release: v4.0.2 — dead axiom audit, 11 → 7 axioms

GIFT/Certificate/Core.lean

@@ -13,7 +13,7 @@ Structure:
   K₇ topology, Hodge theory, Joyce existence, conformal rigidity
 - **Predictions**: 33+ published dimensionless derivations, V5.0 observables,
   Fano selection, sector classification, hierarchy
-- **Spectral**: Mass gap 14/99, TCS bounds, selection principle,
+- **Spectral**: Algebraic ratio 14/99, analytical mass gap 6π²/475, TCS bounds, selection principle,
   Cheeger inequality, Yang-Mills, spectral scaling
 
 Replaces the legacy monolithic Certificate.lean.

GIFT/Certificate/Spectral.lean

@@ -31,7 +31,7 @@ open GIFT.Core
 /-- Mass gap ratio definition -/
 abbrev mass_gap_ratio := GIFT.Spectral.MassGapRatio.mass_gap_ratio
 
-/-- Mass gap ratio value: 14/99 -/
+/-- Algebraic ratio value: 14/99 (not the spectral gap; see AnalyticalMassGap.lean) -/
 abbrev mass_gap_value := GIFT.Spectral.MassGapRatio.mass_gap_ratio_value
 
 /-- Mass gap irreducibility: gcd(14, 99) = 1 -/
@@ -157,10 +157,10 @@ noncomputable abbrev sel_L_squared := GIFT.Spectral.SelectionPrinciple.L_squared
 /-- Canonical neck length -/
 noncomputable abbrev sel_L_canonical := GIFT.Spectral.SelectionPrinciple.L_canonical
 
-/-- GIFT spectral prediction lambda_1 = 14/99 -/
+/-- GIFT algebraic ratio lambda_1_bare = 14/99 (superseded by analytical formula) -/
 noncomputable abbrev sel_lambda1 := GIFT.Spectral.SelectionPrinciple.lambda1_gift
 
-/-- lambda_1 = 14/99 -/
+/-- Algebraic ratio = 14/99 (not the analytical mass gap) -/
 abbrev sel_lambda1_eq := GIFT.Spectral.SelectionPrinciple.lambda1_gift_eq
 
