sync: upload 05_lean_formalization to Hugging Face dataset

05_lean_formalization/ADJACENT_MODULES.txt

@@ -134,6 +134,13 @@ LeptonMassCollar.lean
 # with Re_c = sqrt(2) algebraic duality with theta_geom = 1/sqrt(2).
 NavierStokesCorticalBound.lean
 
+# --- 3D periodic Navier-Stokes conditional-regularity program (added 2026-10-08) ---
+# The periodic target (Fefferman's statement B) as a Prop, the alignment obligation over
+# genuine solutions, and sanity theorems about those definitions. It proves no
+# regularity result. NavierStokesGeometry/Scope/Spec predate this list and are counted
+# in the manuscript's module total.
+NavierStokesTarget.lean
+
 # --- Yang-Mills Gauge Theory & Casimir Mass Gap Program ---
 # Positive spectral mass gap Delta_YM(N) = (kappa / theta) * (N - 1),
 # exact SU(3)/SU(2) ratio = 2, and rigorous enclosure bounds at theta_geom = 1/sqrt(2).

05_lean_formalization/NavierStokesSpec.lean

@@ -61,8 +61,11 @@ theorem alignmentFromGate_eq (Lmax : ℝ) :
   unfold alignmentFromGate alignmentGate
   ring
 
-/-- Open obligation: persistence of `AlignmentPredicate` along a genuine NSE
-solution class. This file records the obligation; it does not prove it. -/
+/-- Historical name: this was meant to record the open obligation, persistence of
+`AlignmentPredicate` along a genuine Navier–Stokes solution class. **As written it does not:**
+it quantifies over every vorticity field, with no equation or solution in sight, and it is
+false (`NavierStokesTarget.persistenceObligation_false` refutes it at `K = L = ρ = 1`, added
+2026-10-08). The obligation over genuine solutions is `NavierStokesTarget.AlignmentPersistence`. -/
 def PersistenceObligation (K L ρ : ℝ) : Prop :=
   ∀ ω : VorticityField, AlignmentPredicate K L ρ ω
 

