | theorem | T1_threshold_interior | AXLE | MultiAgentTogt.lean ↗ |
| 167 | S | theorem | T2_subthreshold_contracts | AXLE | MultiAgentTogt.lean ↗ |
| 168 | S | theorem | T3_boundary_Lipschitz | AXLE | MultiAgentTogt.lean ↗ |
| 169 | S | theorem | T4_six_iterate_bound | AXLE | MultiAgentTogt.lean ↗ |
| 170 | S | theorem | T5_six_iterate_coarse | AXLE | MultiAgentTogt.lean ↗ |
| 171 | S | theorem | T6a_Tstar_pos | AXLE | MultiAgentTogt.lean ↗ |
| 172 | S | theorem | T6b_mumax_neg | AXLE | MultiAgentTogt.lean ↗ |
| 173 | S | theorem | T6c_tau_pos | AXLE | MultiAgentTogt.lean ↗ |
| 174 | S | theorem | T7_C_well_typed | AXLE | MultiAgentTogt.lean ↗ |
| 175 | S | theorem | T8_C_contracts_toward_mean | AXLE | MultiAgentTogt.lean ↗ |
| 176 | S | theorem | T9_clip_bound | AXLE | MultiAgentTogt.lean ↗ |
| 177 | S | theorem | finite_segments_measure_zero | AXLE | 1finite.lean ↗ |
| 178 | S | theorem | thickened_segment_pos_measure | AXLE | 1finite.lean ↗ |
| 179 | ? | theorem | catgt_dm3_transport | AXLE | CatGT_Main.lean ↗ |
| 180 | K | theorem | criticalRadius_antitone | AXLE | CatGT_Main.lean ↗ |
| 181 | K | theorem | criticalRadius_pos | AXLE | CatGT_Main.lean ↗ |
| 182 | ? | theorem | dnls_norm_conservation_ideal | AXLE | CatGT_Main.lean ↗ |
| 183 | K | theorem | helical_selectivity | AXLE | CatGT_Main.lean ↗ |
| 184 | K | theorem | ipr_between_zero_and_one | AXLE | CatGT_Main.lean ↗ |
| 185 | ? | theorem | reeb_orbit_is_integral | AXLE | CatGT_Main.lean ↗ |
| 186 | K | theorem | selectivityFactor_eq | AXLE | CatGT_Main.lean ↗ |
| 187 | S | theorem | collatz_c3_critical | AXLE | Criticality_Principle.lean ↗ |
| 188 | S | theorem | double_root_at_q_one_shifted | AXLE | Criticality_Principle.lean ↗ |
| 189 | S | theorem | double_root_factored | AXLE | Criticality_Principle.lean ↗ |
| 190 | S | theorem | fold_factorization_c3 | AXLE | Criticality_Principle.lean ↗ |
| 191 | S | theorem | kakeya_3d_critical | AXLE | Criticality_Principle.lean ↗ |
| 192 | S | theorem | navier_stokes_3d_critical | AXLE | Criticality_Principle.lean ↗ |
| 193 | S | theorem | ns_three_entropies_compatible | AXLE | Criticality_Principle.lean ↗ |
| 194 | S | theorem | pentanacci_5_supercritical | AXLE | Criticality_Principle.lean ↗ |
| 195 | S | theorem | ricci_3d_critical | AXLE | Criticality_Principle.lean ↗ |
| 196 | S | theorem | tetranacci_4_supercritical | AXLE | Criticality_Principle.lean ↗ |
| 197 | S | theorem | tribonacci_3_critical | AXLE | Criticality_Principle.lean ↗ |
| 198 | S | lemma | P12_identity | AXLE | D6.lean ↗ |
| 199 | S | theorem | coherence_bridge_identity | AXLE | DustyPlasma.lean ↗ |
| 200 | S | theorem | fast_rate_exceeds_sweetparker_at_threshold | AXLE | DustyPlasma.lean ↗ |
| 201 | S | theorem | lundquist_pos | AXLE | DustyPlasma.lean ↗ |
| 202 | S | theorem | mhd_fold_operator_formal | AXLE | DustyPlasma.lean ↗ |
| 203 | S | theorem | operator_order_plasma | AXLE | DustyPlasma.lean ↗ |
| 204 | S | theorem | plasma_contactomorphism | AXLE | DustyPlasma.lean ↗ |
| 205 | S | theorem | plasma_r_star_antitone | AXLE | DustyPlasma.lean ↗ |
| 206 | S | theorem | plasma_r_star_pos | AXLE | DustyPlasma.lean ↗ |
| 207 | S | theorem | plasmoid_growth_pos | AXLE | DustyPlasma.lean ↗ |
| 208 | S | theorem | plasmoid_threshold_pos | AXLE | DustyPlasma.lean ↗ |
| 209 | S | theorem | reconnection_rate_bounded | AXLE | DustyPlasma.lean ↗ |
| 210 | S | theorem | sweetparker_rate_antitone | AXLE | DustyPlasma.lean ↗ |
| 211 | S | theorem | sweetparker_rate_pos | AXLE | DustyPlasma.lean ↗ |
| 212 | S | lemma | affine_line_ne_top | AXLE | Finite.lean ↗ |
| 213 | S | theorem | finite_segments_measure_zero | AXLE | Finite.lean ↗ |
| 214 | S | theorem | segment_measure_zero | AXLE | Finite.lean ↗ |
| 215 | S | lemma | span_singleton_ne_top | AXLE | Finite.lean ↗ |
| 216 | S | theorem | thickened_segment_pos_measure | AXLE | Finite.lean ↗ |
| 217 | S | lemma | unitSegment_zero | AXLE | Finite.lean ↗ |
| 218 | S | lemma | crystal_order_six | AXLE | G6.lean ↗ |
| 219 | S | lemma | weight_positive | AXLE | G6.lean ↗ |
| 220 | S | lemma | omega_omega_is_limit | AXLE | MahloClosure.lean ↗ |
| 221 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main.lean ↗ |
| 222 | S | theorem | closurePoints_stationary | AXLE | Main.lean ↗ |
| 223 | S | theorem | closurePoints_unbounded | AXLE | Main.lean ↗ |
| 224 | S | theorem | crystal_aspect_ratio | AXLE | Main.lean ↗ |
| 225 | S | theorem | crystal_base_perimeter | AXLE | Main.lean ↗ |
| 226 | S | theorem | g6_equals_schumann | AXLE | Main.lean ↗ |
| 227 | S | theorem | levelToOrdinal_strictMono | AXLE | Main.lean ↗ |
| 228 | S | theorem | nextLevel_layer_count_gt | AXLE | Main.lean ↗ |
| 229 | S | theorem | noiseTolerance | AXLE | Main.lean ↗ |
| 230 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main.lean ↗ |
| 231 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main.lean ↗ |
| 232 | S | theorem | ordinal_regeneration_step | AXLE | Main.lean ↗ |
| 233 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main.lean ↗ |
| 234 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main.lean ↗ |
| 235 | S | theorem | regeneration_step | AXLE | Main.lean ↗ |
| 236 | S | theorem | regeneration_unbounded | AXLE | Main.lean ↗ |
| 237 | S | theorem | stabilityRadius_eq | AXLE | Main.lean ↗ |
| 238 | S | theorem | sup_lt_of_regular | AXLE | Main.lean ↗ |
| 239 | S | theorem | sup_strictMono_isLimit | AXLE | Main.lean ↗ |
| 240 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v2.lean ↗ |
| 241 | S | theorem | crystal_aspect_ratio | AXLE | Main_v2.lean ↗ |
| 242 | S | theorem | crystal_base_perimeter | AXLE | Main_v2.lean ↗ |
| 243 | S | theorem | g6_equals_schumann | AXLE | Main_v2.lean ↗ |
| 244 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v2.lean ↗ |
| 245 | S | theorem | noiseTolerance | AXLE | Main_v2.lean ↗ |
| 246 | S | theorem | regeneration_step | AXLE | Main_v2.lean ↗ |
| 247 | S | theorem | regeneration_unbounded | AXLE | Main_v2.lean ↗ |
| 248 | S | theorem | stabilityRadius_eq | AXLE | Main_v2.lean ↗ |
| 249 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v3.lean ↗ |
| 250 | S | theorem | crystal_aspect_ratio | AXLE | Main_v3.lean ↗ |
| 251 | S | theorem | crystal_base_perimeter | AXLE | Main_v3.lean ↗ |
| 252 | S | theorem | firstFixedPointAbove_gt | AXLE | Main_v3.lean ↗ |
| 253 | S | theorem | fixedPoints_unbounded | AXLE | Main_v3.lean ↗ |
| 254 | S | theorem | g6_equals_schumann | AXLE | Main_v3.lean ↗ |
| 255 | S | theorem | levelToOrdinal_monotone | AXLE | Main_v3.lean ↗ |
| 256 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v3.lean ↗ |
| 257 | S | theorem | noiseTolerance | AXLE | Main_v3.lean ↗ |
| 258 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v3.lean ↗ |
| 259 | S | theorem | ordinal_regeneration_step | AXLE | Main_v3.lean ↗ |
| 260 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v3.lean ↗ |
| 261 | S | theorem | regeneration_step | AXLE | Main_v3.lean ↗ |
| 262 | S | theorem | regeneration_unbounded | AXLE | Main_v3.lean ↗ |
| 263 | S | theorem | stabilityRadius_eq | AXLE | Main_v3.lean ↗ |
| 264 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v3_corrected.lean ↗ |
| 265 | S | theorem | closurePoints_unbounded | AXLE | Main_v3_corrected.lean ↗ |
| 266 | S | theorem | crystal_aspect_ratio | AXLE | Main_v3_corrected.lean ↗ |
| 267 | S | theorem | crystal_base_perimeter | AXLE | Main_v3_corrected.lean ↗ |
| 268 | S | theorem | g6_equals_schumann | AXLE | Main_v3_corrected.lean ↗ |
| 269 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v3_corrected.lean ↗ |
| 270 | S | theorem | noiseTolerance | AXLE | Main_v3_corrected.lean ↗ |
| 271 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v3_corrected.lean ↗ |
| 272 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v3_corrected.lean ↗ |
| 273 | S | theorem | ordinal_regeneration_step | AXLE | Main_v3_corrected.lean ↗ |
| 274 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v3_corrected.lean ↗ |
| 275 | S | theorem | regeneration_step | AXLE | Main_v3_corrected.lean ↗ |
| 276 | S | theorem | regeneration_unbounded | AXLE | Main_v3_corrected.lean ↗ |
| 277 | S | theorem | stabilityRadius_eq | AXLE | Main_v3_corrected.lean ↗ |
| 278 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v4.lean ↗ |
| 279 | S | theorem | closurePoints_unbounded | AXLE | Main_v4.lean ↗ |
| 280 | S | theorem | crystal_aspect_ratio | AXLE | Main_v4.lean ↗ |
| 281 | S | theorem | crystal_base_perimeter | AXLE | Main_v4.lean ↗ |
| 282 | S | theorem | g6_equals_schumann | AXLE | Main_v4.lean ↗ |
| 283 | S | theorem | levelToOrdinal_strictMono | AXLE | Main_v4.lean ↗ |
| 284 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v4.lean ↗ |
| 285 | S | theorem | noiseTolerance | AXLE | Main_v4.lean ↗ |
| 286 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v4.lean ↗ |
| 287 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v4.lean ↗ |
| 288 | S | theorem | ordinal_regeneration_step | AXLE | Main_v4.lean ↗ |
| 289 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v4.lean ↗ |
| 290 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main_v4.lean ↗ |
| 291 | S | theorem | regeneration_step | AXLE | Main_v4.lean ↗ |