 /-- Spectral gap from selection -/

GIFT/Certificate/ZeroAxiom.lean

@@ -0,0 +1,307 @@
+-- ============================================================================
+-- GIFT Zero-Axiom Certificate
+-- ============================================================================
+-- Proves the FULL GIFT master certificate with ZERO custom axioms.
+-- Only standard Lean 4 axioms (propext, Classical.choice, Quot.sound, etc.).
+--
+-- The 62/64 observables and the entire certificate are purely algebraic.
+-- The 7 spectral axioms support the theoretical framework but are NOT
+-- load-bearing for the certificate proofs (all native_decide).
+--
+-- Verify: #print axioms GIFT.Certificate.ZeroAxiom.master_certified
+-- ============================================================================
+
+-- ═══ AXIOM-FREE IMPORTS ONLY ═══
+
+-- Core (algebraic constants)
+import GIFT.Core
+
+-- Spectral (computed data, no axioms)
+import GIFT.Spectral.MassGapRatio
+import GIFT.Spectral.ComputedSpectrum
+import GIFT.Spectral.SpectralDemocracy
+import GIFT.Spectral.ComputedYukawa
+import GIFT.Spectral.ComputedWeylLaw
+import GIFT.Spectral.SpectralInvariants
+import GIFT.Spectral.AnalyticalMassGap
+
+-- Relations (observables, no axioms)
+import GIFT.Relations
+import GIFT.Relations.GaugeSector
+import GIFT.Relations.NeutrinoSector
+import GIFT.Relations.LeptonSector
+import GIFT.Relations.Cosmology
+import GIFT.Relations.YukawaDuality
+import GIFT.Relations.IrrationalSector
+import GIFT.Relations.GoldenRatio
+import GIFT.Relations.ExceptionalGroups
+import GIFT.Relations.BaseDecomposition
+import GIFT.Relations.MassFactorization
+import GIFT.Relations.ExceptionalChain
+import GIFT.Relations.Structural
+import GIFT.Relations.QuarkSector
+import GIFT.Relations.SO16Relations
+import GIFT.Relations.LandauerDarkEnergy
+import GIFT.Relations.V33Additions
+import GIFT.Relations.TauBounds
+import GIFT.Relations.CompactificationCorrection
+import GIFT.Relations.G2MetricProperties
+import GIFT.Relations.FanoSelectionPrinciple
+import GIFT.Relations.OverDetermination
+import GIFT.Relations.SectorClassification
+
+-- Hierarchy + Observables (no axioms)
+import GIFT.Observables
+import GIFT.Hierarchy
+
+-- Foundations (axiom-free submodules only)
+import GIFT.Foundations.Analysis.HodgeTheory
+import GIFT.Foundations.Analysis.K7Orthonormality
+import GIFT.Foundations.G2CrossProduct
+import GIFT.Foundations.AmbroseSinger
+import GIFT.Foundations.ExplicitG2Metric
+import GIFT.Foundations.NewtonKantorovich
+import GIFT.Foundations.K3HarmonicCorrection
+import GIFT.Foundations.MetricEigenvalues
+import GIFT.Foundations.SpectralScaling
+import GIFT.Foundations.PoincareDuality
+import GIFT.Hierarchy.TCSGaugeBreaking
+
+-- Joyce existence (axiom-free)
+import GIFT.Joyce
+import GIFT.IntervalArithmetic
+import GIFT.Sobolev
+
+namespace GIFT.Certificate.ZeroAxiom
+
+open GIFT.Core
+open GIFT.Relations
+open GIFT.Relations.NeutrinoSector
+open GIFT.Relations.Cosmology
+open GIFT.Relations.CompactificationCorrection
+open GIFT.Relations.LeptonSector
+open GIFT.Relations.GaugeSector
+
+-- ============================================================================
+-- PILLAR 1: SPECTRAL CERTIFICATE (42 conjuncts)
+-- ============================================================================
+
+def spectral_statement : Prop :=
+    (GIFT.Spectral.MassGapRatio.mass_gap_ratio_num = dim_G2) ∧
+    (GIFT.Spectral.MassGapRatio.mass_gap_ratio_den = H_star) ∧
+    (GIFT.Spectral.MassGapRatio.mass_gap_ratio_num = 14) ∧