05_lean_formalization/NavierStokesTarget.lean

@@ -0,0 +1,258 @@
+import Mathlib.Analysis.Calculus.FDeriv.Basic
+import Mathlib.Analysis.Calculus.Deriv.Basic
+import Mathlib.Analysis.Calculus.ContDiff.Defs
+import Mathlib.Analysis.InnerProductSpace.PiL2
+import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic
+import NavierStokesSpec
+
+/-!
+# The periodic global-regularity target, as a statement (no proof)
+
+This module freezes one target: Fefferman's statement (B), the incompressible Navier–Stokes
+problem on `ℝ³/ℤ³` with zero force (C. L. Fefferman, *Existence and smoothness of the
+Navier–Stokes equation*, 2000). The source text is quoted in
+`NAVIER_STOKES_SOURCE_STATEMENTS.md`.
+
+Everything named below is a definition, except four sanity theorems at the end.
+**Nothing here proves `PeriodicGlobalRegularity`, and no declaration assumes it.**
+
+Representation choices:
+- **Space.** Fields live on Euclidean `ℝ³` (`NavierStokesSpec.Point3`) and are periodic under
+  the unit translations `x ↦ x + e_j`, as in Fefferman's (8) and (10). They are not defined
+  on a quotient type.
+- **Derivatives.** Fréchet derivatives in Euclidean coordinates.
+- **Time.** The equations are imposed for `t > 0`, and smoothness is required on the closed
+  half-space `[0, ∞) × ℝ³`. A function on `ℝ` has no meaningful two-sided time derivative at
+  the initial time, and by continuity the equations then also hold at `t = 0` from the right.
+
+This module also restates the alignment obligation over genuine solutions
+(`AlignmentPersistence`, with vorticity the curl of the velocity).
+`NavierStokesSpec.PersistenceObligation` quantifies over *every* field, and
+`persistenceObligation_false` below shows it is false as stated.
+-/
+
+namespace NavierStokesTarget
+
+open NavierStokesSpec
+open scoped ContDiff
+
+/-- The unit basis vector `e_j`. -/
+noncomputable def e (j : Fin 3) : Point3 := EuclideanSpace.single j (1 : ℝ)
+
+/-- Invariance under the three unit translations (Fefferman's periodicity conditions). -/
+def UnitPeriodic {α : Type*} (f : Point3 → α) : Prop :=
+  ∀ j : Fin 3, ∀ x : Point3, f (x + e j) = f x
+
+/-- The partial derivative `∂_j f (x)`. -/
+noncomputable def pd (j : Fin 3) (f : Point3 → ℝ) (x : Point3) : ℝ :=
+  fderiv ℝ f x (e j)
+
+/-- The `i`-th component of a vector field. -/
+def comp (v : Point3 → Vector3) (i : Fin 3) : Point3 → ℝ := fun x => v x i
+
+/-- `div v`. -/
+noncomputable def divergence (v : Point3 → Vector3) (x : Point3) : ℝ :=
+  ∑ j, pd j (comp v j) x
+
+/-- `Δ f`. -/
+noncomputable def laplacian (f : Point3 → ℝ) (x : Point3) : ℝ :=
+  ∑ j, pd j (pd j f) x
+
+/-- `curl v`, the vorticity of a velocity field. -/
+noncomputable def curl (v : Point3 → Vector3) : VorticityField := fun x =>
+  !₂[pd 1 (comp v 2) x - pd 2 (comp v 1) x,
+     pd 2 (comp v 0) x - pd 0 (comp v 2) x,
+     pd 0 (comp v 1) x - pd 1 (comp v 0) x]
+
+/-- A time-dependent velocity field `u(t, x)`. -/
+abbrev Velocity := ℝ → Point3 → Vector3
+
+/-- A time-dependent pressure `p(t, x)`. -/
+abbrev Pressure := ℝ → Point3 → ℝ
+
+/-- Zero-force incompressible Navier–Stokes at `(t, x)`, componentwise:
+`∂ₜuᵢ + Σⱼ uⱼ ∂ⱼuᵢ = ν Δuᵢ − ∂ᵢp` and `div u = 0`. These are Fefferman's (1) and (2) with
+`f = 0`. -/
+def NavierStokesAt (ν : ℝ) (u : Velocity) (p : Pressure) (t : ℝ) (x : Point3) : Prop :=
+  (∀ i : Fin 3,
+      deriv (fun s => u s x i) t + ∑ j, u t x j * pd j (comp (u t) i) x
+        = ν * laplacian (comp (u t) i) x - pd i (p t) x) ∧
+  divergence (u t) x = 0
+
+/-- Smoothness on `[a, b) × ℝ³`, read as joint smoothness in `(t, x)` on that set. -/
+def SmoothOn {β : Type*} [NormedAddCommGroup β] [NormedSpace ℝ β]
+    (f : ℝ → Point3 → β) (a b : ℝ) : Prop :=
+  ContDiffOn ℝ ∞ (fun z : ℝ × Point3 => f z.1 z.2) (Set.Ico a b ×ˢ Set.univ)
+
+/-- Smoothness on the closed half-space `[0, ∞) × ℝ³` (Fefferman's (11)). -/
+def SmoothOnClosedHalfSpace {β : Type*} [NormedAddCommGroup β] [NormedSpace ℝ β]
+    (f : ℝ → Point3 → β) : Prop :=
+  ContDiffOn ℝ ∞ (fun z : ℝ × Point3 => f z.1 z.2) (Set.Ici 0 ×ˢ Set.univ)
+
+/-- Admissible initial data for statement (B): smooth, divergence-free and unit-periodic. -/
+def AdmissibleData (u₀ : Point3 → Vector3) : Prop :=
+  ContDiff ℝ ∞ u₀ ∧ UnitPeriodic u₀ ∧ ∀ x, divergence u₀ x = 0
+
+/-- A global smooth periodic solution with data `u₀`. It satisfies the equations for `t > 0`,
+is smooth on `[0, ∞) × ℝ³`, has `u(0) = u₀`, and is spatially periodic for `t ≥ 0`. Periodicity
+covers the velocity (Fefferman's (10)) **and the pressure**, per the problem description's
+Errata: "The further condition p(x + ej, t) = p(x, t) should be made explicit". -/
+def GlobalSmoothPeriodicSolution (ν : ℝ) (u₀ : Point3 → Vector3) (u : Velocity)
+    (p : Pressure) : Prop :=
+  SmoothOnClosedHalfSpace u ∧ SmoothOnClosedHalfSpace p ∧
+  (∀ t, 0 ≤ t → UnitPeriodic (u t)) ∧ (∀ t, 0 ≤ t → UnitPeriodic (p t)) ∧ u 0 = u₀ ∧
+  ∀ t, 0 < t → ∀ x, NavierStokesAt ν u p t x
+
+/-- **Statement (B), as a proposition.** This module does not prove it, and no declaration
+assumes it. -/
+def PeriodicGlobalRegularity : Prop :=
+  ∀ ν : ℝ, 0 < ν → ∀ u₀ : Point3 → Vector3, AdmissibleData u₀ →
+    ∃ (u : Velocity) (p : Pressure), GlobalSmoothPeriodicSolution ν u₀ u p
+
+/-- A smooth periodic solution on `[0, T)`. -/
+def SmoothPeriodicSolutionOn (ν : ℝ) (u₀ : Point3 → Vector3) (u : Velocity) (p : Pressure)
+    (T : ℝ) : Prop :=
+  SmoothOn u 0 T ∧ SmoothOn p 0 T ∧ (∀ t, 0 ≤ t → t < T → UnitPeriodic (u t)) ∧
+  (∀ t, 0 ≤ t → t < T → UnitPeriodic (p t)) ∧
+  u 0 = u₀ ∧ ∀ t, 0 < t → t < T → ∀ x, NavierStokesAt ν u p t x
+
+/-- **The open obligation of the conditional program.** Every smooth periodic solution, from
+admissible data, satisfies `AlignmentPredicate K L ρ` for its vorticity `curl (u t)` at every
+time it exists. Not proved here. -/
+def AlignmentPersistence (K L ρ : ℝ) : Prop :=
+  ∀ ν : ℝ, 0 < ν → ∀ (u₀ : Point3 → Vector3) (u : Velocity) (p : Pressure) (T : ℝ),
+    AdmissibleData u₀ → SmoothPeriodicSolutionOn ν u₀ u p T →
+      ∀ t, 0 ≤ t → t < T → AlignmentPredicate K L ρ (curl (u t))
+
+/-! ## Sanity theorems about the definitions (none of them is about regularity) -/
+
+/-- Helper: a component of a constant field is constant. -/
+@[simp] theorem comp_const (c : Vector3) (i : Fin 3) : comp (fun _ => c) i = fun _ => c i := rfl
+
+/-- Helper: a partial derivative of a constant function vanishes. -/
+@[simp] theorem pd_const (j : Fin 3) (c : ℝ) : pd j (fun _ => c) = fun _ => 0 := by
+  funext x
+  simp [pd]
+
+/-- The zero field is admissible data, so `AdmissibleData` is not empty. -/
+theorem zero_admissible : AdmissibleData (fun _ => 0) := by
+  refine ⟨contDiff_const, fun _ _ => rfl, fun x => ?_⟩
+  simp [divergence]
+
+/-- The zero velocity and pressure solve the problem for zero data, so the solution predicate
+is satisfiable and statement (B) is not vacuously false. -/
+theorem zero_solution (ν : ℝ) :
+    GlobalSmoothPeriodicSolution ν (fun _ => 0) (fun _ _ => 0) (fun _ _ => 0) := by
+  refine ⟨contDiffOn_const, contDiffOn_const, fun _ _ _ _ => rfl, fun _ _ _ _ => rfl, rfl,
+    fun t _ x => ?_⟩
+  refine ⟨fun i => ?_, ?_⟩
+  · simp [laplacian]
+  · simp [divergence]
+
+/-- The equations have content. A spatially constant field that grows in time, `u(t, x) = t e₀`
+with zero pressure, fails them at every point: `∂ₜu₀ = 1`, while every other term is `0`. -/
+theorem growing_constant_field_not_a_solution (ν t : ℝ) (x : Point3) :
+    ¬ NavierStokesAt ν (fun s _ => s • e 0) (fun _ _ => 0) t x := by
+  rintro ⟨h, -⟩
+  have h0 := h 0
+  simp [laplacian, e] at h0
+
+/-- `NavierStokesSpec.PersistenceObligation` is false as stated. It asks `AlignmentPredicate`
+of every field, and a field with two nearby high-vorticity points of opposite direction
+violates it. This is why `AlignmentPersistence` quantifies over solutions instead. -/
+theorem persistenceObligation_false : ¬ PersistenceObligation 1 1 1 := by
+  intro h
+  let a : Point3 := 0
+  let b : Point3 := EuclideanSpace.single 0 (1 / 2 : ℝ)
+  let v : Vector3 := EuclideanSpace.single 0 (1 : ℝ)
+  have hab : a ≠ b := by
+    intro hab
+    have := congrArg (fun z : Point3 => z 0) hab
+    simp [a, b] at this
+  let w : VorticityField := fun x => if x = a then v else if x = b then -v else 0
+  have hv : ‖v‖ = 1 := by simp [v]
+  have hωa : w a = v := by simp [w]
+  have hωb : w b = -v := by simp [w, hab.symm]
+  have hdist : dist a b = 1 / 2 := by
+    simp [a, b, dist_eq_norm]
+  obtain ⟨hx, hy, hle⟩ := h w a b (by simp [HighVorticity, hωa, hv]) (by simp [HighVorticity, hωb, hv])
+    (by rw [hdist]; norm_num) (by rw [hdist]; norm_num)
+  have hda : direction w a hx = v := by
+    simp [direction, hωa, hv]
+  have hdb : direction w b hy = -v := by
+    simp [direction, hωb, hv]
+  rw [hda, hdb, hdist, sub_neg_eq_add] at hle
+  have h2 : ‖v + v‖ = 2 := by
+    rw [← two_smul ℝ v, norm_smul, hv]; norm_num
+  rw [h2] at hle
+  norm_num at hle
+
+/-! ## L3a: on one time slice, alignment gives the sine form of the direction condition -/
+
+/-- For unit vectors, the sine of the angle between them is at most the chord length. -/
+theorem sin_angle_le_norm_sub (a b : Vector3) (ha : ‖a‖ = 1) (hb : ‖b‖ = 1) :
+    Real.sin (InnerProductGeometry.angle a b) ≤ ‖a - b‖ := by
+  have hc : Real.cos (InnerProductGeometry.angle a b) = inner ℝ a b := by
+    rw [InnerProductGeometry.cos_angle, ha, hb]; simp
+  have hs0 : 0 ≤ Real.sin (InnerProductGeometry.angle a b) := InnerProductGeometry.sin_angle_nonneg a b
+  have hsq : ‖a - b‖ ^ 2 = 2 - 2 * inner ℝ a b := by
+    rw [@norm_sub_sq_real, ha, hb]; ring
+  have hcos_le : inner ℝ a b ≤ 1 := by
+    have := real_inner_le_norm a b; rw [ha, hb] at this; linarith
+  have hcos_ge : -1 ≤ inner ℝ a b := by
+    have := neg_le_of_abs_le (abs_real_inner_le_norm a b); rw [ha, hb] at this; linarith
+  have hsin2 : Real.sin (InnerProductGeometry.angle a b) ^ 2 = 1 - inner ℝ a b ^ 2 := by
+    rw [← hc]; linarith [Real.sin_sq_add_cos_sq (InnerProductGeometry.angle a b)]
+  have key : Real.sin (InnerProductGeometry.angle a b) ^ 2 ≤ ‖a - b‖ ^ 2 := by
+    rw [hsin2, hsq]; nlinarith
+  nlinarith [key, hs0, norm_nonneg (a - b)]
+
+/-- **L3a: kinematic, one time slice.** Suppose `AlignmentPredicate K L ρ ω` holds. Then for any
+two high-vorticity points at distance in `(0, ρ]`, the angle `φ` between the vorticity vectors
+satisfies `sin φ ≤ L · |x − y|`. This is the sine form of a vorticity-direction condition, with
+`ρ_CF = 1 / L`.
+
+It is only the geometric half of L3. It says nothing about:
+- time, or a solution class;
+- the torus versus `ℝ³`;
+- the source's threshold or `δ` conventions (`exploration/navier_stokes/SOURCE_STATEMENTS.md`). -/
+theorem alignment_gives_sine_condition {K L ρ : ℝ} {w : VorticityField}
+    (h : AlignmentPredicate K L ρ w) {x y : Point3} (hx : HighVorticity K w x)
+    (hy : HighVorticity K w y) (h0 : 0 < dist x y) (hρ : dist x y ≤ ρ) :
+    Real.sin (InnerProductGeometry.angle (w x) (w y)) ≤ L * dist x y := by
+  obtain ⟨hx0, hy0, hle⟩ := h x y hx hy h0 hρ
+  have hrx : 0 < ‖w x‖⁻¹ := inv_pos.mpr (norm_pos_iff.mpr hx0)
+  have hry : 0 < ‖w y‖⁻¹ := inv_pos.mpr (norm_pos_iff.mpr hy0)
+  have hang : InnerProductGeometry.angle (w x) (w y)
+      = InnerProductGeometry.angle (direction w x hx0) (direction w y hy0) := by
+    unfold direction
+    rw [InnerProductGeometry.angle_smul_left_of_pos _ _ hrx,
+      InnerProductGeometry.angle_smul_right_of_pos _ _ hry]
+  rw [hang]
+  exact (sin_angle_le_norm_sub _ _ (direction_unit w x hx0) (direction_unit w y hy0)).trans hle
+
+/-- **L3a, full form on one time slice.** Suppose `0 ≤ K`, `0 < L` and `L · ρ ≥ 1`, and set `Ω = K`. Then
+`AlignmentPredicate K L ρ w` gives `sin φ(x, y) ≤ |x − y| / (1/L)` for **every** pair of points
+with `|w| > Ω` at both. (`0 ≤ K` matters: Mathlib's angle with a zero vector is `π/2`, so with
+`K < 0` and `w x = 0` the case `x = y` would fail.) This is the single-time form of Constantin–Fefferman's Assumption (A) with
+their `ρ = 1/L`; for unit vectors their `|P^⊥_ξ(η)|` equals `sin φ`.
+- For pairs farther apart than `ρ`, the bound is automatic, since `L|x − y| > Lρ ≥ 1 ≥ sin φ`.
+- The time quantifier, the regularized-solution setting on `ℝ³`, and the torus are not addressed
+  (`exploration/navier_stokes/SOURCE_STATEMENTS.md`). -/
+theorem alignment_gives_assumptionA_slice {K L ρ : ℝ} {w : VorticityField} (hK : 0 ≤ K)
+    (hL : 0 < L) (hLρ : 1 ≤ L * ρ) (h : AlignmentPredicate K L ρ w) {x y : Point3}
+    (hx : K < ‖w x‖) (hy : K < ‖w y‖) :
+    Real.sin (InnerProductGeometry.angle (w x) (w y)) ≤ dist x y / (1 / L) := by
+  rw [one_div, div_inv_eq_mul, mul_comm]
+  rcases eq_or_lt_of_le (dist_nonneg : 0 ≤ dist x y) with h0 | h0
+  · have hxy : x = y := dist_eq_zero.mp h0.symm
+    subst hxy
+    have hne : w x ≠ 0 := fun hz => by rw [hz, norm_zero] at hx; linarith
+    rw [InnerProductGeometry.angle_self hne, Real.sin_zero, dist_self, mul_zero]
+  · by_cases hρ : dist x y ≤ ρ
+    · exact alignment_gives_sine_condition h hx.le hy.le h0 hρ
+    · have hρ' : ρ < dist x y := not_le.mp hρ
+      have h1 : 1 < L * dist x y := by nlinarith
+      linarith [Real.sin_le_one (InnerProductGeometry.angle (w x) (w y))]
+
+end NavierStokesTarget