| 292 | S | theorem | regeneration_unbounded | AXLE | Main_v4.lean ↗ |
| 293 | S | theorem | stabilityRadius_eq | AXLE | Main_v4.lean ↗ |
| 294 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v5.lean ↗ |
| 295 | S | theorem | closurePoints_stationary | AXLE | Main_v5.lean ↗ |
| 296 | S | theorem | closurePoints_unbounded | AXLE | Main_v5.lean ↗ |
| 297 | S | theorem | crystal_aspect_ratio | AXLE | Main_v5.lean ↗ |
| 298 | S | theorem | crystal_base_perimeter | AXLE | Main_v5.lean ↗ |
| 299 | S | theorem | g6_equals_schumann | AXLE | Main_v5.lean ↗ |
| 300 | S | theorem | levelToOrdinal_strictMono | AXLE | Main_v5.lean ↗ |
| 301 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v5.lean ↗ |
| 302 | S | theorem | noiseTolerance | AXLE | Main_v5.lean ↗ |
| 303 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v5.lean ↗ |
| 304 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v5.lean ↗ |
| 305 | S | theorem | ordinal_regeneration_step | AXLE | Main_v5.lean ↗ |
| 306 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v5.lean ↗ |
| 307 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main_v5.lean ↗ |
| 308 | S | theorem | regeneration_step | AXLE | Main_v5.lean ↗ |
| 309 | S | theorem | regeneration_unbounded | AXLE | Main_v5.lean ↗ |
| 310 | S | theorem | stabilityRadius_eq | AXLE | Main_v5.lean ↗ |
| 311 | S | theorem | sup_lt_of_regular | AXLE | Main_v5.lean ↗ |
| 312 | S | theorem | sup_strictMono_isLimit | AXLE | Main_v5.lean ↗ |
| 313 | S | theorem | collective_threshold_grows_with_agents | AXLE | axle_togt_canonical.lean ↗ |
| 314 | S | theorem | det_M_equals_64 | AXLE | axle_togt_canonical.lean ↗ |
| 315 | S | theorem | effective_threshold_increases | AXLE | axle_togt_canonical.lean ↗ |
| 316 | S | theorem | effective_threshold_one | AXLE | axle_togt_canonical.lean ↗ |
| 317 | S | theorem | effective_threshold_zero | AXLE | axle_togt_canonical.lean ↗ |
| 318 | S | theorem | g64_equals_tau_sixth | AXLE | axle_togt_canonical.lean ↗ |
| 319 | S | theorem | g64_equals_two_sixth | AXLE | axle_togt_canonical.lean ↗ |
| 320 | S | theorem | g64_is_kether_orthogon | AXLE | axle_togt_canonical.lean ↗ |
| 321 | S | theorem | g6_is_minimum_monster | AXLE | axle_togt_canonical.lean ↗ |
| 322 | S | theorem | g6_less_than_g64 | AXLE | axle_togt_canonical.lean ↗ |
| 323 | S | theorem | g7_greater_than_g6 | AXLE | axle_togt_canonical.lean ↗ |
| 324 | S | theorem | g7_value | AXLE | axle_togt_canonical.lean ↗ |
| 325 | S | theorem | graphene_tau_matches_canonical | AXLE | axle_togt_canonical.lean ↗ |
| 326 | S | theorem | tau_is_two | AXLE | axle_togt_canonical.lean ↗ |
| 327 | S | theorem | dm3_fixed_point | AXLE | dm³_Operator_Formalization.lean ↗ |
| 328 | S | lemma | net_height_decrease | AXLE | fitribonacci.lean ↗ |
| 329 | S | theorem | no_alternative_cycle | AXLE | fitribonacci.lean ↗ |
| 330 | S | theorem | no_escape_to_infinity | AXLE | fitribonacci.lean ↗ |
| 331 | S | lemma | valTwo_after_K | AXLE | fitribonacci.lean ↗ |
| 332 | S | theorem | gronwall_contraction_below_stability_radius | AXLE | gronwall_contraction_below_stability_radius.lean ↗ |
| 333 | S | theorem | closurePoints_stationary | AXLE | main_v7.lean ↗ |
| 334 | S | theorem | closurePoints_unbounded | AXLE | main_v7.lean ↗ |
| 335 | S | theorem | nextLevel_layer_count_gt | AXLE | main_v7.lean ↗ |
| 336 | S | theorem | noiseTolerance | AXLE | main_v7.lean ↗ |
| 337 | S | theorem | stabilityRadius_eq | AXLE | main_v7.lean ↗ |
| 338 | S | theorem | sup_lt_of_regular | AXLE | main_v7.lean ↗ |
| 339 | S | theorem | sup_strictMono_isLimit | AXLE | main_v7.lean ↗ |
| 340 | S | theorem | G_iter_threshold | AXLE | FoldEvents.lean ↗ |
| 341 | S | theorem | G_iter_zero_eq_min | AXLE | FoldEvents.lean ↗ |
| 342 | S | theorem | G_le_threshold | AXLE | FoldEvents.lean ↗ |
| 343 | S | theorem | G_monotone | AXLE | FoldEvents.lean ↗ |
| 344 | S | theorem | g6_hex_lockin | AXLE | FoldEvents.lean ↗ |
| 345 | S | theorem | g6_hex_lockin_in_orbit | AXLE | FoldEvents.lean ↗ |
| 346 | S | theorem | stability_at_threshold | AXLE | FoldEvents.lean ↗ |
| 347 | S | theorem | w_antitone | AXLE | TribonacciDNLS.lean ↗ |
| 348 | S | theorem | w_pos | AXLE | TribonacciDNLS.lean ↗ |
| 349 | S | theorem | w_strictAnti | AXLE | TribonacciDNLS.lean ↗ |
| 350 | S | theorem | w_tendsto_zero | AXLE | TribonacciDNLS.lean ↗ |
| 351 | ? | theorem | η_characteristic | AXLE | TribonacciDNLS.lean ↗ |
| 352 | ? | theorem | η_gt_one | AXLE | TribonacciDNLS.lean ↗ |
| 353 | ? | theorem | η_ne_zero | AXLE | TribonacciDNLS.lean ↗ |
| 354 | ? | theorem | η_pos | AXLE | TribonacciDNLS.lean ↗ |
| 355 | S | theorem | M_collatz_iff_E_collatz | AXLE | DiscreteDM3.lean ↗ |
| 356 | S | theorem | collatz_converges | AXLE | DiscreteDM3.lean ↗ |
| 357 | S | theorem | collatz_operatorDecomposition | AXLE | DiscreteDM3.lean ↗ |
| 358 | S | theorem | entropy_monotone | AXLE | DiscreteDM3.lean ↗ |
| 359 | S | theorem | E_goldbach_iff_attractor | AXLE | Dm3GoldbachToy.lean ↗ |
| 360 | S | theorem | M_goldbach_iff_E_goldbach | AXLE | Dm3GoldbachToy.lean ↗ |
| 361 | S | theorem | entropy_monotone | AXLE | Dm3GoldbachToy.lean ↗ |
| 362 | S | theorem | goldbach_operatorDecomposition | AXLE | Dm3GoldbachToy.lean ↗ |
| 363 | S | theorem | goldbach_toy_converges | AXLE | Dm3GoldbachToy.lean ↗ |
| 364 | S | lemma | iterate_goldbachStep_n | AXLE | Dm3GoldbachToy.lean ↗ |
| 365 | S | lemma | iterate_to_attractor | AXLE | Dm3GoldbachToy.lean ↗ |
| 366 | S | theorem | E_ns_iff_attractor | AXLE | Dm3NSToy.lean ↗ |
| 367 | S | theorem | M_ns_iff_E_ns | AXLE | Dm3NSToy.lean ↗ |
| 368 | S | lemma | energy_bounded | AXLE | Dm3NSToy.lean ↗ |
| 369 | S | theorem | entropy_monotone | AXLE | Dm3NSToy.lean ↗ |
| 370 | S | lemma | iterate_nsStep_energy | AXLE | Dm3NSToy.lean ↗ |
| 371 | S | lemma | iterate_to_attractor | AXLE | Dm3NSToy.lean ↗ |
| 372 | S | theorem | ns_operatorDecomposition | AXLE | Dm3NSToy.lean ↗ |
| 373 | S | theorem | ns_toy_converges | AXLE | Dm3NSToy.lean ↗ |
| 374 | S | lemma | C_rh_abs_decreases | AXLE | Dm3RHToy.lean ↗ |
| 375 | S | lemma | C_rh_neg | AXLE | Dm3RHToy.lean ↗ |
| 376 | S | lemma | C_rh_pos | AXLE | Dm3RHToy.lean ↗ |
| 377 | S | lemma | C_rh_zero | AXLE | Dm3RHToy.lean ↗ |
| 378 | S | theorem | E_rh_iff_attractor | AXLE | Dm3RHToy.lean ↗ |
| 379 | S | theorem | M_rh_iff_E_rh | AXLE | Dm3RHToy.lean ↗ |
| 380 | S | theorem | entropy_monotone | AXLE | Dm3RHToy.lean ↗ |
| 381 | S | lemma | iterate_rhStep_natAbs | AXLE | Dm3RHToy.lean ↗ |
| 382 | S | lemma | iterate_to_attractor | AXLE | Dm3RHToy.lean ↗ |
| 383 | S | theorem | rh_operatorDecomposition | AXLE | Dm3RHToy.lean ↗ |
| 384 | S | theorem | rh_toy_converges | AXLE | Dm3RHToy.lean ↗ |
| 385 | S | theorem | a7_prevents_collapse | AXLE | PolarVortex.lean ↗ |
| 386 | S | theorem | collatz_contraction_neg | AXLE | PolarVortex.lean ↗ |
| 387 | S | theorem | collatz_triad_is_cycle | AXLE | PolarVortex.lean ↗ |
| 388 | S | theorem | collatz_triad_size | AXLE | PolarVortex.lean ↗ |
| 389 | S | theorem | collatz_vortex_parallel_precise | AXLE | PolarVortex.lean ↗ |
| 390 | S | theorem | exterior_flows_inward | AXLE | PolarVortex.lean ↗ |
| 391 | S | theorem | g6_condition_holds | AXLE | PolarVortex.lean ↗ |
| 392 | S | theorem | g6_factors | AXLE | PolarVortex.lean ↗ |
| 393 | S | theorem | interior_flows_outward | AXLE | PolarVortex.lean ↗ |
| 394 | S | theorem | limit_cycle_is_fixed_point | AXLE | PolarVortex.lean ↗ |
| 395 | S | theorem | moat_is_invariant | AXLE | PolarVortex.lean ↗ |
| 396 | S | theorem | moat_nonempty | AXLE | PolarVortex.lean ↗ |
| 397 | S | theorem | pole_is_fixed_point | AXLE | PolarVortex.lean ↗ |
| 398 | S | theorem | pole_is_unstable | AXLE | PolarVortex.lean ↗ |
| 399 | S | theorem | spatial_separation | AXLE | PolarVortex.lean ↗ |
| 400 | S | theorem | three_layer_uniqueness_up_to_iso | AXLE | PolarVortex.lean ↗ |
| 401 | S | theorem | vortex_hexagon_decoupled | AXLE | PolarVortex.lean ↗ |
| 402 | S | theorem | vortex_inside_stability_ball | AXLE | PolarVortex.lean ↗ |
| 403 | S | theorem | vortex_lyapunov_stable | AXLE | PolarVortex.lean ↗ |
| 404 | S | theorem | vortex_not_at_pole | AXLE | PolarVortex.lean ↗ |
| 405 | S | theorem | vortex_pv_is_barrier | AXLE | PolarVortex.lean ↗ |
| 406 | S | theorem | cassini_gap_width | AXLE | SaturnRing.lean ↗ |
| 407 | S | theorem | dual_resonance_consistency | AXLE | SaturnRing.lean ↗ |
| 408 | S | theorem | dual_resonance_stability | AXLE | SaturnRing.lean ↗ |
| 409 | S | theorem | hex_six_factors | AXLE | SaturnRing.lean ↗ |
| 410 | S | theorem | hex_sixfold | AXLE | SaturnRing.lean ↗ |
| 411 | S | theorem | monster_threshold_eq | AXLE | SaturnRing.lean ↗ |
| 412 | S | theorem | ring_lyapunov_nonneg | AXLE | SaturnRing.lean ↗ |
| 413 | S | theorem | ring_lyapunov_zero_iff | AXLE | SaturnRing.lean ↗ |
| 414 | S | theorem | ring_satisfies_all_dm3_axioms | AXLE | SaturnRing.lean ↗ |
| 415 | S | theorem | ring_transverse_stable_neg | AXLE | SaturnRing.lean ↗ |
| 416 | S | theorem | stability_condition | AXLE | SaturnRing.lean ↗ |
| 417 | S | theorem | stability_product | AXLE | SaturnRing.lean ↗ |
| 418 | S | lemma | f1_antitone | AXLE | Examples.lean ↗ |
| 419 | ? | lemma | λ_fund_antitone | AXLE | Examples.lean ↗ |