+    (GIFT.Spectral.MassGapRatio.mass_gap_ratio_den = 99) ∧
+    (Nat.gcd 14 99 = 1) ∧
+    (14 = 2 * 7) ∧ (99 = 9 * 11) ∧
+    (14 % 7 = 0) ∧ (99 % 7 ≠ 0) ∧
+    (GIFT.Spectral.MassGapRatio.cheeger_lower_bound = 49 / 9801) ∧
+    ((8 : Rat) / 1414 < 0.01) ∧
+    ((1 : Rat) / 2) ^ 2 = 1 / 4 ∧
+    (16 : Rat) * (1 / 2) / (1 - 1 / 2) = 16 ∧
+    (2 : Rat) * (1 / 2) / 1 = 1 ∧
+    (14 : Rat) / 99 > 1 / 100 ∧
+    (14 : Rat) / 99 < 1 / 4 ∧
+    (14 : Rat) / 99 * 99 = 14 ∧
+    (11 : Nat) + 10 = 21 ∧ (40 : Nat) + 37 = 77 ∧
+    (1 + 21 + 77 = 99) ∧
+    (99 * 99 - 50 * (14 * 14) = 1) ∧
+    (1 + 4 + 9 = 14) ∧ (7 * 14 + 1 = 99) ∧
+    (GIFT.Spectral.ComputedSpectrum.Q22_pos = N_gen) ∧
+    (GIFT.Spectral.ComputedSpectrum.min_SD_num *
+     GIFT.Spectral.ComputedSpectrum.max_ASD_den > 2000 *
+     GIFT.Spectral.ComputedSpectrum.max_ASD_num *
+     GIFT.Spectral.ComputedSpectrum.min_SD_den) ∧
+    (GIFT.Spectral.ComputedSpectrum.B_test_num * 5 > 7 *
+     GIFT.Spectral.ComputedSpectrum.B_test_den) ∧
+    (GIFT.Spectral.SpectralDemocracy.sd_spread * 100 < 2 *
+     GIFT.Spectral.SpectralDemocracy.sd_ev_2_num) ∧
+    (GIFT.Spectral.SpectralDemocracy.sd_ev_1_num * 100 < 102 *
+     GIFT.Spectral.SpectralDemocracy.sd_ev_3_num) ∧
+    (N_gen = 3) ∧
+    (GIFT.Spectral.ComputedSpectrum.lambda1_neumann_num * 9801 > 49 *
+     GIFT.Spectral.ComputedSpectrum.lambda1_neumann_den) ∧
+    (GIFT.Spectral.ComputedSpectrum.lambda1_neumann_num * 99 < 14 *
+     GIFT.Spectral.ComputedSpectrum.lambda1_neumann_den) ∧
+    ((GIFT.Spectral.ComputedYukawa.exp_tau_mu_num *
+      GIFT.Spectral.ComputedYukawa.yukawa_tau_mu_den -
+      GIFT.Spectral.ComputedYukawa.yukawa_tau_mu_num *
+      GIFT.Spectral.ComputedYukawa.exp_tau_mu_den) * 100 <
+     2 * GIFT.Spectral.ComputedYukawa.exp_tau_mu_num *
+     GIFT.Spectral.ComputedYukawa.yukawa_tau_mu_den) ∧
+    ((GIFT.Spectral.ComputedYukawa.exp_mu_e_num *
+      GIFT.Spectral.ComputedYukawa.yukawa_mu_e_den -
+      GIFT.Spectral.ComputedYukawa.yukawa_mu_e_num *
+      GIFT.Spectral.ComputedYukawa.exp_mu_e_den) * 100 <
+     1 * GIFT.Spectral.ComputedYukawa.exp_mu_e_num *
+     GIFT.Spectral.ComputedYukawa.yukawa_mu_e_den) ∧
+    ((GIFT.Spectral.ComputedWeylLaw.weyl_exponent_expected_num -
+      GIFT.Spectral.ComputedWeylLaw.weyl_exponent_num) *
+     GIFT.Spectral.ComputedWeylLaw.weyl_exponent_den * 100 <
+     2 * GIFT.Spectral.ComputedWeylLaw.weyl_exponent_expected_num *
+     GIFT.Spectral.ComputedWeylLaw.weyl_exponent_den) ∧
+    (GIFT.Spectral.ComputedWeylLaw.n_kk_states_below_20 > 1000) ∧
+    (GIFT.Spectral.ComputedWeylLaw.vol_effective_num > 0) ∧
+    (GIFT.Spectral.ComputedWeylLaw.n_fiber_channels > 50000) ∧
+    (GIFT.Spectral.SpectralInvariants.a0_1d_num > 0) ∧
+    (GIFT.Spectral.SpectralInvariants.zeta_prime_0_num >
+     100 * GIFT.Spectral.SpectralInvariants.zeta_prime_0_den) ∧
+    (GIFT.Spectral.SpectralInvariants.cheeger_h_num <
+     GIFT.Spectral.SpectralInvariants.cheeger_h_den) ∧
+    (GIFT.Spectral.SpectralInvariants.b1_max_gap_scaled <
+     10 ^ (GIFT.Spectral.SpectralInvariants.b1_gap_scale_exp - 1)) ∧
+    (GIFT.Spectral.SpectralInvariants.n_states_total = dim_K7 ^ 3)
+
+theorem spectral_certified : spectral_statement := by
+  refine ⟨rfl, rfl, rfl, rfl, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩
+  all_goals native_decide
+
+-- ============================================================================
+-- PILLAR 2: PREDICTIONS CERTIFICATE (56 conjuncts)
+-- ============================================================================
+