05_lean_formalization/SovereignRegularity.lean

@@ -8,22 +8,34 @@ import Mathlib.Tactic.NormNum
 
 
 /-!
-# Sovereign Regularity for the 3D Navier-Stokes & ADCCL Trajectory Control
+# Conditional scalar bounds for an abstract trajectory (historical file, renamed 2026-10-08)
 
 ## Overview
 
-This file formalizes the SOVEREIGN REGULARITY THEOREM:
-  Under active Anti-Drift Cognitive Control Loop (ADCCL) vorticity bounds,
-  the Beale-Kato-Majda (BKM) integral of unaligned drift remains finite for all T ≥ 0,
-  mathematically preventing finite-time singular blow-up.
-
-## What is proved (zero sorry, non-vacuous)
-
-  ✓ lipschitz_implies_angle_modulus: the key geometric step (Constantin-Fefferman 1993)
-  ✓ chiral_iff_lipschitz_constant: equivalence of χ ≥ θ and Lipschitz alignment
-  ✓ bkm_vorticity_integral_finite: BKM integral bounds under ADCCL control
-  ✓ bkm_no_blowup: non-divergence of trajectory vorticity integral for all T ≥ 0
-  ✓ sovereign_regularity_theorem: global non-singular trajectory stability
+This file records elementary consequences of an *assumed* bound on an abstract state.
+It does **not** formalize the Navier–Stokes equations, a vorticity field, the
+Beale–Kato–Majda time integral, a continuation theorem, or any regularity result.
+
+## What is proved (zero sorry; scope-limited)
+
+  ✓ lipschitz_implies_angle_modulus: for two unit triples, a chord bound ≤ L·d gives a
+    sine bound |sin φ| ≤ L·d. Elementary geometry; no Navier–Stokes content and not the
+    Constantin–Fefferman criterion.
+  ✓ chiral_iff_lipschitz_constant: for scalars, χ ≥ θ ↔ s ≤ L_max·(1 − θ).
+  ✓ pointwise_vorticity_product_bound: an assumed bound times a horizon (a product, not a
+    time integral).
+  ✓ product_bound_below_threshold: an arithmetic consequence of that product bound.
+  ✓ assumed_vorticity_bound_projection: returns the assumed bound itself (`st.h_controlled`).
+
+## Renamed 2026-10-08 (identifiers and comments only; proof terms unchanged)
+
+  sovereign_regularity_theorem   → assumed_vorticity_bound_projection
+  bkm_vorticity_integral_finite  → pointwise_vorticity_product_bound
+  bkm_no_blowup                  → product_bound_below_threshold
+  BKMVorticityState              → AssumedVorticityBoundState
+  SovereignAlignment.lipschitz_xi (a `True` field) → kinematic_placeholder
+The old names described global regularity and a BKM integral; the statements are a
+projection of an assumed field and scalar arithmetic.
 -/
 
 namespace SovereignRegularity
@@ -32,7 +44,8 @@ open Real
 
 /-! ## §1. Abstract Velocity and Vorticity Fields -/
 
-/-- An abstract velocity field: a function from the spatial domain × time to ℝ³. -/
+/-- Four real arguments returning a triple. Reading them as (x, y, z, t) is a convention only:
+no domain, time variable, regularity or divergence condition is encoded. -/
 def VelocityField : Type := ℝ → ℝ → ℝ → ℝ → (ℝ × ℝ × ℝ)
 
 /-- The magnitude of a 3-vector. -/
@@ -41,22 +54,25 @@ noncomputable def vmag (v : ℝ × ℝ × ℝ) : ℝ := Real.sqrt (v.1^2 + v.2.1
 theorem vmag_nonneg (v : ℝ × ℝ × ℝ) : vmag v ≥ 0 := Real.sqrt_nonneg _
 
 
-/-! ## §2. The Sovereign Alignment Condition -/
+/-! ## §2. A placeholder structure (historically called the alignment condition) -/
 
-/-- Sovereign Alignment SA(K, L): vorticity direction ξ = ω/|ω| is L-Lipschitz. -/
+/-- Carries `K > 0`, `L > 0` and a `True` placeholder only. It contains no vorticity, no
+direction field and no Lipschitz inequality, so it is **not** an alignment condition. -/
 structure SovereignAlignment (u : VelocityField) (K L : ℝ) (t : ℝ) : Prop where
   K_pos : K > 0
   L_pos : L > 0
-  lipschitz_xi : True
+  kinematic_placeholder : True
 
-/-- The Sovereign Class: velocity fields satisfying SA(K, L) for all time. -/
+/-- Fields for which `SovereignAlignment` holds at every `t ≥ 0`. Since that structure has no
+alignment content, this constrains only `K` and `L`. -/
 def SovereignClass (K L : ℝ) (u : VelocityField) : Prop :=
   ∀ t : ℝ, t ≥ 0 → SovereignAlignment u K L t
 
 
 /-! ## §3. The Chiral Invariant of a Velocity Field -/
 
-/-- The Chiral Invariant χ(u, t) as a function of the sup |∇ξ| on high-vorticity set. -/
+/-- A scalar function of two inputs, read as `sup |∇ξ|` and `L_max` by convention only: no
+supremum, gradient, velocity or time enters. -/
 noncomputable def velocity_chi (sup_grad_xi L_max : ℝ) : ℝ :=
   1 - min 1 (sup_grad_xi / L_max)
 
@@ -74,12 +90,13 @@ theorem velocity_chi_nonneg (s L_max : ℝ) (hL : L_max > 0) :
   have : min 1 (s / L_max) ≤ 1 := min_le_left _ _
   linarith
 
-/-- The Sovereign Boundary condition: χ ≥ θ = 0.70. -/
+/-- The scalar predicate `velocity_chi s L_max ≥ θ` for an arbitrary real `θ`; the value 0.70 is
+not imposed here. -/
 def sovereign_boundary (sup_grad_xi L_max : ℝ) (θ : ℝ) : Prop :=
   velocity_chi sup_grad_xi L_max ≥ θ
 
 
-/-! ## §4. Equivalence Theorem: χ ≥ θ ↔ SA(K, L) -/
+/-! ## §4. A scalar threshold equivalence (it does not mention `SovereignAlignment`) -/
 
 theorem chiral_iff_lipschitz_constant (sup_grad_xi L_max θ : ℝ)
     (hL : L_max > 0) (hθ_low : 0 ≤ θ) (hθ_high : θ ≤ 1) (h_sup_nn : 0 ≤ sup_grad_xi)
@@ -103,7 +120,7 @@ theorem chiral_iff_lipschitz_constant (sup_grad_xi L_max θ : ℝ)
     linarith
 
 
-/-! ## §5. The Lipschitz-to-Angle Geometric Step -/
+/-! ## §5. Chord bound to sine bound for two unit triples (elementary geometry) -/
 
 theorem lipschitz_implies_angle_modulus
     (xi_x xi_y : ℝ × ℝ × ℝ)
@@ -189,33 +206,32 @@ theorem lipschitz_implies_angle_modulus
     exact Real.sq_sqrt h_one_minus_cos_nn
 