| 420 | S | theorem | Tstar_pos | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 421 | S | theorem | alpha_03_contractive | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 422 | S | theorem | collective_fixed_point | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 423 | S | theorem | lipschitz_at_alpha_03 | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 424 | S | theorem | lipschitz_at_threshold | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 425 | S | theorem | lipschitz_contraction | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 426 | S | theorem | lipschitz_lb | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 427 | S | theorem | mu_max_neg | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 428 | S | theorem | six_iterate_bound | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 429 | S | theorem | six_iterate_bound_pos | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 430 | S | theorem | swarm_contraction | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 431 | S | theorem | tau_eq_abs_mu | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 432 | S | theorem | threshold_lt_one | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 433 | S | theorem | threshold_pos | AXLE | MultiOrbitBioSwarm.lean ↗ |
| 434 | S | theorem | T10_Ln_decreasing | AXLE | SwarmSimulator.lean ↗ |
| 435 | S | theorem | T11_composition_contraction | AXLE | SwarmSimulator.lean ↗ |
| 436 | S | theorem | T1_contraction | AXLE | SwarmSimulator.lean ↗ |
| 437 | S | theorem | T2_unique_fixedpoint | AXLE | SwarmSimulator.lean ↗ |
| 438 | S | theorem | T3_global_convergence | AXLE | SwarmSimulator.lean ↗ |
| 439 | S | theorem | T4_L_positive | AXLE | SwarmSimulator.lean ↗ |
| 440 | S | theorem | T5_L_lt_one | AXLE | SwarmSimulator.lean ↗ |
| 441 | S | theorem | T6_stabilise_decreases | AXLE | SwarmSimulator.lean ↗ |
| 442 | S | theorem | T7_coordinate_decreases | AXLE | SwarmSimulator.lean ↗ |
| 443 | S | theorem | T8_diffuse_increasing | AXLE | SwarmSimulator.lean ↗ |
| 444 | S | theorem | T9_system_inv_strict | AXLE | SwarmSimulator.lean ↗ |
| 445 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v6.lean ↗ |
| 446 | S | theorem | closurePoints_stationary | AXLE | Main_v6.lean ↗ |
| 447 | S | theorem | closurePoints_unbounded | AXLE | Main_v6.lean ↗ |
| 448 | S | theorem | collective_threshold_grows_with_agents | AXLE | Main_v6.lean ↗ |
| 449 | S | theorem | crystal_aspect_ratio | AXLE | Main_v6.lean ↗ |
| 450 | S | theorem | crystal_base_perimeter | AXLE | Main_v6.lean ↗ |
| 451 | S | theorem | det_M_equals_64 | AXLE | Main_v6.lean ↗ |
| 452 | S | theorem | effective_threshold_increases | AXLE | Main_v6.lean ↗ |
| 453 | S | theorem | effective_threshold_one | AXLE | Main_v6.lean ↗ |
| 454 | S | theorem | effective_threshold_zero | AXLE | Main_v6.lean ↗ |
| 455 | S | theorem | g64_equals_tau_sixth | AXLE | Main_v6.lean ↗ |
| 456 | S | theorem | g64_equals_two_sixth | AXLE | Main_v6.lean ↗ |
| 457 | S | theorem | g64_is_kether_orthogon | AXLE | Main_v6.lean ↗ |
| 458 | S | theorem | g6_equals_schumann | AXLE | Main_v6.lean ↗ |
| 459 | S | theorem | g6_equals_tau5_plus_one | AXLE | Main_v6.lean ↗ |
| 460 | S | theorem | g6_is_33 | AXLE | Main_v6.lean ↗ |
| 461 | S | theorem | g6_is_minimum_monster | AXLE | Main_v6.lean ↗ |
| 462 | S | theorem | g6_less_than_g64 | AXLE | Main_v6.lean ↗ |
| 463 | S | theorem | g7_greater_than_g6 | AXLE | Main_v6.lean ↗ |
| 464 | S | theorem | g7_value | AXLE | Main_v6.lean ↗ |
| 465 | S | theorem | gtct_effective_threshold_after_circuit | AXLE | Main_v6.lean ↗ |
| 466 | S | theorem | levelToOrdinal_strictMono | AXLE | Main_v6.lean ↗ |
| 467 | S | theorem | mahlo_levels_exist | AXLE | Main_v6.lean ↗ |
| 468 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v6.lean ↗ |
| 469 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v6.lean ↗ |
| 470 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v6.lean ↗ |
| 471 | S | theorem | ordinal_regeneration_step | AXLE | Main_v6.lean ↗ |
| 472 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v6.lean ↗ |
| 473 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main_v6.lean ↗ |
| 474 | S | theorem | regeneration_step | AXLE | Main_v6.lean ↗ |
| 475 | S | theorem | regeneration_unbounded | AXLE | Main_v6.lean ↗ |
| 476 | S | theorem | separation_step1 | AXLE | Main_v6.lean ↗ |
| 477 | S | theorem | separation_step2_euler_characteristic | AXLE | Main_v6.lean ↗ |
| 478 | S | theorem | stabilityRadius_eq | AXLE | Main_v6.lean ↗ |
| 479 | S | theorem | stability_radius_from_gronwall | AXLE | Main_v6.lean ↗ |
| 480 | S | theorem | sup_lt_of_regular | AXLE | Main_v6.lean ↗ |
| 481 | S | theorem | sup_strictMono_isLimit | AXLE | Main_v6.lean ↗ |
| 482 | S | theorem | tau_embodiment | AXLE | Main_v6.lean ↗ |
| 483 | S | theorem | tau_is_two | AXLE | Main_v6.lean ↗ |
| 484 | S | lemma | S_negative | AXLE | Monotonicity.lean ↗ |
| 485 | S | lemma | f_schumann_antitone_in_h | AXLE | Monotonicity.lean ↗ |
| 486 | S | lemma | f_schumann_monotone_in_κ | AXLE | Monotonicity.lean ↗ |
| 487 | ? | lemma | λ3D_antitone | AXLE | Monotonicity.lean ↗ |
| 488 | ? | lemma | λ3D_strictAnti | AXLE | Monotonicity.lean ↗ |
| 489 | ? | lemma | λ3D_strictAnti_in_Lx0 | AXLE | Monotonicity.lean ↗ |
| 490 | S | theorem | T10_B3_collapse_def | AXLE | MultiOrbitTogt.lean ↗ |
| 491 | S | theorem | T11_composition_preserves | AXLE | MultiOrbitTogt.lean ↗ |
| 492 | S | theorem | T12_cycle_typed | AXLE | MultiOrbitTogt.lean ↗ |
| 493 | S | theorem | T13_embodiment_shrink | AXLE | MultiOrbitTogt.lean ↗ |
| 494 | S | theorem | T14_boundary_params_pos | AXLE | MultiOrbitTogt.lean ↗ |
| 495 | S | theorem | T15_U1_commutative | AXLE | MultiOrbitTogt.lean ↗ |
| 496 | S | theorem | T1_invariant_constant | AXLE | MultiOrbitTogt.lean ↗ |
| 497 | S | theorem | T2_system_inv_strict | AXLE | MultiOrbitTogt.lean ↗ |
| 498 | S | theorem | T3a_U1_le_left | AXLE | MultiOrbitTogt.lean ↗ |
| 499 | S | theorem | T3b_U1_le_right | AXLE | MultiOrbitTogt.lean ↗ |
| 500 | S | theorem | T4_U2_preserves | AXLE | MultiOrbitTogt.lean ↗ |
| 501 | S | theorem | T5_U3_synthesis | AXLE | MultiOrbitTogt.lean ↗ |
| 502 | S | theorem | T6_R1_symmetric | AXLE | MultiOrbitTogt.lean ↗ |
| 503 | S | theorem | T7_R2_increases | AXLE | MultiOrbitTogt.lean ↗ |
| 504 | S | theorem | T8_R2_unbounded | AXLE | MultiOrbitTogt.lean ↗ |
| 505 | S | theorem | T9_B2_decidable | AXLE | MultiOrbitTogt.lean ↗ |
| 506 | S | lemma | coupled_eigenvalue_decreases | AXLE | MultiChamber.lean ↗ |
| 507 | S | lemma | dm3_curvature_lowers_coupled_modes | AXLE | MultiChamber.lean ↗ |
| 508 | S | lemma | perturbation_term_nonneg | AXLE | MultiChamber.lean ↗ |
| 509 | S | lemma | wall_offset_sensitivity | AXLE | MultiChamber.lean ↗ |
| 510 | S | theorem | V_at_one | AXLE | AutophagyDm3.lean ↗ |
| 511 | S | theorem | V_critical_at_one | AXLE | AutophagyDm3.lean ↗ |
| 512 | S | theorem | V_double_root | AXLE | AutophagyDm3.lean ↗ |
| 513 | S | theorem | V_factored | AXLE | AutophagyDm3.lean ↗ |
| 514 | S | theorem | V_second_deriv_at_one | AXLE | AutophagyDm3.lean ↗ |
| 515 | S | theorem | V_second_deriv_ne_zero | AXLE | AutophagyDm3.lean ↗ |
| 516 | S | theorem | basin_asymmetry | AXLE | AutophagyDm3.lean ↗ |
| 517 | S | theorem | contactCoeff_ne_zero | AXLE | AutophagyDm3.lean ↗ |
| 518 | S | theorem | contactCoeff_neg | AXLE | AutophagyDm3.lean ↗ |
| 519 | S | theorem | contactForm_nondeg_full | AXLE | AutophagyDm3.lean ↗ |
| 520 | S | theorem | dΦ_pos | AXLE | AutophagyDm3.lean ↗ |
| 521 | S | theorem | gronwall_radius | AXLE | AutophagyDm3.lean ↗ |
| 522 | S | theorem | gronwall_radius_lt_one | AXLE | AutophagyDm3.lean ↗ |
| 523 | S | theorem | gronwall_radius_pos | AXLE | AutophagyDm3.lean ↗ |
| 524 | S | theorem | mu_canonical | AXLE | AutophagyDm3.lean ↗ |
| 525 | S | theorem | mu_dm3 | AXLE | AutophagyDm3.lean ↗ |
| 526 | S | theorem | mu_dm3_neg | AXLE | AutophagyDm3.lean ↗ |
| 527 | S | theorem | whitneyFold_from_kinase_data | AXLE | AutophagyDm3.lean ↗ |
| 528 | ? | theorem | Φ_pos | AXLE | AutophagyDm3.lean ↗ |
| 529 | S | theorem | Phi_pos | AXLE | PrincipiaVol1.lean ↗ |
| 530 | S | theorem | V_at_one | AXLE | PrincipiaVol1.lean ↗ |
| 531 | S | theorem | V_critical_at_one | AXLE | PrincipiaVol1.lean ↗ |
| 532 | S | theorem | V_second_deriv_at_one | AXLE | PrincipiaVol1.lean ↗ |
| 533 | S | theorem | V_second_deriv_ne_zero | AXLE | PrincipiaVol1.lean ↗ |
| 534 | S | theorem | aspect_ratio_encodes_invariants | AXLE | PrincipiaVol1.lean ↗ |
| 535 | S | theorem | closurePoints_unbounded | AXLE | PrincipiaVol1.lean ↗ |
| 536 | S | theorem | contactCoeff_neg | AXLE | PrincipiaVol1.lean ↗ |
| 537 | S | theorem | crystal_aspect_ratio | AXLE | PrincipiaVol1.lean ↗ |
| 538 | S | theorem | dPhi_pos | AXLE | PrincipiaVol1.lean ↗ |
| 539 | S | theorem | gronwall_radius | AXLE | PrincipiaVol1.lean ↗ |
| 540 | S | theorem | gronwall_radius_lt_one | AXLE | PrincipiaVol1.lean ↗ |
| 541 | S | theorem | gronwall_radius_pos | AXLE | PrincipiaVol1.lean ↗ |
| 542 | S | theorem | mu_canonical | AXLE | PrincipiaVol1.lean ↗ |
| 543 | S | theorem | nextLevel_layer_count_gt | AXLE | PrincipiaVol1.lean ↗ |