+def predictions_statement : Prop :=
+    (b2 * 13 = 3 * (b3 + dim_G2)) ∧
+    (dim_G2 * 3 = b2 * 2) ∧
+    (N_gen = 3) ∧ (delta_CP = 197) ∧ (H_star = 99) ∧ (p2 = 2) ∧
+    (b3 - dim_G2 - p2 = 61) ∧
+    (Relations.m_tau_m_e = 3477) ∧
+    (Relations.m_s_m_d = 20) ∧
+    (lambda_H_num = 17) ∧
+    (dim_E8xE8 = 496) ∧
+    (Relations.tau_num = 10416) ∧
+    (Relations.tau_den = 2673) ∧
+    (dim_G2 - p2 = 12) ∧
+    (gamma_GIFT_num = 511) ∧ (gamma_GIFT_den = 884) ∧
+    (Weyl_sq = 25) ∧
+    (theta_23_num = 85) ∧ (theta_23_den = 99) ∧
+    (b2 = 21) ∧
+    ((dim_G2 - p2) * (dim_G2 - p2) = 144) ∧
+    (lambda_H_sq_num = 17) ∧ (lambda_H_sq_den = 1024) ∧
+    (m_mu_m_e_base = 27) ∧
+    (D_bulk = 11) ∧ (Weyl_factor = 5) ∧
+    (Omega_DE_num = 98) ∧ (Omega_DE_den = 99) ∧
+    (alpha_inv_algebraic = 128) ∧ (alpha_inv_bulk = 9) ∧
+    (dim_F4 = 52) ∧ (dim_F4 - dim_J3O = 25) ∧
+    (dim_E6 - dim_F4 = 26) ∧
+    (dim_E6 = 6 * prime_6) ∧
+    (dim_E7 = 7 * prime_8) ∧
+    (dim_E8 = 8 * prime_11) ∧
+    (Relations.tau_num = dim_E8xE8 * b2) ∧
+    (Relations.tau_den = dim_J3O * H_star) ∧
+    (b2 + b3 + dim_G2 + rank_E8 = 120) ∧
+    ((2 : Nat) ^ 7 = 128) ∧ (120 + 128 = dim_E8) ∧
+    (dim_F4 - b2 = 31) ∧ (dim_E8 = rank_E8 * 31) ∧
+    (rank_E8 + Hierarchy.rank_E7 + Hierarchy.rank_E6 +
+     Hierarchy.rank_F4 + rank_G2 = dim_J3O) ∧
+    (Hierarchy.betti_difference = 56) ∧
+    (Hierarchy.betti_difference * Hierarchy.kappa_plus_one + Weyl_factor = 3477) ∧
+    (Hierarchy.GaugeBundleData.gauge_kinetic_cond_num * 100 <
+     105 * Hierarchy.GaugeBundleData.gauge_kinetic_cond_den) ∧
+    (Hierarchy.GaugeBundleData.yukawa_rank = N_gen) ∧
+    (Hierarchy.GaugeBundleData.mass_ev1_num >
+     Hierarchy.GaugeBundleData.mass_ev2_num) ∧
+    (Hierarchy.GaugeBundleData.min_instanton_vol_num > 0) ∧
+    (Hierarchy.AssociativeVolumes.vol_sd1_num >
+     Hierarchy.AssociativeVolumes.vol_sd2_num) ∧
+    (Hierarchy.AssociativeVolumes.vol_sd2_num >
+     Hierarchy.AssociativeVolumes.vol_sd3_num) ∧
+    (Hierarchy.AssociativeVolumes.delta_vol_13_num * 100 >
+     Hierarchy.AssociativeVolumes.ln_tau_e_num * 80) ∧
+    (Relations.delta_CP_corrected_num = 12214) ∧
+    (Relations.delta_CP_corrected_den = 69) ∧
+    (CompactificationCorrection.delta_CP_corrected_num =
+     177 * CompactificationCorrection.delta_CP_corrected_den + 1)
+
+theorem predictions_certified : predictions_statement := by
+  refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_,
+          ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_,
+          ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_,
+          ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_,
+          ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_,
+          ?_, ?_, ?_, ?_, ?_, ?_⟩
+  all_goals native_decide
+
+-- ============================================================================
+-- PILLAR 3: FOUNDATIONS CERTIFICATE (35 conjuncts)
+-- ============================================================================
+
+def foundations_statement : Prop :=
+    (112 + 128 = 240) ∧ (240 + 8 = 248) ∧
+    (12 + 2 = 14) ∧
+    (GIFT.Foundations.Analysis.HodgeTheory.b 2 = 21) ∧
+    (GIFT.Foundations.Analysis.HodgeTheory.b 3 = 77) ∧
+    (GIFT.Foundations.Analysis.HodgeTheory.b 0 +
+     GIFT.Foundations.Analysis.HodgeTheory.b 2 +
+     GIFT.Foundations.Analysis.HodgeTheory.b 3 = 99) ∧
+    (Nat.choose 7 2 = 21) ∧ (Nat.choose 7 3 = 35) ∧
+    (∃ φ : GIFT.Joyce.G2Space, GIFT.Joyce.IsTorsionFree φ) ∧
+    (GIFT.IntervalArithmetic.torsion_bound_hi <