 
-/-! ## §6. Beale-Kato-Majda (BKM) Non-Divergence & Sovereign Regularity -/
+/-! ## §6. Consequences of an assumed bound (not the BKM integral, not a regularity result) -/
 
-/-- Structure representing the Beale-Kato-Majda (BKM) vorticity integral under ADCCL control. -/
-structure BKMVorticityState where
-  omega_sup : ℝ → ℝ     -- Vorticity supremum over time t
-  B : ℝ                 -- ADCCL active control upper bound
+/-- Carries an *assumed* bound `omega_sup t ≤ B` for `t ≥ 0`. `omega_sup` is an arbitrary
+function `ℝ → ℝ`: no supremum, vorticity field, PDE or time integral is defined. -/
+structure AssumedVorticityBoundState where
+  omega_sup : ℝ → ℝ     -- an arbitrary function (named for its intended reading)
+  B : ℝ                 -- the assumed bound
   h_B_pos : 0 < B       -- Positive bound
-  h_controlled : ∀ t ≥ 0, omega_sup t ≤ B  -- ADCCL vorticity bound
+  h_controlled : ∀ t ≥ 0, omega_sup t ≤ B  -- the assumption itself
 
-/-- **THEOREM (BKM Vorticity Integral Finiteness):**
-    Under ADCCL active control, the integrated vorticity over [0, T] is bounded by B * T. -/
-theorem bkm_vorticity_integral_finite (st : BKMVorticityState) (T : ℝ) (hT : 0 ≤ T) :
+/-- The product `omega_sup T * T` is at most `B * T`. A product, not a time integral. -/
+theorem pointwise_vorticity_product_bound (st : AssumedVorticityBoundState) (T : ℝ) (hT : 0 ≤ T) :
     st.omega_sup T * T ≤ st.B * T := by
   have h_bnd := st.h_controlled T hT
   nlinarith
 
-/-- **THEOREM (BKM Non-Blowup Criterion):**
-    For any finite time horizon T ≥ 0, the controlled vorticity integral cannot diverge. -/
-theorem bkm_no_blowup (st : BKMVorticityState) (T : ℝ) (hT : 0 ≤ T) (M : ℝ) (hM : st.B * T < M) :
+/-- If `B * T < M` then `omega_sup T * T < M`. Arithmetic, not a non-blowup criterion. -/
+theorem product_bound_below_threshold (st : AssumedVorticityBoundState) (T : ℝ) (hT : 0 ≤ T) (M : ℝ) (hM : st.B * T < M) :
     st.omega_sup T * T < M := by
   have h_bnd := st.h_controlled T hT
   have : st.omega_sup T * T ≤ st.B * T := by nlinarith
   linarith
 
-/-- **THEOREM (Sovereign Regularity Theorem):**
-    Any trajectory satisfying ADCCL vorticity control is globally regular and non-singular. -/
-theorem sovereign_regularity_theorem (st : BKMVorticityState) (T : ℝ) (hT : 0 ≤ T) :
+/-- Returns the assumed bound itself (`st.h_controlled T hT`). Not a regularity theorem, not a
+continuation statement; formerly named `sovereign_regularity_theorem`. -/
+theorem assumed_vorticity_bound_projection (st : AssumedVorticityBoundState) (T : ℝ) (hT : 0 ≤ T) :
     st.omega_sup T ≤ st.B := st.h_controlled T hT
 
 end SovereignRegularity

05_lean_formalization/VERIFICATION_RUN_2026-10-08_NAVIER_STOKES/gate_transcript.txt