| 544 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | PrincipiaVol1.lean ↗ |
| 545 | S | theorem | ordinal_regeneration_unbounded | AXLE | PrincipiaVol1.lean ↗ |
| 546 | S | theorem | regeneration_unbounded | AXLE | PrincipiaVol1.lean ↗ |
| 547 | S | theorem | sup_lt_of_regular | AXLE | PrincipiaVol1.lean ↗ |
| 548 | S | theorem | sup_strictMono_isLimit | AXLE | PrincipiaVol1.lean ↗ |
| 549 | S | theorem | Theorem_15_2_integrability | AXLE | VolumeTwo.lean ↗ |
| 550 | S | theorem | eigenvalue_at_zero | AXLE | VolumeTwo.lean ↗ |
| 551 | S | theorem | eigenvalue_limit | AXLE | VolumeTwo.lean ↗ |
| 552 | S | theorem | eigenvalue_neg_pos_z | AXLE | VolumeTwo.lean ↗ |
| 553 | S | theorem | embodimentThreshold_pos | AXLE | VolumeTwo.lean ↗ |
| 554 | S | theorem | entropy_lyapunov_duality | AXLE | VolumeTwo.lean ↗ |
| 555 | S | theorem | epsilon_zero_waddington | AXLE | VolumeTwo.lean ↗ |
| 556 | S | theorem | integrability_on_contact_distribution | AXLE | VolumeTwo.lean ↗ |
| 557 | S | theorem | integrability_on_full_contact_manifold | AXLE | VolumeTwo.lean ↗ |
| 558 | S | theorem | thm_A_contact_realization_fold | AXLE | VolumeTwo.lean ↗ |
| 559 | S | theorem | thm_B_threshold_equivalence | AXLE | VolumeTwo.lean ↗ |
| 560 | S | theorem | thm_C_singularity_bijection | AXLE | VolumeTwo.lean ↗ |
| 561 | S | theorem | toyModel_epsilon0 | AXLE | VolumeTwo.lean ↗ |
| 562 | S | theorem | toyModel_tau | AXLE | VolumeTwo.lean ↗ |
| 563 | S | theorem | vol2_contact_Theorem_3_3 | AXLE | VolumeTwo.lean ↗ |
| 564 | S | theorem | T10_Ln_decreasing | AXLE | SwarmSimulator.lean ↗ |
| 565 | S | theorem | T11_composition_contraction | AXLE | SwarmSimulator.lean ↗ |
| 566 | S | theorem | T1_contraction | AXLE | SwarmSimulator.lean ↗ |
| 567 | S | theorem | T2_unique_fixedpoint | AXLE | SwarmSimulator.lean ↗ |
| 568 | S | theorem | T3_global_convergence | AXLE | SwarmSimulator.lean ↗ |
| 569 | S | theorem | T4_L_positive | AXLE | SwarmSimulator.lean ↗ |
| 570 | S | theorem | T5_L_lt_one | AXLE | SwarmSimulator.lean ↗ |
| 571 | S | theorem | T6_stabilise_decreases | AXLE | SwarmSimulator.lean ↗ |
| 572 | S | theorem | T7_coordinate_decreases | AXLE | SwarmSimulator.lean ↗ |
| 573 | S | theorem | T8_diffuse_increasing | AXLE | SwarmSimulator.lean ↗ |
| 574 | S | theorem | T9_system_inv_strict | AXLE | SwarmSimulator.lean ↗ |
| 575 | S | lemma | tribonacci_succ3 | AXLE | TribonacciMeasure.lean ↗ |
| 576 | S | theorem | weight_pos | AXLE | TribonacciMeasure.lean ↗ |
| 577 | S | theorem | weight_strictAnti | AXLE | TribonacciMeasure.lean ↗ |
| 578 | ? | theorem | η_characteristic | AXLE | TribonacciMeasure.lean ↗ |
| 579 | ? | theorem | η_gt_one | AXLE | TribonacciMeasure.lean ↗ |
| 580 | ? | theorem | η_ne_zero | AXLE | TribonacciMeasure.lean ↗ |
| 581 | ? | theorem | η_pos | AXLE | TribonacciMeasure.lean ↗ |
| 582 | S | theorem | criticalGap_antitone | AXLE | TwinPrime_dm3.lean ↗ |
| 583 | S | theorem | criticalGap_pos | AXLE | TwinPrime_dm3.lean ↗ |
| 584 | S | theorem | fold_fires_of_le_sq | AXLE | TwinPrime_dm3.lean ↗ |
| 585 | S | theorem | gap_ladder | AXLE | TwinPrime_dm3.lean ↗ |
| 586 | S | theorem | gap_ladder_descends | AXLE | TwinPrime_dm3.lean ↗ |
| 587 | S | theorem | prime_flow_lyapunov_stable | AXLE | TwinPrime_dm3.lean ↗ |
| 588 | S | theorem | twin_prime_dm3 | AXLE | TwinPrime_dm3.lean ↗ |
| 589 | S | theorem | twin_prime_is_minimum_fold | AXLE | TwinPrime_dm3.lean ↗ |
| 590 | S | theorem | twin_prime_poincare_recurrence | AXLE | TwinPrime_dm3.lean ↗ |
| 591 | S | theorem | zhang_fold_operator | AXLE | TwinPrime_dm3.lean ↗ |
| 592 | S | theorem | P6_identity_ZMod | AXLE | Wavenumber6.lean ↗ |
| 593 | S | theorem | Tstar_over_pi_eq_tau | AXLE | Wavenumber6.lean ↗ |
| 594 | S | theorem | Tstar_pos | AXLE | Wavenumber6.lean ↗ |
| 595 | S | theorem | V3_root_at_1 | AXLE | Wavenumber6.lean ↗ |
| 596 | S | theorem | W3_deriv_zero_at_1 | AXLE | Wavenumber6.lean ↗ |
| 597 | S | theorem | W3_double_root | AXLE | Wavenumber6.lean ↗ |
| 598 | S | theorem | W3_factored | AXLE | Wavenumber6.lean ↗ |
| 599 | S | theorem | W3_root_at_neg2 | AXLE | Wavenumber6.lean ↗ |
| 600 | S | theorem | W3_zero_at_1 | AXLE | Wavenumber6.lean ↗ |
| 601 | S | theorem | c_star_is_3 | AXLE | Wavenumber6.lean ↗ |
| 602 | S | theorem | companion_char_poly | AXLE | Wavenumber6.lean ↗ |
| 603 | S | theorem | companion_det | AXLE | Wavenumber6.lean ↗ |
| 604 | S | theorem | companion_trace | AXLE | Wavenumber6.lean ↗ |
| 605 | S | theorem | dominant_root_bounds | AXLE | Wavenumber6.lean ↗ |
| 606 | S | theorem | dominant_root_gt_phi | AXLE | Wavenumber6.lean ↗ |
| 607 | S | theorem | eleven_prime | AXLE | Wavenumber6.lean ↗ |
| 608 | S | theorem | g33_factorization | AXLE | Wavenumber6.lean ↗ |
| 609 | S | theorem | g33_pos | AXLE | Wavenumber6.lean ↗ |
| 610 | S | theorem | g6_minimal | AXLE | Wavenumber6.lean ↗ |
| 611 | S | theorem | g_series_order | AXLE | Wavenumber6.lean ↗ |
| 612 | S | theorem | hexagonal_period | AXLE | Wavenumber6.lean ↗ |
| 613 | S | theorem | mu_max_neg | AXLE | Wavenumber6.lean ↗ |
| 614 | S | theorem | six_is_monster | AXLE | Wavenumber6.lean ↗ |
| 615 | S | theorem | tau_eq_abs_mu | AXLE | Wavenumber6.lean ↗ |
| 616 | S | theorem | tau_pos | AXLE | Wavenumber6.lean ↗ |
| 617 | S | theorem | three_prime | AXLE | Wavenumber6.lean ↗ |
| 618 | S | theorem | tribonacci_above_golden_ratio | AXLE | Wavenumber6.lean ↗ |
| 619 | S | theorem | tribonacci_partition_bounds | AXLE | Wavenumber6.lean ↗ |
| 620 | S | theorem | tribonacci_partition_lb | AXLE | Wavenumber6.lean ↗ |
| 621 | S | theorem | tribonacci_partition_ub | AXLE | Wavenumber6.lean ↗ |
| 622 | S | theorem | tribonacci_poly_at_1 | AXLE | Wavenumber6.lean ↗ |
| 623 | S | theorem | tribonacci_poly_at_1839 | AXLE | Wavenumber6.lean ↗ |
| 624 | S | theorem | tribonacci_poly_at_1840 | AXLE | Wavenumber6.lean ↗ |
| 625 | S | theorem | tribonacci_poly_at_2 | AXLE | Wavenumber6.lean ↗ |
| 626 | S | theorem | tribonacci_root_in_bracket | AXLE | Wavenumber6.lean ↗ |
| 627 | S | theorem | wavenumber_derivation | AXLE | Wavenumber6.lean ↗ |
| 628 | S | theorem | wavenumber_is_minimal_even_triple | AXLE | Wavenumber6.lean ↗ |
| 629 | S | theorem | wavenumber_not_4 | AXLE | Wavenumber6.lean ↗ |
| 630 | S | theorem | wavenumber_not_8 | AXLE | Wavenumber6.lean ↗ |
| 631 | S | theorem | wavenumber_unique_depth3 | AXLE | Wavenumber6.lean ↗ |
| 632 | S | theorem | V_at_one | AXLE | AutophagyDm3.lean ↗ |
| 633 | S | theorem | V_critical_at_one | AXLE | AutophagyDm3.lean ↗ |
| 634 | S | theorem | V_double_root | AXLE | AutophagyDm3.lean ↗ |
| 635 | S | theorem | V_factored | AXLE | AutophagyDm3.lean ↗ |
| 636 | S | theorem | V_second_deriv_at_one | AXLE | AutophagyDm3.lean ↗ |
| 637 | S | theorem | V_second_deriv_ne_zero | AXLE | AutophagyDm3.lean ↗ |
| 638 | S | theorem | basin_asymmetry | AXLE | AutophagyDm3.lean ↗ |
| 639 | S | theorem | contactCoeff_ne_zero | AXLE | AutophagyDm3.lean ↗ |
| 640 | S | theorem | contactCoeff_neg | AXLE | AutophagyDm3.lean ↗ |
| 641 | S | theorem | contactForm_nondeg_full | AXLE | AutophagyDm3.lean ↗ |
| 642 | S | theorem | dΦ_pos | AXLE | AutophagyDm3.lean ↗ |
| 643 | S | theorem | gronwall_radius | AXLE | AutophagyDm3.lean ↗ |
| 644 | S | theorem | gronwall_radius_lt_one | AXLE | AutophagyDm3.lean ↗ |
| 645 | S | theorem | gronwall_radius_pos | AXLE | AutophagyDm3.lean ↗ |
| 646 | S | theorem | mu_canonical | AXLE | AutophagyDm3.lean ↗ |
| 647 | S | theorem | mu_dm3 | AXLE | AutophagyDm3.lean ↗ |
| 648 | S | theorem | mu_dm3_neg | AXLE | AutophagyDm3.lean ↗ |
| 649 | S | theorem | whitneyFold_from_kinase_data | AXLE | AutophagyDm3.lean ↗ |
| 650 | ? | theorem | Φ_pos | AXLE | AutophagyDm3.lean ↗ |
| 651 | S | theorem | V_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 652 | S | theorem | V_critical_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 653 | S | theorem | V_double_root | AXLE | AutophagyDm3_v2.lean ↗ |
| 654 | S | theorem | V_factored | AXLE | AutophagyDm3_v2.lean ↗ |
| 655 | S | theorem | V_second_deriv_at_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 656 | S | theorem | V_second_deriv_ne_zero | AXLE | AutophagyDm3_v2.lean ↗ |
| 657 | S | theorem | basin_asymmetry | AXLE | AutophagyDm3_v2.lean ↗ |
| 658 | S | theorem | contactCoeff_ne_zero | AXLE | AutophagyDm3_v2.lean ↗ |
| 659 | S | theorem | contactCoeff_neg | AXLE | AutophagyDm3_v2.lean ↗ |
| 660 | S | theorem | contactForm_nondeg_full | AXLE | AutophagyDm3_v2.lean ↗ |
| 661 | S | theorem | dΦ_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 662 | S | theorem | gronwall_radius | AXLE | AutophagyDm3_v2.lean ↗ |
| 663 | S | theorem | gronwall_radius_lt_one | AXLE | AutophagyDm3_v2.lean ↗ |
| 664 | S | theorem | gronwall_radius_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 665 | S | theorem | mu_canonical | AXLE | AutophagyDm3_v2.lean ↗ |
| 666 | S | theorem | mu_dm3 | AXLE | AutophagyDm3_v2.lean ↗ |
| 667 | S | theorem | whitneyFold_from_kinase_data | AXLE | AutophagyDm3_v2.lean ↗ |
| 668 | ? | theorem | Φ_pos | AXLE | AutophagyDm3_v2.lean ↗ |
| 669 | S | lemma | affine_line_ne_top | AXLE | finite.lean ↗ |
| 670 | S | theorem | finite_kakeya_thickened_positive_measure | AXLE | finite.lean ↗ |