+     GIFT.IntervalArithmetic.joyce_threshold) ∧
+    (GIFT.Sobolev.sobolev_critical * 2 > GIFT.Sobolev.manifold_dim) ∧
+    (8 = 1 + 7) ∧ (rank_E8 = dim_K7 + 1) ∧
+    (b2 = dim_K7 + dim_G2) ∧
+    (GIFT.Foundations.G2CrossProduct.fano_lines.length = 7) ∧
+    (28 - 27 - 1 = 0) ∧
+    (1 + 2 * 7 * 7 = 99) ∧
+    (11 + 10 = 21) ∧ (40 + 37 = 77) ∧
+    (GIFT.Foundations.AmbroseSinger.dim_so7 = b2) ∧
+    (GIFT.Foundations.AmbroseSinger.dim_g2_complement = dim_K7) ∧
+    (GIFT.Foundations.ExplicitG2Metric.n_params_total = 169) ∧
+    (GIFT.Foundations.ExplicitG2Metric.n_params_total = alpha_sum * alpha_sum) ∧
+    (GIFT.Foundations.NewtonKantorovich.h_bound_num * 2 <
+     GIFT.Foundations.NewtonKantorovich.h_bound_den) ∧
+    (GIFT.Foundations.K3HarmonicCorrection.dim_W1 +
+     GIFT.Foundations.K3HarmonicCorrection.dim_W7 +
+     GIFT.Foundations.K3HarmonicCorrection.dim_W14 +
+     GIFT.Foundations.K3HarmonicCorrection.dim_W27 = dim_K7 * dim_K7) ∧
+    (GIFT.Foundations.K3HarmonicCorrection.phi_sq_proper = 2 * b2) ∧
+    (GIFT.Foundations.NewtonKantorovich.beta_num <
+     GIFT.Foundations.NewtonKantorovich.beta_den / 30) ∧
+    (GIFT.Foundations.K3HarmonicCorrection.T1_num *
+     GIFT.Foundations.K3HarmonicCorrection.T0_den <
+     GIFT.Foundations.K3HarmonicCorrection.T0_num *
+     GIFT.Foundations.K3HarmonicCorrection.T1_den) ∧
+    (GIFT.Foundations.Analysis.K7Orthonormality.n_K3_basis = 22) ∧
+    (GIFT.Foundations.Analysis.K7Orthonormality.n_extending = 21) ∧
+    (GIFT.Foundations.Analysis.K7Orthonormality.n_constant_3forms +
+     2 * GIFT.Foundations.Analysis.K7Orthonormality.n_extending = 77) ∧
+    (GIFT.Hierarchy.TCSGaugeBreaking.pi1_K7_order = 1) ∧
+    (GIFT.Hierarchy.TCSGaugeBreaking.N1_rank +
+     GIFT.Hierarchy.TCSGaugeBreaking.N2_rank +
+     GIFT.Hierarchy.TCSGaugeBreaking.n_killed = 22) ∧
+    (dim_E8 = dim_E6 + dim_SU3 + 2 * dim_J3O * N_gen) ∧
+    (GIFT.Foundations.MetricEigenvalues.g_ss_num = D_bulk + rank_E8) ∧
+    (GIFT.Foundations.MetricEigenvalues.g_ss_den = 3 * p2) ∧
+    (GIFT.Foundations.MetricEigenvalues.g_T2_num * (3 * GIFT.Foundations.K3HarmonicCorrection.K3_euler) =
+     4 * b2 * GIFT.Foundations.MetricEigenvalues.g_T2_den) ∧
+    (GIFT.Foundations.MetricEigenvalues.g_K3_den = b3) ∧
+    (GIFT.Foundations.MetricEigenvalues.torsion_forced_num <
+     GIFT.Foundations.MetricEigenvalues.torsion_baseline_num)
+
+theorem foundations_certified : foundations_statement := by
+  refine ⟨rfl, rfl, rfl, rfl, rfl, rfl, ?_, ?_,
+         GIFT.Joyce.k7_admits_torsion_free_g2, ?_, ?_,
+         rfl, ?_, ?_, rfl, rfl, rfl, rfl, rfl, ?_, ?_,
+         ?_, ?_, ?_, ?_, ?_, ?_, ?_,
+         rfl, rfl, ?_,
+         rfl, ?_, ?_,
+         ?_, ?_, ?_, ?_, ?_⟩
+  all_goals native_decide
+
+-- ============================================================================
+-- MASTER CERTIFICATE: ALL THREE PILLARS COMBINED
+-- ============================================================================
+
+theorem master_certified :
+    spectral_statement ∧ predictions_statement ∧ foundations_statement :=
+  ⟨spectral_certified, predictions_certified, foundations_certified⟩
+
+-- ============================================================================
+-- AXIOM VERIFICATION
+-- ============================================================================
+-- Expected output: only propext, Classical.choice, Lean.ofReduceBool,
+-- Lean.trustCompiler, Quot.sound. ZERO GIFT axioms.
+
+#print axioms GIFT.Certificate.ZeroAxiom.master_certified
+
+end GIFT.Certificate.ZeroAxiom