@@ -0,0 +1,648 @@
+# Official gate witness, 2026-10-08T21:03:23-05:00
+branch: research/navier-stokes-remediation-2026-10-08  head: 931238158da81d3ffb9e80dd85f28ccf8d907e23  (plus uncommitted: NavierStokesTarget.lean pressure periodicity + full-slice L3a)
+lean-toolchain: leanprover/lean4:v4.33.0-rc1
+lean --version: Lean (version 4.33.0-rc1, x86_64-unknown-linux-gnu, commit 62eed1db4d67327ec8120be05f1a1b0847d74561, Release)
+mathlib rev (lake-manifest): 5eec30bc56ed5a23be2e27c544a949ba0bceddeb
+NavierStokesTarget.lean sha256: 1b1231fa268c72face60ace94d792c95e73a415958f8cbe776a3c2b114ba84d6
+
+$ lake exe cache get
+Current branch: HEAD
+Using cache from origin: (some leanprover-community/mathlib4)
+No files to download
+Already decompressed 8678 file(s)
+cache_get_exit=0 secs=15
+$ lake build
+⚠ [1942/2197] Replayed FiniteSU2Envelope
+warning: FiniteSU2Envelope.lean:64:10: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+warning: FiniteSU2Envelope.lean:67:10: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+warning: FiniteSU2Envelope.lean:70:19: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+warning: FiniteSU2Envelope.lean:70:43: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+⚠ [2221/2502] Replayed SU2MatrixEnvelope
+warning: SU2MatrixEnvelope.lean:74:6: This simp argument is unused:
+  qnorm
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [Matrix.conjTranspose, qMatrix, Matrix.mul_apply, Fin.sum_univ_two, Complex.ext_iff]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+ℹ [2301/2502] Replayed ChiralHolonomyOrientation
+info: ChiralHolonomyOrientation.lean:100:0: 'ChiralHolonomy.orientation_asymmetry_witness' does not depend on any axioms
+info: ChiralHolonomyOrientation.lean:101:0: 'ChiralHolonomy.involution_destroys_orientation' does not depend on any axioms
+info: ChiralHolonomyOrientation.lean:102:0: 'ChiralHolonomy.orientation_iff_not_involution' depends on axioms: [propext]
+info: ChiralHolonomyOrientation.lean:103:0: 'ChiralHolonomy.only_identity_is_orientation_blind' does not depend on any axioms
+ℹ [2302/2502] Replayed GenerationCycleChirality
+info: GenerationCycleChirality.lean:103:0: 'GenerationCycle.cycle_orientation_asymmetry' depends on axioms: [propext, Quot.sound]
+info: GenerationCycleChirality.lean:104:0: 'GenerationCycle.orientation_disagrees_everywhere' depends on axioms: [propext]
+info: GenerationCycleChirality.lean:105:0: 'GenerationCycle.sigma_squared_ne_id' depends on axioms: [propext, Quot.sound]
+info: GenerationCycleChirality.lean:106:0: 'GenerationCycle.three_cycle_chiral_two_cycle_not' depends on axioms: [propext]
+⚠ [3022/3131] Replayed DeSitterExtremal
+warning: DeSitterExtremal.lean:74:57: Variable name `hr` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hr
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3024/3131] Replayed GODActionKinematics
+info: GODActionKinematics.lean:49:0: 'GODTheory.dual_channel_poly_identity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GODActionKinematics.lean:50:0: 'GODTheory.aqual_simple_mu_ratio' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GODActionKinematics.lean:51:0: 'GODTheory.btfr_algebraic_scaling' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3159/3415] Replayed NavierStokesSpec
+warning: NavierStokesSpec.lean:33:63: Variable name `h` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _h
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+warning: NavierStokesSpec.lean:41:30: This simp argument is unused:
+  abs_of_pos (norm_pos_iff.mpr h)
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [direction, norm_smul, inv_mul_cancel₀ hx]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+⚠ [3257/3415] Replayed MuProjection
+warning: MuProjection.lean:87:52: Variable name `hb` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hb
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+⚠ [3288/3415] Replayed PrecessionBound
+warning: PrecessionBound.lean:66:54: Variable name `hr` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hr
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3293/3415] Replayed PrintAxiomsD8
+info: PrintAxiomsD8.lean:42:0: 'ResNova.TensorSpeed.c_T_sq_at_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:43:0: 'ResNova.TensorSpeed.maxwellian_c13_vanishes' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:44:0: 'ResNova.TensorSpeed.einstein_frame_tensor_speed_luminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:45:0: 'ResNova.TensorSpeed.conformal_preserves_tensor_speed' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:46:0: 'ResNova.TensorSpeed.physical_frame_tensor_speed_unity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:47:0: 'ResNova.TensorSpeed.gw170817_concordance' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3297/3415] Replayed SovereignSpinCeiling
+info: SovereignSpinCeiling.lean:125:0: 'SovereignSpinCeiling.two_theta_sub_theta_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SovereignSpinCeiling.lean:126:0: 'SovereignSpinCeiling.sovereign_spin_ceiling_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SovereignSpinCeiling.lean:127:0: 'SovereignSpinCeiling.sovereign_spin_ceiling_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SovereignSpinCeiling.lean:128:0: 'SovereignSpinCeiling.novikov_thorne_torque_apparent_spin_shift' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3298/3415] Replayed SkordisZlosnikEmbedding
+info: SkordisZlosnikEmbedding.lean:128:0: 'ResNova.SkordisZlosnik.sz_aqual_reduction' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:129:0: 'ResNova.SkordisZlosnik.dJ_dY_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:130:0: 'ResNova.SkordisZlosnik.sz_newtonian_limit_diff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:131:0: 'ResNova.SkordisZlosnik.sz_mond_limit_diff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:132:0: 'ResNova.SkordisZlosnik.sz_std_aqual_reduction' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:133:0: 'ResNova.SkordisZlosnik.dJ_dY_std_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:134:0: 'ResNova.SkordisZlosnik.sz_tensor_speed_luminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:135:0: 'ResNova.SkordisZlosnik.sz_weak_field_lensing' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3299/3415] Replayed SovereignRegularity
+warning: SovereignRegularity.lean:87:43: Variable name `hL` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hL
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+warning: SovereignRegularity.lean:102:22: Variable name `hθ_low` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hθ_low
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+warning: SovereignRegularity.lean:102:39: Variable name `hθ_high` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hθ_high
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3301/3415] Replayed TensorSpeed
+info: TensorSpeed.lean:124:0: 'ResNova.TensorSpeed.c_T_sq_at_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:125:0: 'ResNova.TensorSpeed.maxwellian_c13_vanishes' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:126:0: 'ResNova.TensorSpeed.einstein_frame_tensor_speed_luminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:127:0: 'ResNova.TensorSpeed.alpha_1_num_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:128:0: 'ResNova.TensorSpeed.alpha_1_den_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:129:0: 'ResNova.TensorSpeed.foster_jacobson_alpha_1_eval' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:130:0: 'ResNova.TensorSpeed.disformal_photon_speed_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:131:0: 'ResNova.TensorSpeed.speed_ratio_unity_iff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:132:0: 'ResNova.TensorSpeed.speed_ratio_lt_one_of_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:133:0: 'ResNova.TensorSpeed.gw170817_deviation_of_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3302/3415] Replayed TrialityG2
+warning: TrialityG2.lean:48:10: This simp argument is unused:
+  Matrix.one_apply
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [M, Matrix.mul_apply, Matrix.transpose_apply, Fin.sum_univ_four, Matrix.smul_apply]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+warning: TrialityG2.lean:56:50: This simp argument is unused:
+  Matrix.one_apply
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [M, Matrix.mul_apply, Fin.sum_univ_four, Matrix.smul_apply]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+warning: TrialityG2.lean:75:31: this tactic is never executed
+
+Note: This linter can be disabled with `set_option linter.unreachableTactic false`
+warning: TrialityG2.lean:75:31: 'norm_num' tactic does nothing
+
+Note: This linter can be disabled with `set_option linter.unusedTactic false`
+ℹ [3304/3415] Replayed RamanujanGapDerivation
+info: RamanujanGapDerivation.lean:94:0: 'ResNova.RamanujanGap.RamanujanSpectrum.gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RamanujanGapDerivation.lean:95:0: 'ResNova.RamanujanGap.RamanujanSpectrum.kappa_sq_le_gap' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RamanujanGapDerivation.lean:96:0: 'ResNova.RamanujanGap.petersen_gap' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3305/3415] Replayed LeptonMassCollar
+info: LeptonMassCollar.lean:217:0: 'ResNova.LeptonMassCollar.tau_ratio_three_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:218:0: 'ResNova.LeptonMassCollar.tauBaseScale_eq_six_sqrt_seven' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:219:0: 'ResNova.LeptonMassCollar.tau_mu_mass_ratio_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:220:0: 'ResNova.LeptonMassCollar.model_discrepancy_bound' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:221:0: 'ResNova.LeptonMassCollar.muon_mass_model_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:222:0: 'ResNova.LeptonMassCollar.tau_mass_model_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:223:0: 'ResNova.LeptonMassCollar.universal_lepton_collar_bound' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:224:0: 'ResNova.LeptonMassCollar.muon_mass_interval_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:225:0: 'ResNova.LeptonMassCollar.tau_mass_interval_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:226:0: 'ResNova.LeptonMassCollar.second_order_generational_consistency' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3306/3415] Replayed NavierStokesCorticalBound
+info: NavierStokesCorticalBound.lean:104:0: 'ResNova.NavierStokesCorticalBound.re_critical_mul_theta_geom' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+info: NavierStokesCorticalBound.lean:105:0: 'ResNova.NavierStokesCorticalBound.two_channel_at_theta_geom' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: NavierStokesCorticalBound.lean:106:0: 'ResNova.NavierStokesCorticalBound.reCritical_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: NavierStokesCorticalBound.lean:107:0: 'ResNova.NavierStokesCorticalBound.enstrophy_rate_nonpos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: NavierStokesCorticalBound.lean:108:0: 'ResNova.NavierStokesCorticalBound.vortex_stretching_planar_vanishes' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3307/3415] Replayed YangMillsCasimirBound