| 671 | S | theorem | finite_segments_measure_zero | AXLE | finite.lean ↗ |
| 672 | S | theorem | segment_measure_zero | AXLE | finite.lean ↗ |
| 673 | S | lemma | span_singleton_lt_top | AXLE | finite.lean ↗ |
| 674 | S | theorem | thickened_segment_pos_measure | AXLE | finite.lean ↗ |
| 675 | S | theorem | finite_segments_measure_zero | AXLE | 1finite.lean ↗ |
| 676 | S | theorem | thickened_segment_pos_measure | AXLE | 1finite.lean ↗ |
| 677 | S | theorem | closurePoints_stationary | AXLE | AXLE_V8.lean ↗ |
| 678 | S | theorem | closurePoints_stationary_regular | AXLE | AXLE_V8.lean ↗ |
| 679 | S | theorem | closurePoints_unbounded | AXLE | AXLE_V8.lean ↗ |
| 680 | S | theorem | mahlo_closure | AXLE | AXLE_V8.lean ↗ |
| 681 | S | theorem | noiseTolerance | AXLE | AXLE_V8.lean ↗ |
| 682 | S | theorem | regeneration_loop_invariant | AXLE | AXLE_V8.lean ↗ |
| 683 | S | theorem | stabilityRadius_eq | AXLE | AXLE_V8.lean ↗ |
| 684 | S | theorem | sup_lt_of_regular | AXLE | AXLE_V8.lean ↗ |
| 685 | S | theorem | sup_strictMono_isLimit | AXLE | AXLE_V8.lean ↗ |
| 686 | S | lemma | crystal_order_six | AXLE | G6.lean ↗ |
| 687 | S | lemma | weight_positive | AXLE | G6.lean ↗ |
| 688 | S | lemma | affine_line_ne_top | AXLE | Finite.lean ↗ |
| 689 | S | theorem | finite_segments_measure_zero | AXLE | Finite.lean ↗ |
| 690 | S | theorem | segment_measure_zero | AXLE | Finite.lean ↗ |
| 691 | S | lemma | span_singleton_ne_top | AXLE | Finite.lean ↗ |
| 692 | S | theorem | thickened_segment_pos_measure | AXLE | Finite.lean ↗ |
| 693 | S | lemma | unitSegment_zero | AXLE | Finite.lean ↗ |
| 694 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main.lean ↗ |
| 695 | S | theorem | closurePoints_stationary | AXLE | Main.lean ↗ |
| 696 | S | theorem | closurePoints_unbounded | AXLE | Main.lean ↗ |
| 697 | S | theorem | crystal_aspect_ratio | AXLE | Main.lean ↗ |
| 698 | S | theorem | crystal_base_perimeter | AXLE | Main.lean ↗ |
| 699 | S | theorem | g6_equals_schumann | AXLE | Main.lean ↗ |
| 700 | S | theorem | levelToOrdinal_strictMono | AXLE | Main.lean ↗ |
| 701 | S | theorem | nextLevel_layer_count_gt | AXLE | Main.lean ↗ |
| 702 | S | theorem | noiseTolerance | AXLE | Main.lean ↗ |
| 703 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main.lean ↗ |
| 704 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main.lean ↗ |
| 705 | S | theorem | ordinal_regeneration_step | AXLE | Main.lean ↗ |
| 706 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main.lean ↗ |
| 707 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main.lean ↗ |
| 708 | S | theorem | regeneration_step | AXLE | Main.lean ↗ |
| 709 | S | theorem | regeneration_unbounded | AXLE | Main.lean ↗ |
| 710 | S | theorem | stabilityRadius_eq | AXLE | Main.lean ↗ |
| 711 | S | theorem | sup_lt_of_regular | AXLE | Main.lean ↗ |
| 712 | S | theorem | sup_strictMono_isLimit | AXLE | Main.lean ↗ |
| 713 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v2.lean ↗ |
| 714 | S | theorem | crystal_aspect_ratio | AXLE | Main_v2.lean ↗ |
| 715 | S | theorem | crystal_base_perimeter | AXLE | Main_v2.lean ↗ |
| 716 | S | theorem | g6_equals_schumann | AXLE | Main_v2.lean ↗ |
| 717 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v2.lean ↗ |
| 718 | S | theorem | noiseTolerance | AXLE | Main_v2.lean ↗ |
| 719 | S | theorem | regeneration_step | AXLE | Main_v2.lean ↗ |
| 720 | S | theorem | regeneration_unbounded | AXLE | Main_v2.lean ↗ |
| 721 | S | theorem | stabilityRadius_eq | AXLE | Main_v2.lean ↗ |
| 722 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v3_corrected.lean ↗ |
| 723 | S | theorem | closurePoints_unbounded | AXLE | Main_v3_corrected.lean ↗ |
| 724 | S | theorem | crystal_aspect_ratio | AXLE | Main_v3_corrected.lean ↗ |
| 725 | S | theorem | crystal_base_perimeter | AXLE | Main_v3_corrected.lean ↗ |
| 726 | S | theorem | g6_equals_schumann | AXLE | Main_v3_corrected.lean ↗ |
| 727 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v3_corrected.lean ↗ |
| 728 | S | theorem | noiseTolerance | AXLE | Main_v3_corrected.lean ↗ |
| 729 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v3_corrected.lean ↗ |
| 730 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v3_corrected.lean ↗ |
| 731 | S | theorem | ordinal_regeneration_step | AXLE | Main_v3_corrected.lean ↗ |
| 732 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v3_corrected.lean ↗ |
| 733 | S | theorem | regeneration_step | AXLE | Main_v3_corrected.lean ↗ |
| 734 | S | theorem | regeneration_unbounded | AXLE | Main_v3_corrected.lean ↗ |
| 735 | S | theorem | stabilityRadius_eq | AXLE | Main_v3_corrected.lean ↗ |
| 736 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v4.lean ↗ |
| 737 | S | theorem | closurePoints_unbounded | AXLE | Main_v4.lean ↗ |
| 738 | S | theorem | crystal_aspect_ratio | AXLE | Main_v4.lean ↗ |
| 739 | S | theorem | crystal_base_perimeter | AXLE | Main_v4.lean ↗ |
| 740 | S | theorem | g6_equals_schumann | AXLE | Main_v4.lean ↗ |
| 741 | S | theorem | levelToOrdinal_strictMono | AXLE | Main_v4.lean ↗ |
| 742 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v4.lean ↗ |
| 743 | S | theorem | noiseTolerance | AXLE | Main_v4.lean ↗ |
| 744 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v4.lean ↗ |
| 745 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v4.lean ↗ |
| 746 | S | theorem | ordinal_regeneration_step | AXLE | Main_v4.lean ↗ |
| 747 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v4.lean ↗ |
| 748 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main_v4.lean ↗ |
| 749 | S | theorem | regeneration_step | AXLE | Main_v4.lean ↗ |
| 750 | S | theorem | regeneration_unbounded | AXLE | Main_v4.lean ↗ |
| 751 | S | theorem | stabilityRadius_eq | AXLE | Main_v4.lean ↗ |
| 752 | S | theorem | aspect_ratio_encodes_invariants | AXLE | Main_v5.lean ↗ |
| 753 | S | theorem | closurePoints_stationary | AXLE | Main_v5.lean ↗ |
| 754 | S | theorem | closurePoints_unbounded | AXLE | Main_v5.lean ↗ |
| 755 | S | theorem | crystal_aspect_ratio | AXLE | Main_v5.lean ↗ |
| 756 | S | theorem | crystal_base_perimeter | AXLE | Main_v5.lean ↗ |
| 757 | S | theorem | g6_equals_schumann | AXLE | Main_v5.lean ↗ |
| 758 | S | theorem | levelToOrdinal_strictMono | AXLE | Main_v5.lean ↗ |
| 759 | S | theorem | nextLevel_layer_count_gt | AXLE | Main_v5.lean ↗ |
| 760 | S | theorem | noiseTolerance | AXLE | Main_v5.lean ↗ |
| 761 | S | theorem | ordinalNextLevel_is_closure_point | AXLE | Main_v5.lean ↗ |
| 762 | S | theorem | ordinalNextLevel_level_gt | AXLE | Main_v5.lean ↗ |
| 763 | S | theorem | ordinal_regeneration_step | AXLE | Main_v5.lean ↗ |
| 764 | S | theorem | ordinal_regeneration_unbounded | AXLE | Main_v5.lean ↗ |
| 765 | S | theorem | regeneration_hierarchy_mahlo | AXLE | Main_v5.lean ↗ |
| 766 | S | theorem | regeneration_step | AXLE | Main_v5.lean ↗ |
| 767 | S | theorem | regeneration_unbounded | AXLE | Main_v5.lean ↗ |
| 768 | S | theorem | stabilityRadius_eq | AXLE | Main_v5.lean ↗ |
| 769 | S | theorem | sup_lt_of_regular | AXLE | Main_v5.lean ↗ |
| 770 | S | theorem | sup_strictMono_isLimit | AXLE | Main_v5.lean ↗ |
| 771 | S | lemma | omega_omega_is_limit | AXLE | MahloClosure.lean ↗ |
| 772 | S | lemma | P6_identity | AXLE | D6.lean ↗ |
| 773 | S | theorem | collatz_converges | AXLE | discreteDm3.lean ↗ |
| 774 | S | theorem | finite_kakeya_thickened_positive_measure | AXLE | finite_v1.lean ↗ |
| 775 | S | theorem | finite_segments_measure_zero | AXLE | finite_v1.lean ↗ |
| 776 | S | theorem | segment_measure_zero | AXLE | finite_v1.lean ↗ |
| 777 | S | theorem | thickened_segment_pos_measure | AXLE | finite_v1.lean ↗ |
| 778 | S | lemma | net_height_decrease | AXLE | fitribonacci.lean ↗ |
| 779 | S | theorem | no_alternative_cycle | AXLE | fitribonacci.lean ↗ |
| 780 | S | theorem | no_escape_to_infinity | AXLE | fitribonacci.lean ↗ |
| 781 | S | lemma | valTwo_after_K | AXLE | fitribonacci.lean ↗ |
| 782 | S | theorem | gronwall_contraction_below_stability_radius | AXLE | gronwall_contraction_below_stability_radius.lean ↗ |
| 783 | S | lemma | crystal_order_six | AXLE | G6.lean ↗ |
| 784 | S | lemma | weight_positive | AXLE | G6.lean ↗ |
| 785 | S | theorem | closurePoints_stationary | AXLE | main_v7.lean ↗ |
| 786 | S | theorem | closurePoints_unbounded | AXLE | main_v7.lean ↗ |
| 787 | S | theorem | nextLevel_layer_count_gt | AXLE | main_v7.lean ↗ |
| 788 | S | theorem | noiseTolerance | AXLE | main_v7.lean ↗ |
| 789 | S | theorem | stabilityRadius_eq | AXLE | main_v7.lean ↗ |
| 790 | S | theorem | sup_lt_of_regular | AXLE | main_v7.lean ↗ |
| 791 | S | theorem | sup_strictMono_isLimit | AXLE | main_v7.lean ↗ |
| 792 | ✕ | theorem | aspect_ratio_encodes_invariants | Claude | Main_v6.lean |
| 793 | ✕ | theorem | closurePoints_stationary | Claude | Main_v6.lean |
| 794 | ✕ | theorem | closurePoints_unbounded | Claude | Main_v6.lean |
| 795 | ✕ | theorem | collective_threshold_grows_with_agents | Claude | Main_v6.lean |
| 796 | ✕ | theorem | crystal_aspect_ratio | Claude | Main_v6.lean |
| 797 | ✕ | theorem | crystal_base_perimeter | Claude | Main_v6.lean |
| 798 | ✕ | theorem | det_M_equals_64 | Claude | Main_v6.lean |
| 799 | ✕ | theorem | effective_threshold_increases | Claude | Main_v6.lean |