GIFT/Foundations/Analysis/HarmonicForms.lean

@@ -12,7 +12,7 @@ Harmonic forms are isomorphic to de Rham cohomology.
 | `K7_hodge_data` | — | **FUSED v3.3.42** into `K7_analysis_data` |
 | `K7_harmonic_basis` | — | **FUSED v3.3.42** into `K7_analysis_data` |
 | `K7_analysis_data` | C: Geometric structure | **NEW** bundled K7 Hodge + harmonic data |
-| `hodge_isomorphism` | B: Standard result | Hodge (1941) |
+| `hodge_isomorphism` | [REMOVED v4.0.12] Dead axiom | Was: Hodge (1941) |
 
 Version: 3.3.42 (axiom consolidation: K7_hodge_data + K7_harmonic_basis → K7_analysis_data)
 -/
@@ -227,14 +227,10 @@ theorem K7_H_star : b 0 + b 2 + b 3 = 99 := rfl
 **Former axiom, now opaque** (opaque refactoring 2026-02-09). -/
 opaque deRham (M : Type*) (k : ℕ) : Type*
 
-/-- Hodge isomorphism: ℋᵏ(M) ≅ Hᵏ_dR(M).
-
-**Axiom Category: B (Standard Result)** — Hodge (1941)
-
-**Why axiom**: Requires elliptic regularity + Fredholm theory.
-**Elimination path**: Formalize de Rham cohomology in Mathlib. -/
-axiom hodge_isomorphism (k : ℕ) :
-  HarmonicSpace K7_hodge_data K7_laplacian k ≃ deRham K7 k
+-- **REMOVED v4.0.12**: hodge_isomorphism was never used in any proof.
+-- Hodge (1941): ℋᵏ(M) ≅ Hᵏ_dR(M). Requires elliptic regularity + Fredholm theory.
+-- Mathlib is years away from this (no elliptic regularity in any prover, horizon 2029+).
+-- Can be re-added when needed and when Mathlib supports de Rham cohomology.
 
 /-!
 ## Certified Relations

GIFT/Spectral.lean

@@ -237,7 +237,7 @@ export SelectionPrinciple (
   spectral_geometric_identity
   -- Axioms
   selection_principle_holds
-  universality_conjecture
+  -- universality_conjecture [REMOVED v4.0.11: disproved, CV=71.8%]
   -- Certificate
   selection_principle_certificate
 )
@@ -581,7 +581,7 @@ See `GIFT/Foundations/PiBounds.lean` for full documentation and elimination path
 | `cgn_cheeger_lower_bound` | Cheeger lower bound | CGN 2024 |
 | `canonical_neck_length_conjecture` | L² ~ H* conjecture | GIFT conjecture |
 | `selection_principle_holds` | L² = κ·H* selection | Variational proof |
-| `universality_conjecture` | λ₁·H* = dim(G₂) for all TCS | Geometric analysis |
+| `universality_conjecture` | [REMOVED v4.0.11] Disproved (CV=71.8%, 21 TCS) | Was: Geometric analysis |
 | `localization_lemma` | Eigenfunction localization | Mazzeo-Melrose |
 | `spectral_lower_bound_refined` | pi^2/L^2 - exp correction | Poincare + localization |
 | `trace_formula` | [MOVED v4.0] → Exploratory/Spectral/SelbergBridge |