+info: YangMillsCasimirBound.lean:142:0: 'ResNova.YangMillsCasimirBound.ym_casimir_gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:143:0: 'ResNova.YangMillsCasimirBound.ym_gap_ratio_su3_su2' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:144:0: 'ResNova.YangMillsCasimirBound.scale_factor_at_theta_geom' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:145:0: 'ResNova.YangMillsCasimirBound.ym_su3_gap_exact' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:146:0: 'ResNova.YangMillsCasimirBound.ym_su3_gap_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3308/3415] Replayed RiemannSpectralExpander
+info: RiemannSpectralExpander.lean:124:0: 'ResNova.RiemannSpectralExpander.expander_gap_eq_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:125:0: 'ResNova.RiemannSpectralExpander.expander_gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:126:0: 'ResNova.RiemannSpectralExpander.expander_gap_three_exact' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:127:0: 'ResNova.RiemannSpectralExpander.expander_gap_three_enclosure' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+info: RiemannSpectralExpander.lean:128:0: 'ResNova.RiemannSpectralExpander.expander_gap_le_degree' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:129:0: 'ResNova.RiemannSpectralExpander.normalized_expander_gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3387/3415] Replayed MuStdUniqueness
+info: MuStdUniqueness.lean:472:0: 'ResNova.MuStdUniqueness.theorem_A_constitutive' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:473:0: 'ResNova.MuStdUniqueness.theorem_A_conjugacy' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:474:0: 'ResNova.MuStdUniqueness.theorem_A_postulate_R_ode' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:475:0: 'ResNova.MuStdUniqueness.theorem_A_celerity_forced' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:476:0: 'ResNova.MuStdUniqueness.theorem_A_uniqueness' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:477:0: 'ResNova.MuStdUniqueness.mu_fam_hasDerivAt_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:478:0: 'ResNova.MuStdUniqueness.mu_fam_normalization' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:479:0: 'ResNova.MuStdUniqueness.theorem_B_fisher_identity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:480:0: 'ResNova.MuStdUniqueness.theorem_B_uniqueness' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:481:0: 'ResNova.MuStdUniqueness.theorem_C_exponent_family' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:482:0: 'ResNova.MuStdUniqueness.theorem_C_selects_n_one' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:483:0: 'ResNova.MuStdUniqueness.theorem_C_rejects_n_ge_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:484:0: 'ResNova.MuStdUniqueness.F_std_deriv2_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:485:0: 'ResNova.MuStdUniqueness.F_std_strictConvexOn' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3388/3415] Replayed MuStdDuality
+info: MuStdDuality.lean:173:0: 'ResNova.MuStdDuality.sqrt_inv_arg_mul' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:174:0: 'ResNova.MuStdDuality.mu_std_inv' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:175:0: 'ResNova.MuStdDuality.theorem_livedual' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:176:0: 'ResNova.MuStdDuality.mu_std_inv_eq_inv_cosh_arsinh' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:177:0: 'ResNova.MuStdDuality.livedual_is_lorentz' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:178:0: 'ResNova.MuStdDuality.mu_std_fixed_point' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:179:0: 'ResNova.MuStdDuality.odds_one_sub' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:180:0: 'ResNova.MuStdDuality.mu_dual_inv' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3391/3415] Replayed GateHolonomySusceptibility
+info: GateHolonomySusceptibility.lean:145:0: 'ResNova.GateHolonomy.kappa_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:146:0: 'ResNova.GateHolonomy.pythagorean' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:147:0: 'ResNova.GateHolonomy.gate_mem' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:148:0: 'ResNova.GateHolonomy.kappa_gate_eq_sin' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:149:0: 'ResNova.GateHolonomy.susceptibility_eq_kappa' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:150:0: 'ResNova.GateHolonomy.deriv_gate' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:151:0: 'ResNova.GateHolonomy.kappa_unique' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:152:0: 'ResNova.GateHolonomy.height_eq_cos' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3393/3415] Replayed MuStdFoundations
+info: MuStdFoundations.lean:144:0: 'ResNova.MuStdFoundations.F_std_deriv_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:145:0: 'ResNova.MuStdFoundations.F_std_deriv2_positivity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:146:0: 'ResNova.MuStdFoundations.F_std_strict_convexity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:147:0: 'ResNova.MuStdFoundations.c_long_sq_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:148:0: 'ResNova.MuStdFoundations.c_long_sq_superluminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:149:0: 'ResNova.MuStdFoundations.c_long_sq_le_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:150:0: 'ResNova.MuStdFoundations.deviation_le_inv_two_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:151:0: 'ResNova.MuStdFoundations.saturn_monopole_deviation_le' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3395/3415] Replayed PillarIV_AntiDriftGate
+info: PillarIV_AntiDriftGate.lean:86:0: @le_div_iff₀ : ∀ {G₀ : Type u_1} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [MulPosReflectLT G₀] {a b c : G₀},
+  0 < c → (a ≤ b / c ↔ a * c ≤ b)
+info: PillarIV_AntiDriftGate.lean:87:0: @div_le_iff₀ : ∀ {G₀ : Type u_1} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [MulPosReflectLT G₀] {a b c : G₀},
+  0 < c → (b / c ≤ a ↔ b ≤ a * c)
+info: PillarIV_AntiDriftGate.lean:88:0: @one_le_div : ∀ {α : Type u_1} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α},
+  0 < b → (1 ≤ a / b ↔ b ≤ a)
+info: PillarIV_AntiDriftGate.lean:416:0: 'PillarIV.mu_eq_tanh_arsinh' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:417:0: 'PillarIV.mu_one' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:418:0: 'PillarIV.mu_ge_chiFloor_iff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:419:0: 'PillarIV.antiDrift_gate' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:420:0: 'PillarIV.gksl_steady_state_exists' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:421:0: 'PillarIV.steady_state_is_fixed_point' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:573:0: 'PillarIV.kappaBand_at_chiral_floor' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:574:0: 'PillarIV.trace_steady_state' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:575:0: 'PillarIV.bloch_coherence_le_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:576:0: 'PillarIV.bloch_coherence_eq_theta_iff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:577:0: 'PillarIV.steady_state_coherence_im_eq_bloch' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:578:0: 'PillarIV.coherence_pinned_by_floor_and_ceiling' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:579:0: 'PillarIV.saturating_ratio_eq_half_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:580:0: 'PillarIV.twoChannel_gate' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:581:0: 'PillarIV.kappaBand_sq_add_complement_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:582:0: 'PillarIV.theta_le_kappaBand' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:583:0: 'PillarIV.kappaBand_at_seven_tenths' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3396/3415] Replayed PrintAxioms
+info: PrintAxioms.lean:17:0: 'ResNova.CovariantCompletion.raqual_superluminal_obstruction' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:18:0: 'ResNova.CovariantCompletion.foliation_anchoring_identity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:19:0: 'ResNova.CovariantCompletion.disformal_gamma_ppn_unity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:20:0: 'ResNova.CovariantCompletion.preferred_frame_parameters_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:21:0: 'ResNova.CovariantCompletion.flrw_projected_gradient_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:22:0: 'ResNova.CovariantCompletion.no_dynamical_dark_energy_density' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3397/3415] Replayed RapidityEquipartition
+info: RapidityEquipartition.lean:54:0: 'RapidityEquipartition.arsinh_one_eq_log_one_add_sqrt_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RapidityEquipartition.lean:55:0: 'RapidityEquipartition.tanh_arsinh_one_eq_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RapidityEquipartition.lean:56:0: 'RapidityEquipartition.arsinh_one_eq_artanh_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RapidityEquipartition.lean:57:0: 'RapidityEquipartition.theta_odds_eq_silver_ratio' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3399/3415] Replayed QuarkMassLadder
+info: QuarkMassLadder.lean:141:0: 'ResNova.QuarkMassLadder.color_casimir_positive' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:142:0: 'ResNova.QuarkMassLadder.u_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:143:0: 'ResNova.QuarkMassLadder.d_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:144:0: 'ResNova.QuarkMassLadder.s_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:145:0: 'ResNova.QuarkMassLadder.c_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:146:0: 'ResNova.QuarkMassLadder.b_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:147:0: 'ResNova.QuarkMassLadder.t_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:148:0: 'ResNova.QuarkMassLadder.top_to_up_hierarchy' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:149:0: 'ResNova.QuarkMassLadder.light_quark_isospin_ratio' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:150:0: 'ResNova.QuarkMassLadder.universal_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+Build completed successfully (3415 jobs).
+lake_build_exit=0 secs=2
+$ bash verify_all_proofs.sh
+[gate] TARGETS == lakefile roots (67 modules)
+building library (required for cross-module imports)…
+⚠ [1942/2226] Replayed FiniteSU2Envelope
+warning: FiniteSU2Envelope.lean:64:10: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+warning: FiniteSU2Envelope.lean:67:10: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+warning: FiniteSU2Envelope.lean:70:19: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+warning: FiniteSU2Envelope.lean:70:43: Used `tac1 <;> tac2` where `(tac1; tac2)` would suffice
+
+Note: This linter can be disabled with `set_option linter.unnecessarySeqFocus false`
+⚠ [2221/2226] Replayed SU2MatrixEnvelope
+warning: SU2MatrixEnvelope.lean:74:6: This simp argument is unused:
+  qnorm
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [Matrix.conjTranspose, qMatrix, Matrix.mul_apply, Fin.sum_univ_two, Complex.ext_iff]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+ℹ [2301/2539] Replayed ChiralHolonomyOrientation
+info: ChiralHolonomyOrientation.lean:100:0: 'ChiralHolonomy.orientation_asymmetry_witness' does not depend on any axioms
+info: ChiralHolonomyOrientation.lean:101:0: 'ChiralHolonomy.involution_destroys_orientation' does not depend on any axioms
+info: ChiralHolonomyOrientation.lean:102:0: 'ChiralHolonomy.orientation_iff_not_involution' depends on axioms: [propext]
+info: ChiralHolonomyOrientation.lean:103:0: 'ChiralHolonomy.only_identity_is_orientation_blind' does not depend on any axioms
+ℹ [2302/2539] Replayed GenerationCycleChirality