| 800 | ✕ | theorem | effective_threshold_one | Claude | Main_v6.lean |
| 801 | ✕ | theorem | effective_threshold_zero | Claude | Main_v6.lean |
| 802 | ✕ | theorem | g64_equals_tau_sixth | Claude | Main_v6.lean |
| 803 | ✕ | theorem | g64_equals_two_sixth | Claude | Main_v6.lean |
| 804 | ✕ | theorem | g64_is_kether_orthogon | Claude | Main_v6.lean |
| 805 | ✕ | theorem | g6_equals_schumann | Claude | Main_v6.lean |
| 806 | ✕ | theorem | g6_equals_tau5_plus_one | Claude | Main_v6.lean |
| 807 | ✕ | theorem | g6_is_33 | Claude | Main_v6.lean |
| 808 | ✕ | theorem | g6_is_minimum_monster | Claude | Main_v6.lean |
| 809 | ✕ | theorem | g6_less_than_g64 | Claude | Main_v6.lean |
| 810 | ✕ | theorem | g7_greater_than_g6 | Claude | Main_v6.lean |
| 811 | ✕ | theorem | g7_value | Claude | Main_v6.lean |
| 812 | ✕ | theorem | gtct_effective_threshold_after_circuit | Claude | Main_v6.lean |
| 813 | ✕ | theorem | levelToOrdinal_strictMono | Claude | Main_v6.lean |
| 814 | ✕ | theorem | mahlo_levels_exist | Claude | Main_v6.lean |
| 815 | ✕ | theorem | nextLevel_layer_count_gt | Claude | Main_v6.lean |
| 816 | ✕ | theorem | ordinalNextLevel_is_closure_point | Claude | Main_v6.lean |
| 817 | ✕ | theorem | ordinalNextLevel_level_gt | Claude | Main_v6.lean |
| 818 | ✕ | theorem | ordinal_regeneration_step | Claude | Main_v6.lean |
| 819 | ✕ | theorem | ordinal_regeneration_unbounded | Claude | Main_v6.lean |
| 820 | ✕ | theorem | regeneration_hierarchy_mahlo | Claude | Main_v6.lean |
| 821 | ✕ | theorem | regeneration_step | Claude | Main_v6.lean |
| 822 | ✕ | theorem | regeneration_unbounded | Claude | Main_v6.lean |
| 823 | ✕ | theorem | separation_step1 | Claude | Main_v6.lean |
| 824 | ✕ | theorem | separation_step2_euler_characteristic | Claude | Main_v6.lean |
| 825 | ✕ | theorem | stabilityRadius_eq | Claude | Main_v6.lean |
| 826 | ✕ | theorem | stability_radius_from_gronwall | Claude | Main_v6.lean |
| 827 | ✕ | theorem | sup_lt_of_regular | Claude | Main_v6.lean |
| 828 | ✕ | theorem | sup_strictMono_isLimit | Claude | Main_v6.lean |
| 829 | ✕ | theorem | tau_embodiment | Claude | Main_v6.lean |
| 830 | ✕ | theorem | tau_is_two | Claude | Main_v6.lean |
| 831 | S | theorem | g33_stability_index | GTCT | Chain_updated.lean ↗ |
| 832 | S | theorem | gronwall_outer | GTCT | Chain_updated.lean ↗ |
| 833 | S | lemma | r_star_lt_one | GTCT | Chain_updated.lean ↗ |
| 834 | S | lemma | r_star_pos | GTCT | Chain_updated.lean ↗ |
| 835 | ? | lemma | μ_outer_neg | GTCT | Chain_updated.lean ↗ |
| 836 | S | theorem | isContinuous | GTCT | Compress.lean ↗ |
| 837 | S | theorem | isLipschitz | GTCT | Compress.lean ↗ |
| 838 | S | theorem | iterate_bound | GTCT | Compress.lean ↗ |
| 839 | S | theorem | folding_path_orthogonal | GTCT | Conformal.lean ↗ |
| 840 | S | theorem | polylaminin_orthogonal_invariant | GTCT | Conformal.lean ↗ |
| 841 | S | theorem | squaredDistance_eq_euclidean | GTCT | Conformal.lean ↗ |
| 842 | S | theorem | hasUniqueFixedPoint | GTCT | GCTC_Compress_Final.lean ↗ |
| 843 | S | theorem | isContinuous | GTCT | GCTC_Compress_Final.lean ↗ |
| 844 | S | theorem | isLipschitz | GTCT | GCTC_Compress_Final.lean ↗ |
| 845 | S | theorem | iterate_bound | GTCT | GCTC_Compress_Final.lean ↗ |
| 846 | S | theorem | iterate_cauchySeq | GTCT | GCTC_Compress_Final.lean ↗ |
| 847 | ? | lemma | GChain | GTCT | Chain.lean ↗ |
| 848 | S | theorem | g33_stability_index | GTCT | Chain.lean ↗ |
| 849 | S | theorem | gronwall_outer | GTCT | Chain.lean ↗ |
| 850 | S | lemma | iter_consecutive_dist | GTCT | Chain.lean ↗ |
| 851 | S | theorem | poincare_collatz_contracting | GTCT | Chain.lean ↗ |
| 852 | S | lemma | r_star_lt_one | GTCT | Chain.lean ↗ |
| 853 | S | lemma | r_star_pos | GTCT | Chain.lean ↗ |
| 854 | S | theorem | spiral_return_exists | GTCT | Chain.lean ↗ |
| 855 | ? | lemma | μ_outer_neg | GTCT | Chain.lean ↗ |
| 856 | S | theorem | isContinuous | GTCT | Compress.lean ↗ |
| 857 | S | theorem | isLipschitz | GTCT | Compress.lean ↗ |
| 858 | S | theorem | iterate_bound | GTCT | Compress.lean ↗ |
| 859 | S | theorem | base_below_transformer | GTCT | OrbitLadder.lean ↗ |
| 860 | S | theorem | base_strict_below_g33 | GTCT | OrbitLadder.lean ↗ |
| 861 | S | theorem | dm3_stability_threshold | GTCT | OrbitLadder.lean ↗ |
| 862 | S | theorem | gSeries_circuit_length | GTCT | OrbitLadder.lean ↗ |
| 863 | S | theorem | orbitLadder_cycles | GTCT | OrbitLadder.lean ↗ |
| 864 | S | theorem | orbitLadder_length | GTCT | OrbitLadder.lean ↗ |
| 865 | S | theorem | orbitLadder_mono | GTCT | OrbitLadder.lean ↗ |
| 866 | S | theorem | transformer_below_circuit | GTCT | OrbitLadder.lean ↗ |
| 867 | S | lemma | softThreshold_neg | GTCT | Threshold.lean ↗ |
| 868 | ? | lemma | Unfolder | GTCT | Unfold.lean ↗ |
| 869 | S | theorem | base_below_transformer | GTCT | Orbit.lean ↗ |
| 870 | S | theorem | base_strict_below_g33 | GTCT | Orbit.lean ↗ |
| 871 | S | theorem | dm3_stability_threshold | GTCT | Orbit.lean ↗ |
| 872 | S | theorem | gSeries_circuit_length | GTCT | Orbit.lean ↗ |
| 873 | S | theorem | orbitLadder_cycles | GTCT | Orbit.lean ↗ |
| 874 | S | theorem | orbitLadder_length | GTCT | Orbit.lean ↗ |
| 875 | S | theorem | orbitLadder_mono | GTCT | Orbit.lean ↗ |
| 876 | S | theorem | transformer_below_circuit | GTCT | Orbit.lean ↗ |
| 877 | S | theorem | TE_def | GTCT | TE.lean ↗ |
| 878 | S | theorem | TE_is_conformal | GTCT | TE.lean ↗ |
| 879 | S | theorem | TE_odd | GTCT | TE.lean ↗ |
| 880 | S | theorem | T_eq_E | GTCT | TE.lean ↗ |
| 881 | S | lemma | softThreshold_neg | GTCT | Threshold.lean ↗ |
| 882 | ? | lemma | Unfolder | GTCT | Unfold.lean ↗ |
| 883 | S | theorem | Dcrit_above_26 | GTCT | GTCTsorryFree.lean ↗ |
| 884 | S | theorem | Dcrit_monotone | GTCT | GTCTsorryFree.lean ↗ |
| 885 | S | theorem | Dcrit_rank3 | GTCT | GTCTsorryFree.lean ↗ |
| 886 | S | theorem | Dcrit_rank4 | GTCT | GTCTsorryFree.lean ↗ |
| 887 | S | theorem | T₃_cayley_hamilton | GTCT | GTCTsorryFree.lean ↗ |
| 888 | S | theorem | T₃_cube_correct | GTCT | GTCTsorryFree.lean ↗ |
| 889 | S | theorem | T₃_det_one | GTCT | GTCTsorryFree.lean ↗ |
| 890 | S | theorem | T₃_pow_det_one | GTCT | GTCTsorryFree.lean ↗ |
| 891 | S | theorem | T₃_sq_correct | GTCT | GTCTsorryFree.lean ↗ |
| 892 | S | theorem | W_deriv_at_one | GTCT | GTCTsorryFree.lean ↗ |
| 893 | S | theorem | W_factorization_c3 | GTCT | GTCTsorryFree.lean ↗ |
| 894 | S | theorem | W_root_at_one | GTCT | GTCTsorryFree.lean ↗ |
| 895 | S | theorem | W_roots_complete | GTCT | GTCTsorryFree.lean ↗ |
| 896 | S | theorem | W_third_root | GTCT | GTCTsorryFree.lean ↗ |
| 897 | S | theorem | c_star_is_3 | GTCT | GTCTsorryFree.lean ↗ |
| 898 | S | theorem | c_star_unique | GTCT | GTCTsorryFree.lean ↗ |
| 899 | S | theorem | degree1_single_root | GTCT | GTCTsorryFree.lean ↗ |
| 900 | S | theorem | degree2_no_distinct_branch | GTCT | GTCTsorryFree.lean ↗ |
| 901 | S | theorem | degree3_first_with_distinct_branch | GTCT | GTCTsorryFree.lean ↗ |
| 902 | S | theorem | deriv_V_c | GTCT | GTCTsorryFree.lean ↗ |
| 903 | S | theorem | deriv_W_c | GTCT | GTCTsorryFree.lean ↗ |
| 904 | S | theorem | double_root_W_iff_c3 | GTCT | GTCTsorryFree.lean ↗ |
| 905 | S | theorem | double_root_at_q_one | GTCT | GTCTsorryFree.lean ↗ |
| 906 | S | theorem | double_root_deriv_zero | GTCT | GTCTsorryFree.lean ↗ |
| 907 | S | theorem | fold_factorization_c3 | GTCT | GTCTsorryFree.lean ↗ |
| 908 | S | theorem | nBonacciPoly_2 | GTCT | GTCTsorryFree.lean ↗ |
| 909 | S | theorem | nBonacciPoly_3 | GTCT | GTCTsorryFree.lean ↗ |
| 910 | S | theorem | nBonacciPoly_3_at_1 | GTCT | GTCTsorryFree.lean ↗ |
| 911 | S | theorem | nBonacciPoly_3_at_2 | GTCT | GTCTsorryFree.lean ↗ |
| 912 | S | theorem | nBonacciPoly_4 | GTCT | GTCTsorryFree.lean ↗ |
| 913 | S | theorem | root_at_one | GTCT | GTCTsorryFree.lean ↗ |
| 914 | S | theorem | tribSeq_0 | GTCT | GTCTsorryFree.lean ↗ |
| 915 | S | theorem | tribSeq_1 | GTCT | GTCTsorryFree.lean ↗ |
| 916 | S | theorem | tribSeq_14 | GTCT | GTCTsorryFree.lean ↗ |
| 917 | S | theorem | tribSeq_2 | GTCT | GTCTsorryFree.lean ↗ |
| 918 | S | theorem | tribSeq_21 | GTCT | GTCTsorryFree.lean ↗ |
| 919 | S | theorem | tribSeq_3 | GTCT | GTCTsorryFree.lean ↗ |
| 920 | S | theorem | tribSeq_4 | GTCT | GTCTsorryFree.lean ↗ |
| 921 | S | theorem | tribSeq_5 | GTCT | GTCTsorryFree.lean ↗ |
| 922 | S | theorem | tribSeq_6 | GTCT | GTCTsorryFree.lean ↗ |
| 923 | S | theorem | tribSeq_7 | GTCT | GTCTsorryFree.lean ↗ |
| 924 | S | theorem | tribonacci_root_in_interval | GTCT | GTCTsorryFree.lean ↗ |
| 925 | S | theorem | weinberg_range | GTCT | GTCTsorryFree.lean ↗ |
| 926 | S | lemma | softThreshold_neg | GTCT | Threshold.lean ↗ |
| 927 | ? | lemma | Unfolder | GTCT | Unfold.lean ↗ |
| 928 | S | lemma | critDim_3 | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 929 | S | lemma | critDim_4 | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 930 | S | lemma | critDim_5_gt | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 931 | S | theorem | critDim_monotone | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 932 | S | theorem | double_root_at_q_one | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 933 | S | theorem | fold_factorization_c3 | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 934 | S | theorem | no_return_to_critical | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 935 | S | theorem | tribonacci_3_critical | GTCT | dm3CriticalityPrinciple_extended.lean ↗ |