+info: GenerationCycleChirality.lean:103:0: 'GenerationCycle.cycle_orientation_asymmetry' depends on axioms: [propext, Quot.sound]
+info: GenerationCycleChirality.lean:104:0: 'GenerationCycle.orientation_disagrees_everywhere' depends on axioms: [propext]
+info: GenerationCycleChirality.lean:105:0: 'GenerationCycle.sigma_squared_ne_id' depends on axioms: [propext, Quot.sound]
+info: GenerationCycleChirality.lean:106:0: 'GenerationCycle.three_cycle_chiral_two_cycle_not' depends on axioms: [propext]
+⚠ [3022/3123] Replayed DeSitterExtremal
+warning: DeSitterExtremal.lean:74:57: Variable name `hr` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hr
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3024/3123] Replayed GODActionKinematics
+info: GODActionKinematics.lean:49:0: 'GODTheory.dual_channel_poly_identity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GODActionKinematics.lean:50:0: 'GODTheory.aqual_simple_mu_ratio' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GODActionKinematics.lean:51:0: 'GODTheory.btfr_algebraic_scaling' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3159/3415] Replayed NavierStokesSpec
+warning: NavierStokesSpec.lean:33:63: Variable name `h` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _h
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+warning: NavierStokesSpec.lean:41:30: This simp argument is unused:
+  abs_of_pos (norm_pos_iff.mpr h)
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [direction, norm_smul, inv_mul_cancel₀ hx]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+⚠ [3341/3415] Replayed MuProjection
+warning: MuProjection.lean:87:52: Variable name `hb` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hb
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3377/3415] Replayed MuStdUniqueness
+info: MuStdUniqueness.lean:472:0: 'ResNova.MuStdUniqueness.theorem_A_constitutive' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:473:0: 'ResNova.MuStdUniqueness.theorem_A_conjugacy' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:474:0: 'ResNova.MuStdUniqueness.theorem_A_postulate_R_ode' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:475:0: 'ResNova.MuStdUniqueness.theorem_A_celerity_forced' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:476:0: 'ResNova.MuStdUniqueness.theorem_A_uniqueness' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:477:0: 'ResNova.MuStdUniqueness.mu_fam_hasDerivAt_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:478:0: 'ResNova.MuStdUniqueness.mu_fam_normalization' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:479:0: 'ResNova.MuStdUniqueness.theorem_B_fisher_identity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:480:0: 'ResNova.MuStdUniqueness.theorem_B_uniqueness' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:481:0: 'ResNova.MuStdUniqueness.theorem_C_exponent_family' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:482:0: 'ResNova.MuStdUniqueness.theorem_C_selects_n_one' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:483:0: 'ResNova.MuStdUniqueness.theorem_C_rejects_n_ge_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:484:0: 'ResNova.MuStdUniqueness.F_std_deriv2_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdUniqueness.lean:485:0: 'ResNova.MuStdUniqueness.F_std_strictConvexOn' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3378/3415] Replayed MuStdDuality
+info: MuStdDuality.lean:173:0: 'ResNova.MuStdDuality.sqrt_inv_arg_mul' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:174:0: 'ResNova.MuStdDuality.mu_std_inv' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:175:0: 'ResNova.MuStdDuality.theorem_livedual' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:176:0: 'ResNova.MuStdDuality.mu_std_inv_eq_inv_cosh_arsinh' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:177:0: 'ResNova.MuStdDuality.livedual_is_lorentz' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:178:0: 'ResNova.MuStdDuality.mu_std_fixed_point' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:179:0: 'ResNova.MuStdDuality.odds_one_sub' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdDuality.lean:180:0: 'ResNova.MuStdDuality.mu_dual_inv' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3382/3415] Replayed GateHolonomySusceptibility
+info: GateHolonomySusceptibility.lean:145:0: 'ResNova.GateHolonomy.kappa_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:146:0: 'ResNova.GateHolonomy.pythagorean' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:147:0: 'ResNova.GateHolonomy.gate_mem' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:148:0: 'ResNova.GateHolonomy.kappa_gate_eq_sin' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:149:0: 'ResNova.GateHolonomy.susceptibility_eq_kappa' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:150:0: 'ResNova.GateHolonomy.deriv_gate' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:151:0: 'ResNova.GateHolonomy.kappa_unique' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: GateHolonomySusceptibility.lean:152:0: 'ResNova.GateHolonomy.height_eq_cos' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3384/3415] Replayed MuStdFoundations
+info: MuStdFoundations.lean:144:0: 'ResNova.MuStdFoundations.F_std_deriv_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:145:0: 'ResNova.MuStdFoundations.F_std_deriv2_positivity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:146:0: 'ResNova.MuStdFoundations.F_std_strict_convexity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:147:0: 'ResNova.MuStdFoundations.c_long_sq_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:148:0: 'ResNova.MuStdFoundations.c_long_sq_superluminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:149:0: 'ResNova.MuStdFoundations.c_long_sq_le_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:150:0: 'ResNova.MuStdFoundations.deviation_le_inv_two_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: MuStdFoundations.lean:151:0: 'ResNova.MuStdFoundations.saturn_monopole_deviation_le' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3388/3415] Replayed PrecessionBound
+warning: PrecessionBound.lean:66:54: Variable name `hr` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hr
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3392/3415] Replayed PillarIV_AntiDriftGate
+info: PillarIV_AntiDriftGate.lean:86:0: @le_div_iff₀ : ∀ {G₀ : Type u_1} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [MulPosReflectLT G₀] {a b c : G₀},
+  0 < c → (a ≤ b / c ↔ a * c ≤ b)
+info: PillarIV_AntiDriftGate.lean:87:0: @div_le_iff₀ : ∀ {G₀ : Type u_1} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [MulPosReflectLT G₀] {a b c : G₀},
+  0 < c → (b / c ≤ a ↔ b ≤ a * c)
+info: PillarIV_AntiDriftGate.lean:88:0: @one_le_div : ∀ {α : Type u_1} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a b : α},
+  0 < b → (1 ≤ a / b ↔ b ≤ a)
+info: PillarIV_AntiDriftGate.lean:416:0: 'PillarIV.mu_eq_tanh_arsinh' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:417:0: 'PillarIV.mu_one' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:418:0: 'PillarIV.mu_ge_chiFloor_iff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:419:0: 'PillarIV.antiDrift_gate' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:420:0: 'PillarIV.gksl_steady_state_exists' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:421:0: 'PillarIV.steady_state_is_fixed_point' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:573:0: 'PillarIV.kappaBand_at_chiral_floor' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:574:0: 'PillarIV.trace_steady_state' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:575:0: 'PillarIV.bloch_coherence_le_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:576:0: 'PillarIV.bloch_coherence_eq_theta_iff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:577:0: 'PillarIV.steady_state_coherence_im_eq_bloch' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:578:0: 'PillarIV.coherence_pinned_by_floor_and_ceiling' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:579:0: 'PillarIV.saturating_ratio_eq_half_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:580:0: 'PillarIV.twoChannel_gate' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:581:0: 'PillarIV.kappaBand_sq_add_complement_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:582:0: 'PillarIV.theta_le_kappaBand' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PillarIV_AntiDriftGate.lean:583:0: 'PillarIV.kappaBand_at_seven_tenths' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3394/3415] Replayed PrintAxioms
+info: PrintAxioms.lean:17:0: 'ResNova.CovariantCompletion.raqual_superluminal_obstruction' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:18:0: 'ResNova.CovariantCompletion.foliation_anchoring_identity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:19:0: 'ResNova.CovariantCompletion.disformal_gamma_ppn_unity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:20:0: 'ResNova.CovariantCompletion.preferred_frame_parameters_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:21:0: 'ResNova.CovariantCompletion.flrw_projected_gradient_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxioms.lean:22:0: 'ResNova.CovariantCompletion.no_dynamical_dark_energy_density' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3395/3415] Replayed PrintAxiomsD8
+info: PrintAxiomsD8.lean:42:0: 'ResNova.TensorSpeed.c_T_sq_at_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:43:0: 'ResNova.TensorSpeed.maxwellian_c13_vanishes' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:44:0: 'ResNova.TensorSpeed.einstein_frame_tensor_speed_luminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:45:0: 'ResNova.TensorSpeed.conformal_preserves_tensor_speed' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:46:0: 'ResNova.TensorSpeed.physical_frame_tensor_speed_unity' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: PrintAxiomsD8.lean:47:0: 'ResNova.TensorSpeed.gw170817_concordance' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3398/3415] Replayed RapidityEquipartition
+info: RapidityEquipartition.lean:54:0: 'RapidityEquipartition.arsinh_one_eq_log_one_add_sqrt_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RapidityEquipartition.lean:55:0: 'RapidityEquipartition.tanh_arsinh_one_eq_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RapidityEquipartition.lean:56:0: 'RapidityEquipartition.arsinh_one_eq_artanh_theta' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RapidityEquipartition.lean:57:0: 'RapidityEquipartition.theta_odds_eq_silver_ratio' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3400/3415] Replayed SovereignSpinCeiling
+info: SovereignSpinCeiling.lean:125:0: 'SovereignSpinCeiling.two_theta_sub_theta_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SovereignSpinCeiling.lean:126:0: 'SovereignSpinCeiling.sovereign_spin_ceiling_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SovereignSpinCeiling.lean:127:0: 'SovereignSpinCeiling.sovereign_spin_ceiling_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SovereignSpinCeiling.lean:128:0: 'SovereignSpinCeiling.novikov_thorne_torque_apparent_spin_shift' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3401/3415] Replayed SkordisZlosnikEmbedding
+info: SkordisZlosnikEmbedding.lean:128:0: 'ResNova.SkordisZlosnik.sz_aqual_reduction' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:129:0: 'ResNova.SkordisZlosnik.dJ_dY_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:130:0: 'ResNova.SkordisZlosnik.sz_newtonian_limit_diff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:131:0: 'ResNova.SkordisZlosnik.sz_mond_limit_diff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:132:0: 'ResNova.SkordisZlosnik.sz_std_aqual_reduction' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:133:0: 'ResNova.SkordisZlosnik.dJ_dY_std_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:134:0: 'ResNova.SkordisZlosnik.sz_tensor_speed_luminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: SkordisZlosnikEmbedding.lean:135:0: 'ResNova.SkordisZlosnik.sz_weak_field_lensing' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3402/3415] Replayed SovereignRegularity
+warning: SovereignRegularity.lean:87:43: Variable name `hL` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hL
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+warning: SovereignRegularity.lean:102:22: Variable name `hθ_low` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hθ_low
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+warning: SovereignRegularity.lean:102:39: Variable name `hθ_high` is not explicitly referenced.
+
+Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:
+  [apply] _hθ_high
+
+Note: This linter can be disabled with `set_option linter.unusedVariables false`
+ℹ [3404/3415] Replayed TensorSpeed
+info: TensorSpeed.lean:124:0: 'ResNova.TensorSpeed.c_T_sq_at_zero' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:125:0: 'ResNova.TensorSpeed.maxwellian_c13_vanishes' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:126:0: 'ResNova.TensorSpeed.einstein_frame_tensor_speed_luminal' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:127:0: 'ResNova.TensorSpeed.alpha_1_num_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:128:0: 'ResNova.TensorSpeed.alpha_1_den_eq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:129:0: 'ResNova.TensorSpeed.foster_jacobson_alpha_1_eval' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:130:0: 'ResNova.TensorSpeed.disformal_photon_speed_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:131:0: 'ResNova.TensorSpeed.speed_ratio_unity_iff' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:132:0: 'ResNova.TensorSpeed.speed_ratio_lt_one_of_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: TensorSpeed.lean:133:0: 'ResNova.TensorSpeed.gw170817_deviation_of_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+⚠ [3405/3415] Replayed TrialityG2
+warning: TrialityG2.lean:48:10: This simp argument is unused:
+  Matrix.one_apply
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [M, Matrix.mul_apply, Matrix.transpose_apply, Fin.sum_univ_four, Matrix.smul_apply]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+warning: TrialityG2.lean:56:50: This simp argument is unused:
+  Matrix.one_apply
+
+Hint: Omit it from the simp argument list.
+  [apply] simp [M, Matrix.mul_apply, Fin.sum_univ_four, Matrix.smul_apply]
+
+Note: This linter can be disabled with `set_option linter.unusedSimpArgs false`
+warning: TrialityG2.lean:75:31: this tactic is never executed
+
+Note: This linter can be disabled with `set_option linter.unreachableTactic false`
+warning: TrialityG2.lean:75:31: 'norm_num' tactic does nothing
+
+Note: This linter can be disabled with `set_option linter.unusedTactic false`
+ℹ [3408/3415] Replayed RamanujanGapDerivation
+info: RamanujanGapDerivation.lean:94:0: 'ResNova.RamanujanGap.RamanujanSpectrum.gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RamanujanGapDerivation.lean:95:0: 'ResNova.RamanujanGap.RamanujanSpectrum.kappa_sq_le_gap' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RamanujanGapDerivation.lean:96:0: 'ResNova.RamanujanGap.petersen_gap' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3409/3415] Replayed LeptonMassCollar
+info: LeptonMassCollar.lean:217:0: 'ResNova.LeptonMassCollar.tau_ratio_three_two' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:218:0: 'ResNova.LeptonMassCollar.tauBaseScale_eq_six_sqrt_seven' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:219:0: 'ResNova.LeptonMassCollar.tau_mu_mass_ratio_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:220:0: 'ResNova.LeptonMassCollar.model_discrepancy_bound' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:221:0: 'ResNova.LeptonMassCollar.muon_mass_model_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:222:0: 'ResNova.LeptonMassCollar.tau_mass_model_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:223:0: 'ResNova.LeptonMassCollar.universal_lepton_collar_bound' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:224:0: 'ResNova.LeptonMassCollar.muon_mass_interval_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:225:0: 'ResNova.LeptonMassCollar.tau_mass_interval_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: LeptonMassCollar.lean:226:0: 'ResNova.LeptonMassCollar.second_order_generational_consistency' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3410/3415] Replayed NavierStokesCorticalBound
+info: NavierStokesCorticalBound.lean:104:0: 'ResNova.NavierStokesCorticalBound.re_critical_mul_theta_geom' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+info: NavierStokesCorticalBound.lean:105:0: 'ResNova.NavierStokesCorticalBound.two_channel_at_theta_geom' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: NavierStokesCorticalBound.lean:106:0: 'ResNova.NavierStokesCorticalBound.reCritical_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: NavierStokesCorticalBound.lean:107:0: 'ResNova.NavierStokesCorticalBound.enstrophy_rate_nonpos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: NavierStokesCorticalBound.lean:108:0: 'ResNova.NavierStokesCorticalBound.vortex_stretching_planar_vanishes' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+ℹ [3411/3415] Replayed YangMillsCasimirBound
+info: YangMillsCasimirBound.lean:142:0: 'ResNova.YangMillsCasimirBound.ym_casimir_gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:143:0: 'ResNova.YangMillsCasimirBound.ym_gap_ratio_su3_su2' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:144:0: 'ResNova.YangMillsCasimirBound.scale_factor_at_theta_geom' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:145:0: 'ResNova.YangMillsCasimirBound.ym_su3_gap_exact' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: YangMillsCasimirBound.lean:146:0: 'ResNova.YangMillsCasimirBound.ym_su3_gap_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3412/3415] Replayed RiemannSpectralExpander
+info: RiemannSpectralExpander.lean:124:0: 'ResNova.RiemannSpectralExpander.expander_gap_eq_sq' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:125:0: 'ResNova.RiemannSpectralExpander.expander_gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:126:0: 'ResNova.RiemannSpectralExpander.expander_gap_three_exact' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:127:0: 'ResNova.RiemannSpectralExpander.expander_gap_three_enclosure' depends on axioms: [propext,
+ Classical.choice,
+ Quot.sound]
+info: RiemannSpectralExpander.lean:128:0: 'ResNova.RiemannSpectralExpander.expander_gap_le_degree' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: RiemannSpectralExpander.lean:129:0: 'ResNova.RiemannSpectralExpander.normalized_expander_gap_pos' depends on axioms: [propext, Classical.choice, Quot.sound]
+ℹ [3414/3415] Replayed QuarkMassLadder
+info: QuarkMassLadder.lean:141:0: 'ResNova.QuarkMassLadder.color_casimir_positive' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:142:0: 'ResNova.QuarkMassLadder.u_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:143:0: 'ResNova.QuarkMassLadder.d_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:144:0: 'ResNova.QuarkMassLadder.s_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:145:0: 'ResNova.QuarkMassLadder.c_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:146:0: 'ResNova.QuarkMassLadder.b_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:147:0: 'ResNova.QuarkMassLadder.t_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:148:0: 'ResNova.QuarkMassLadder.top_to_up_hierarchy' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:149:0: 'ResNova.QuarkMassLadder.light_quark_isospin_ratio' depends on axioms: [propext, Classical.choice, Quot.sound]
+info: QuarkMassLadder.lean:150:0: 'ResNova.QuarkMassLadder.universal_quark_mass_enclosure' depends on axioms: [propext, Classical.choice, Quot.sound]
+Build completed successfully (3415 jobs).
+OK    BinaryTetrahedral.lean
+OK    TetrahedralQuotient.lean
+OK    TetrahedralAction.lean
+OK    TetrahedralEvenness.lean
+OK    FiniteSU2Envelope.lean
+OK    SU2MatrixEnvelope.lean
+OK    SU2CarrierRungs.lean
+OK    SU2FiniteFaithfulness.lean
+OK    PillarII_SecularRootQEC.lean
+OK    AXIOMS_V2.lean
+OK    CartanTrialityGenerations.lean
+OK    ChiralCellularDuality.lean
+OK    ChiralCrackSketch.lean
+OK    ChiralResidue.lean
+OK    ChiralPartner.lean
+OK    ChiralHolonomyOrientation.lean
+OK    GenerationCycleChirality.lean
+OK    CosmologicalSector.lean
+OK    CovariantCompletion.lean
+OK    DeSitterExtremal.lean
+OK    DualChannelDerivation.lean
+OK    GODActionKinematics.lean
+OK    NavierStokesGeometry.lean
+OK    NavierStokesScope.lean
+OK    NavierStokesSpec.lean
+OK    NavierStokesTarget.lean
+OK    GenerationIndex.lean
+OK    DiagonalConeIndex.lean
+OK    Hamilgrangian.lean
+OK    HorizonScale.lean
+OK    ITActionClosure.lean
+OK    MuProjection.lean
+OK    MuStdUniqueness.lean
+OK    MuStdDuality.lean
+OK    MuNDuality.lean
+OK    SZStdEmbedding.lean
+OK    GateHolonomySusceptibility.lean
+OK    MuStdSelection.lean
+OK    MuStdFoundations.lean
+OK    AeSTStealthSector.lean
+OK    PPNLimitsStd.lean
+OK    LambdaSBound.lean
+OK    PrecessionBound.lean
+OK    CoshCosmology.lean
+OK    PPNLimits.lean
+OK    PillarIV_AntiDriftGate.lean
+OK    PrintAxioms.lean
+OK    PrintAxiomsD8.lean
+OK    RamanujanGapDerivation.lean
+OK    RamanujanModularBounds.lean
+OK    RelativisticStability.lean
+OK    RapidityEquipartition.lean
+OK    SOCasimirGenuine.lean
+OK    SovereignSpinCeiling.lean
+OK    SkordisZlosnikEmbedding.lean
+OK    SovereignRegularity.lean
+OK    SovereignSemiotics.lean
+OK    TensorSpeed.lean
+OK    TrialityFixedSubalgebra.lean
+OK    TrialityG2.lean
+OK    YettParadigm.lean
+OK    LeptonMassCollar.lean
+OK    NavierStokesCorticalBound.lean
+OK    YangMillsCasimirBound.lean
+OK    RiemannSpectralExpander.lean
+OK    StiefelLaplaceEigenvalue.lean
+OK    QuarkMassLadder.lean
+
+verified: 67 / 67 target(s)
+RESULT: PASS
+NOTE: this certifies elaboration, absence of sorry, and a standard axiom
+      footprint. It does not certify that assumptions carried as typeclass
+      or structure fields are physically justified — see THEORY_ASSUMPTION_AUDIT.md.
+gate_exit=0 secs=336

05_lean_formalization/lakefile.lean

@@ -52,6 +52,9 @@ lean_lib «ResNovaFormal» where
     `NavierStokesGeometry,
     `NavierStokesScope,
     `NavierStokesSpec,
+    -- ADDED 2026-10-08. The periodic target (Fefferman's statement B) as a Prop, the
+    -- alignment obligation over genuine solutions, and four sanity theorems. No proof of B.
+    `NavierStokesTarget,
     -- AUDITED VACUOUS 2026-08-29 (D47_generation_index_audit.md). Compiles and is
     -- sorry-free, which is why it is gated -- but `z3NetChirality` returns 3/-3/0
     -- because those literals are written into its if-then-else, and the theorem

05_lean_formalization/verify_all_proofs.sh

@@ -58,6 +58,7 @@ TARGETS=(
   NavierStokesGeometry.lean
   NavierStokesScope.lean
   NavierStokesSpec.lean
+  NavierStokesTarget.lean
   GenerationIndex.lean
   DiagonalConeIndex.lean
   Hamilgrangian.lean