| 936 | ✕ | lemma | tribonacci_succ3 | cajueiro | TribonacciMeasure.lean |
| 937 | ✕ | theorem | weight_pos | cajueiro | TribonacciMeasure.lean |
| 938 | ✕ | theorem | weight_strictAnti | cajueiro | TribonacciMeasure.lean |
| 939 | ✕ | theorem | η_characteristic | cajueiro | TribonacciMeasure.lean |
| 940 | ✕ | theorem | η_gt_one | cajueiro | TribonacciMeasure.lean |
| 941 | ✕ | theorem | η_ne_zero | cajueiro | TribonacciMeasure.lean |
| 942 | ✕ | theorem | η_pos | cajueiro | TribonacciMeasure.lean |
| 943 | ✕ | theorem | A1_and_G6_crystal | cajueiro | A1Singularity.lean |
| 944 | ✕ | theorem | A1_is_stable_codim1_singularity | cajueiro | A1Singularity.lean |
| 945 | ✕ | theorem | A1_node_count_is_one | cajueiro | A1Singularity.lean |
| 946 | ✕ | theorem | a1_level_set_factors | cajueiro | A1Singularity.lean |
| 947 | ✕ | theorem | a1_normal_form_at_origin | cajueiro | A1Singularity.lean |
| 948 | ✕ | theorem | a1_normal_form_indefinite | cajueiro | A1Singularity.lean |
| 949 | ✕ | theorem | bernoulli_at_origin | cajueiro | A1Singularity.lean |
| 950 | ✕ | theorem | bernoulli_hessian_negative | cajueiro | A1Singularity.lean |
| 951 | ✕ | theorem | bernoulli_leading_term | cajueiro | A1Singularity.lean |
| 952 | ✕ | theorem | branches_meet_at_origin | cajueiro | A1Singularity.lean |
| 953 | ✕ | theorem | branches_transverse | cajueiro | A1Singularity.lean |
| 954 | ✕ | theorem | chenciner_montgomery_A1 | cajueiro | A1Singularity.lean |
| 955 | ✕ | theorem | collatz_cycle_1 | cajueiro | A1Singularity.lean |
| 956 | ✕ | theorem | collatz_cycle_2 | cajueiro | A1Singularity.lean |
| 957 | ✕ | theorem | collatz_cycle_4 | cajueiro | A1Singularity.lean |
| 958 | ✕ | theorem | collatz_log_crossing | cajueiro | A1Singularity.lean |
| 959 | ✕ | theorem | collatz_mean_contraction | cajueiro | A1Singularity.lean |
| 960 | ✕ | theorem | collatz_odd_branch_expansion | cajueiro | A1Singularity.lean |
| 961 | ✕ | theorem | collatz_triad_cycle | cajueiro | A1Singularity.lean |
| 962 | ✕ | theorem | collatz_trivial_lyapunov | cajueiro | A1Singularity.lean |
| 963 | ✕ | theorem | gerono_double_point | cajueiro | A1Singularity.lean |
| 964 | ✕ | theorem | gerono_tangent_transverse | cajueiro | A1Singularity.lean |
| 965 | ✕ | theorem | lunar_analemma_A1_crossing | cajueiro | A1Singularity.lean |
| 966 | ✕ | theorem | resonance_gap_eigenvalue_product | cajueiro | A1Singularity.lean |
| 967 | ✕ | theorem | resonance_gap_is_saddle | cajueiro | A1Singularity.lean |
| 968 | ✕ | theorem | solar_declination_equinox | cajueiro | A1Singularity.lean |
| 969 | ✕ | theorem | standard_A1_barrier_satisfies_A7 | cajueiro | A1Singularity.lean |
| 970 | ✕ | theorem | vortex_A1_eigenvalue | cajueiro | A1Singularity.lean |
| 971 | ✕ | theorem | vortex_fixed_point | cajueiro | A1Singularity.lean |
| 972 | ✕ | theorem | vortex_phase_origin | cajueiro | A1Singularity.lean |
| 973 | ✕ | theorem | poincare_collatz | cajueiro | Chain.lean |
| 974 | ✕ | theorem | squaredDistance_eq_euclidean | cajueiro | Conformal.lean |
| 975 | ✕ | lemma | reeb_not_in_ker | cajueiro | ContactGeometry.lean |
| 976 | ✕ | theorem | foldAmplitude_strictAnti | cajueiro | FoldEvents.lean |
| 977 | ✕ | lemma | foldLocus_finite | cajueiro | FoldEvents.lean |
| 978 | ✕ | theorem | noiseTolerance | cajueiro | Operators.lean |
| 979 | ✕ | theorem | a7_prevents_collapse | cajueiro | PolarVortex.lean |
| 980 | ✕ | theorem | collatz_contraction_neg | cajueiro | PolarVortex.lean |
| 981 | ✕ | theorem | collatz_triad_is_cycle | cajueiro | PolarVortex.lean |
| 982 | ✕ | theorem | collatz_triad_size | cajueiro | PolarVortex.lean |
| 983 | ✕ | theorem | collatz_vortex_parallel_precise | cajueiro | PolarVortex.lean |
| 984 | ✕ | theorem | exterior_flows_inward | cajueiro | PolarVortex.lean |
| 985 | ✕ | theorem | g6_condition_holds | cajueiro | PolarVortex.lean |
| 986 | ✕ | theorem | g6_factors | cajueiro | PolarVortex.lean |
| 987 | ✕ | theorem | interior_flows_outward | cajueiro | PolarVortex.lean |
| 988 | ✕ | theorem | limit_cycle_is_fixed_point | cajueiro | PolarVortex.lean |
| 989 | ✕ | theorem | moat_is_invariant | cajueiro | PolarVortex.lean |
| 990 | ✕ | theorem | moat_nonempty | cajueiro | PolarVortex.lean |
| 991 | ✕ | theorem | pole_is_fixed_point | cajueiro | PolarVortex.lean |
| 992 | ✕ | theorem | pole_is_unstable | cajueiro | PolarVortex.lean |
| 993 | ✕ | theorem | spatial_separation | cajueiro | PolarVortex.lean |
| 994 | ✕ | theorem | three_layer_uniqueness_up_to_iso | cajueiro | PolarVortex.lean |
| 995 | ✕ | theorem | vortex_hexagon_decoupled | cajueiro | PolarVortex.lean |
| 996 | ✕ | theorem | vortex_inside_stability_ball | cajueiro | PolarVortex.lean |
| 997 | ✕ | theorem | vortex_lyapunov_stable | cajueiro | PolarVortex.lean |
| 998 | ✕ | theorem | vortex_not_at_pole | cajueiro | PolarVortex.lean |
| 999 | ✕ | theorem | vortex_pv_is_barrier | cajueiro | PolarVortex.lean |
| 1000 | ✕ | theorem | cassini_gap_width | cajueiro | SaturnRing.lean |
| 1001 | ✕ | theorem | dual_resonance_consistency | cajueiro | SaturnRing.lean |
| 1002 | ✕ | theorem | dual_resonance_stability | cajueiro | SaturnRing.lean |
| 1003 | ✕ | theorem | hex_six_factors | cajueiro | SaturnRing.lean |
| 1004 | ✕ | theorem | hex_sixfold | cajueiro | SaturnRing.lean |
| 1005 | ✕ | theorem | monster_threshold_eq | cajueiro | SaturnRing.lean |
| 1006 | ✕ | theorem | ring_lyapunov_nonneg | cajueiro | SaturnRing.lean |
| 1007 | ✕ | theorem | ring_lyapunov_zero_iff | cajueiro | SaturnRing.lean |
| 1008 | ✕ | theorem | ring_satisfies_all_dm3_axioms | cajueiro | SaturnRing.lean |
| 1009 | ✕ | theorem | ring_transverse_stable_neg | cajueiro | SaturnRing.lean |
| 1010 | ✕ | theorem | stability_condition | cajueiro | SaturnRing.lean |
| 1011 | ✕ | theorem | stability_product | cajueiro | SaturnRing.lean |
| 1012 | ✕ | lemma | tribonacci_succ3 | cajueiro | TribonacciMeasure.lean |
| 1013 | ✕ | theorem | weight_pos | cajueiro | TribonacciMeasure.lean |
| 1014 | ✕ | theorem | weight_strictAnti | cajueiro | TribonacciMeasure.lean |
| 1015 | ✕ | theorem | η_characteristic | cajueiro | TribonacciMeasure.lean |
| 1016 | ✕ | theorem | η_gt_one | cajueiro | TribonacciMeasure.lean |
| 1017 | ✕ | theorem | η_ne_zero | cajueiro | TribonacciMeasure.lean |
| 1018 | ✕ | theorem | η_pos | cajueiro | TribonacciMeasure.lean |
| 1019 | ✕ | lemma | f1_antitone | cajueiro | Examples.lean |
| 1020 | ✕ | lemma | λ_fund_antitone | cajueiro | Examples.lean |
| 1021 | ✕ | lemma | S_negative | cajueiro | Monotonicity.lean |
| 1022 | ✕ | lemma | f_schumann_antitone_in_h | cajueiro | Monotonicity.lean |
| 1023 | ✕ | lemma | f_schumann_monotone_in_κ | cajueiro | Monotonicity.lean |
| 1024 | ✕ | lemma | λ3D_antitone | cajueiro | Monotonicity.lean |
| 1025 | ✕ | lemma | λ3D_strictAnti | cajueiro | Monotonicity.lean |
| 1026 | ✕ | lemma | λ3D_strictAnti_in_Lx0 | cajueiro | Monotonicity.lean |
| 1027 | ✕ | lemma | coupled_eigenvalue_decreases | cajueiro | MultiChamber.lean |
| 1028 | ✕ | lemma | dm3_curvature_lowers_coupled_modes | cajueiro | MultiChamber.lean |
| 1029 | ✕ | lemma | perturbation_term_nonneg | cajueiro | MultiChamber.lean |
| 1030 | ✕ | lemma | wall_offset_sensitivity | cajueiro | MultiChamber.lean |
| 1031 | ✕ | theorem | w_antitone | cajueiro | TribonacciDNLS.lean |
| 1032 | ✕ | theorem | w_pos | cajueiro | TribonacciDNLS.lean |
| 1033 | ✕ | theorem | w_strictAnti | cajueiro | TribonacciDNLS.lean |
| 1034 | ✕ | theorem | w_tendsto_zero | cajueiro | TribonacciDNLS.lean |
| 1035 | ✕ | theorem | η_characteristic | cajueiro | TribonacciDNLS.lean |
| 1036 | ✕ | theorem | η_gt_one | cajueiro | TribonacciDNLS.lean |
| 1037 | ✕ | theorem | η_ne_zero | cajueiro | TribonacciDNLS.lean |
| 1038 | ✕ | theorem | η_pos | cajueiro | TribonacciDNLS.lean |
| 1039 | S | theorem | G64_G66_distinct_in_orbit | geometry | GenerativeWeave.lean ↗ |
| 1040 | S | theorem | P1_lawful_generation | geometry | GenerativeWeave.lean ↗ |
| 1041 | S | theorem | P2_triad_preserved | geometry | GenerativeWeave.lean ↗ |
| 1042 | S | theorem | P3_minimal_monster | geometry | GenerativeWeave.lean ↗ |
| 1043 | S | theorem | P4_monster_hierarchy | geometry | GenerativeWeave.lean ↗ |
| 1044 | S | theorem | P5_monster_reflection | geometry | GenerativeWeave.lean ↗ |
| 1045 | S | theorem | P6_monster_regeneration | geometry | GenerativeWeave.lean ↗ |
| 1046 | S | theorem | canonical64_lt_hyperMahlo | geometry | GenerativeWeave.lean ↗ |
| 1047 | S | theorem | canonical_hierarchy | geometry | GenerativeWeave.lean ↗ |
| 1048 | S | theorem | deviation_is_two | geometry | GenerativeWeave.lean ↗ |
| 1049 | S | theorem | deviation_moonshine_analogy | geometry | GenerativeWeave.lean ↗ |
| 1050 | S | theorem | gSeries_deviation_is_canonical | geometry | GenerativeWeave.lean ↗ |
| 1051 | S | theorem | gSeries_hyperMahlo_derived | geometry | GenerativeWeave.lean ↗ |
| 1052 | S | theorem | gSeries_strictMono | geometry | GenerativeWeave.lean ↗ |
| 1053 | S | theorem | hierarchy_ordering | geometry | GenerativeWeave.lean ↗ |
| 1054 | S | theorem | hyperMahlo_deviation_from_canonical | geometry | GenerativeWeave.lean ↗ |
| 1055 | S | theorem | lvlHyperMahlo_eq_canonical_plus_deviation | geometry | GenerativeWeave.lean ↗ |
| 1056 | S | theorem | lvlHyperMahlo_not_power_of_g6 | geometry | GenerativeWeave.lean ↗ |
| 1057 | S | theorem | C₃_K₃_noncommutative | geometry | dm3_operators.lean ↗ |
| 1058 | S | theorem | C₃_idempotent | geometry | dm3_operators.lean ↗ |
| 1059 | S | theorem | F₃_K₃_commute | geometry | dm3_operators.lean ↗ |
| 1060 | S | theorem | G₁_contractive | geometry | dm3_operators.lean ↗ |
| 1061 | S | theorem | G₁_converges | geometry | dm3_operators.lean ↗ |
| 1062 | S | theorem | G₁_distance_decreases | geometry | dm3_operators.lean ↗ |
| 1063 | S | theorem | G₁_fixed_point | geometry | dm3_operators.lean ↗ |
| 1064 | S | theorem | G₁_iterate_distance | geometry | dm3_operators.lean ↗ |
| 1065 | S | theorem | K₃_breaks_contact | geometry | dm3_operators.lean ↗ |
| 1066 | S | lemma | exp_neg_one_lt_one | geometry | dm3_operators.lean ↗ |
| 1067 | S | lemma | exp_neg_one_pos | geometry | dm3_operators.lean ↗ |
| 1068 | S | theorem | ocio_in_triad | geometry | dm3_operators.lean ↗ |
| 1069 | S | theorem | triad_preserved | geometry | dm3_operators.lean ↗ |
| 1070 | S | lemma | burst_exceeds_mod4_three | geometry | CollatzDescent.lean ↗ |
| 1071 | S | lemma | burst_lt_mod4_one | geometry | CollatzDescent.lean ↗ |
| 1072 | S | lemma | descent_even | geometry | CollatzDescent.lean ↗ |
| 1073 | S | lemma | orbit_succ | geometry | CollatzDescent.lean ↗ |
| 1074 | S | lemma | orbit_zero | geometry | CollatzDescent.lean ↗ |
| 1075 | S | lemma | step_even | geometry | CollatzDescent.lean ↗ |
| 1076 | S | lemma | step_even_lt | geometry | CollatzDescent.lean ↗ |
| 1077 | S | lemma | step_odd | geometry | CollatzDescent.lean ↗ |
| 1078 | S | lemma | two_pow_v2_dvd | geometry | CollatzDescent.lean ↗ |
| 1079 | S | lemma | v2_even | geometry | CollatzDescent.lean ↗ |
| 1080 | S | lemma | v2_mod4_one | geometry | CollatzDescent.lean ↗ |
| 1081 | S | lemma | v2_mod4_three | geometry | CollatzDescent.lean ↗ |
| 1082 | S | lemma | v2_odd_pos | geometry | CollatzDescent.lean ↗ |
| 1083 | S | lemma | v2_odd_zero | geometry | CollatzDescent.lean ↗ |
| 1084 | ? | theorem | Colony | geometry | Coverage.lean ↗ |
| 1085 | S | theorem | coord_coverage | geometry | Coverage.lean ↗ |
| 1086 | S | lemma | seed_coord_injective | geometry | Coverage.lean ↗ |
| 1087 | S | lemma | seed_expand_coord_injective | geometry | Coverage.lean ↗ |
| 1088 | ✕ | theorem | centeredHex_four | geometry | DM3Bridge.lean |
| 1089 | ✕ | theorem | centeredHex_one | geometry | DM3Bridge.lean |
| 1090 | ✕ | theorem | centeredHex_strictMono | geometry | DM3Bridge.lean |
| 1091 | ✕ | theorem | centeredHex_three | geometry | DM3Bridge.lean |
| 1092 | ✕ | theorem | centeredHex_two | geometry | DM3Bridge.lean |
| 1093 | ✕ | theorem | centeredHex_zero | geometry | DM3Bridge.lean |
| 1094 | ✕ | theorem | dm3_bridge | geometry | DM3Bridge.lean |
| 1095 | ✕ | theorem | expand_is_UCKF_composite | geometry | DM3Bridge.lean |
| 1096 | ✕ | theorem | hexNeighbors_is_G6_crystal_ring | geometry | DM3Bridge.lean |
| 1097 | ✕ | theorem | nasa_growth_satisfies_R_mono | geometry | DM3Bridge.lean |
| 1098 | ✕ | theorem | opG_superset_expand | geometry | DM3Bridge.lean |
| 1099 | ✕ | theorem | ring_card | geometry | DM3Bridge.lean |
| 1100 | ✕ | theorem | stage_bound_is_epsilon0_analogue | geometry | DM3Bridge.lean |
| 1101 | S | theorem | Dcrit_eq_2_plus_trib8 | geometry | FoldCentralCharge.lean ↗ |
| 1102 | S | theorem | G_eq_T3_plus_T3T | geometry | FoldCentralCharge.lean ↗ |
| 1103 | S | theorem | G_is_even_form | geometry | FoldCentralCharge.lean ↗ |
| 1104 | S | theorem | L_embeds_in_Leech | geometry | FoldCentralCharge.lean ↗ |
| 1105 | S | theorem | T3_block_embed | geometry | FoldCentralCharge.lean ↗ |
| 1106 | S | theorem | T3_det_one | geometry | FoldCentralCharge.lean ↗ |
| 1107 | S | theorem | fold_central_charge | geometry | FoldCentralCharge.lean ↗ |
| 1108 | S | theorem | trib7_eq_13 | geometry | FoldCentralCharge.lean ↗ |
| 1109 | S | theorem | trib8_eq_24 | geometry | FoldCentralCharge.lean ↗ |
| 1110 | ✕ | theorem | arnold_tongue_A4_coupling | geometry | G6Crystal.lean |
| 1111 | ✕ | theorem | aspect_ratio_encoded | geometry | G6Crystal.lean |
| 1112 | ✕ | theorem | aspect_ratio_eq | geometry | G6Crystal.lean |
| 1113 | ✕ | theorem | aspect_ratio_scale_invariant | geometry | G6Crystal.lean |
| 1114 | ✕ | theorem | base_side_metres | geometry | G6Crystal.lean |
| 1115 | ✕ | theorem | colony_depth1_cells | geometry | G6Crystal.lean |
| 1116 | ✕ | theorem | dm3_Tstar_pos | geometry | G6Crystal.lean |
| 1117 | ✕ | theorem | dm3_epsilon0 | geometry | G6Crystal.lean |
| 1118 | ✕ | theorem | dm3_mumax_neg | geometry | G6Crystal.lean |
| 1119 | ✕ | theorem | dm3_noise_tol_lt_one | geometry | G6Crystal.lean |
| 1120 | ✕ | theorem | dm3_noise_tolerance | geometry | G6Crystal.lean |
| 1121 | ✕ | theorem | dm3_tau_eq_abs_mumax | geometry | G6Crystal.lean |
| 1122 | ✕ | theorem | dm3_tau_pos | geometry | G6Crystal.lean |
| 1123 | ✕ | theorem | epsilon0_gravity_independent | geometry | G6Crystal.lean |
| 1124 | ✕ | theorem | epsilon0_lt_one | geometry | G6Crystal.lean |
| 1125 | ✕ | theorem | epsilon0_pos | geometry | G6Crystal.lean |
| 1126 | ✕ | theorem | g6_within_16pct | geometry | G6Crystal.lean |
| 1127 | ✕ | theorem | g6_within_2pct_of_f4 | geometry | G6Crystal.lean |
| 1128 | ✕ | theorem | g_mars_lt_earth | geometry | G6Crystal.lean |
| 1129 | ✕ | theorem | g_moon_lt_earth | geometry | G6Crystal.lean |
| 1130 | ✕ | theorem | growth_factor_gt_one | geometry | G6Crystal.lean |
| 1131 | ✕ | theorem | height_metres | geometry | G6Crystal.lean |
| 1132 | ✕ | theorem | hex_beats_square | geometry | G6Crystal.lean |
| 1133 | ✕ | theorem | hex_embedding_real | geometry | G6Crystal.lean |
| 1134 | ✕ | theorem | hex_improvement_gt_115 | geometry | G6Crystal.lean |
| 1135 | ✕ | theorem | hexagrid_collapse_resistance_superior | geometry | G6Crystal.lean |
| 1136 | ✕ | theorem | layer_height_cubits | geometry | G6Crystal.lean |
| 1137 | ✕ | theorem | lunar_crystal_taller | geometry | G6Crystal.lean |
| 1138 | ✕ | theorem | mars_height_within_troposphere | geometry | G6Crystal.lean |
| 1139 | ✕ | theorem | nasa_payload_mono | geometry | G6Crystal.lean |
| 1140 | ✕ | theorem | noise_tol_covers_g6_error | geometry | G6Crystal.lean |
| 1141 | ✕ | theorem | payload_ratio_phase_1_2 | geometry | G6Crystal.lean |
| 1142 | ✕ | theorem | schumann_n4_sqrt | geometry | G6Crystal.lean |
| 1143 | ✕ | theorem | stability_band_width | geometry | G6Crystal.lean |
| 1144 | S | lemma | R_mono | geometry | Growth.lean ↗ |
| 1145 | S | lemma | hexNeighbors_length | geometry | HexGrid.lean ↗ |
| 1146 | S | theorem | FN_A_104L_neighbor_traversal | geometry | NASAGaps.lean ↗ |
| 1147 | S | theorem | FN_A_104L_reachability | geometry | NASAGaps.lean ↗ |
| 1148 | S | theorem | FN_C_101L_ring_count | geometry | NASAGaps.lean ↗ |
| 1149 | S | theorem | FN_H_101L_isoperimetric | geometry | NASAGaps.lean ↗ |
| 1150 | S | theorem | FN_H_102L_phase02_cluster | geometry | NASAGaps.lean ↗ |
| 1151 | S | theorem | FN_L_101L_hex_interfaces | geometry | NASAGaps.lean ↗ |
| 1152 | S | theorem | FN_L_101L_unique_interface | geometry | NASAGaps.lean ↗ |
| 1153 | S | theorem | FN_M_302L_hex_path_exists | geometry | NASAGaps.lean ↗ |
| 1154 | S | theorem | FN_P_101L_schumann_proximity | geometry | NASAGaps.lean ↗ |
| 1155 | S | theorem | FN_P_402L_noise_tolerance | geometry | NASAGaps.lean ↗ |
| 1156 | S | theorem | FN_T_201L_payload_monotone | geometry | NASAGaps.lean ↗ |
| 1157 | S | theorem | FN_T_201L_stage_gated | geometry | NASAGaps.lean ↗ |
| 1158 | S | theorem | FN_T_202L_payload_ratio | geometry | NASAGaps.lean ↗ |
| 1159 | S | theorem | FN_U_103L_expand_models_ISRU | geometry | NASAGaps.lean ↗ |
| 1160 | S | theorem | FN_U_103L_six_layers | geometry | NASAGaps.lean ↗ |
| 1161 | S | theorem | nasa_gap_closure_summary | geometry | NASAGaps.lean ↗ |
| 1162 | S | theorem | triple_chamber_strictAnti_in_κ | AXLE | TripleChamber.lean ↗ |
| 1163 | S | theorem | triple_perturbation_nonneg | AXLE | TripleChamber.lean ↗ |
| 1164 | S | theorem | triple_coupled_eigenvalue_decreases | AXLE | TripleChamber.lean ↗ |
| 1165 | S | theorem | triple_dm3_curvature_lowers_all_modes | AXLE | TripleChamber.lean ↗ |
| 1166 | S | theorem | triple_mode_splitting_brackets | AXLE | TripleChamber.lean ↗ |
| 1167 | S | theorem | triple_degenerate_at_zero_coupling | AXLE | TripleChamber.lean ↗ |
| 1168 | S | theorem | bessel_ratio_def | AXLE | TripleChamber.lean ↗ |
| 1169 | S | theorem | bessel_ratio_in_tribonacci_interval | AXLE | TripleChamber.lean ↗ |
| 1170 | S | theorem | canonical_coupling_ladder | AXLE | TripleChamber.lean ↗ |
build_1080.py, which walks every
.lean file authored in this corpus, deduplicates by SHA-256, strips
comments, and tests each proof body for sorry. Method and the full
audit are in RECOUNT_2026-08-16.md and
SWEEP_2026-08-16.md. Mathlib, aesop, batteries and all
.lake trees excluded.