diff --git a/formal/SilverSight/PIST/UnifiedCovariant.lean b/formal/SilverSight/PIST/UnifiedCovariant.lean index 3d61caad..4d32df65 100644 --- a/formal/SilverSight/PIST/UnifiedCovariant.lean +++ b/formal/SilverSight/PIST/UnifiedCovariant.lean @@ -65,7 +65,6 @@ import Mathlib.Data.Real.Basic import Mathlib.Data.Nat.Fib.Basic import Mathlib.Data.Matrix.Basic -import Mathlib.LinearAlgebra.Matrix.Adjoints import Mathlib.Tactic import SilverSight.PIST.CartanConnection @@ -319,35 +318,29 @@ theorem cp_FS_Kaehler (n : ℕ) : is_Kaehler (Fin (n+1) → ℂ) := by A Cartan connection is a principal bundle connection infinitesimally modeled on a homogeneous space G/P. - HONESTY CLASS: OPAQUE (predicate signature — NOT True, NOT axiom) - BLOCKED ON: Mathlib Cartan geometry API - This is a named Prop with mathematical content (existence of a - connection with specific structure group properties). It is - deliberately NOT `True` — that would make the companion conjecture - vacuously proven via `trivial`, the exact smuggle pattern the - anti-smuggle scanner catches. The companion theorem carries a - CONJECTURE sorry. -/ -def admits_Cartan_connection (M : Type) : Prop := - -- When Cartan geometry API lands, replace with: - -- ∃ (G H : Type) [LieGroup G] [ClosedSubgroup H G], - -- Nonempty (CartanConnection M G H) - -- For now: an opaque Prop that is neither True nor provable. - -- It references a hypothetical structure, making it impossible to - -- close with `trivial` or `rfl`. - Nonempty (M → M) -- placeholder: real content needs Cartan API + HONESTY CLASS: OPAQUE (axiom predicate signature — asserts nothing). + BLOCKED ON: Mathlib Cartan geometry API. + Declared as an opaque `axiom` predicate, NOT a `def`. Every concrete + `def` body writable today (e.g. `Nonempty (M → M)`) is *trivially + inhabited* — closable by `⟨id⟩` — which would let the companion + conjecture be discharged vacuously, a silent smuggle the scanner + cannot see (it is not literally `:= True`). An opaque axiom symbol + carries no content, so the ONLY proof of the companion conjecture is + its CONJECTURE `sorry`. When Mathlib ships Cartan geometry, replace + with `∃ (G H : Type) [LieGroup G] [ClosedSubgroup H G], + Nonempty (CartanConnection M G H)`. -/ +axiom admits_Cartan_connection (M : Type) : Prop /-- OPAQUE: M has holonomy contained in SO⁰(1,6). The pseudo-orthogonal group SO⁰(1,6) preserves a quadratic form of signature (1,6). - HONESTY CLASS: OPAQUE (predicate signature — NOT True, NOT axiom) - BLOCKED ON: Mathlib holonomy + indefinite orthogonal group API - Same treatment as admits_Cartan_connection. NOT True. -/ -def has_SO_1_6_holonomy (M : Type) : Prop := - -- When holonomy API lands, replace with: - -- HolonomyGroup M ⊆ SO(1,6) - -- For now: an opaque Prop referencing M's structure. - Nonempty (M → M) -- placeholder: real content needs holonomy API + HONESTY CLASS: OPAQUE (axiom predicate signature — asserts nothing). + BLOCKED ON: Mathlib holonomy + indefinite orthogonal group API. + Same treatment as `admits_Cartan_connection`: an opaque axiom, not a + secretly-inhabited `def`. Replace with `HolonomyGroup M ⊆ SO(1,6)` + when the API lands. -/ +axiom has_SO_1_6_holonomy (M : Type) : Prop -- ============================================================ -- §6 THE GEOMETRIC CONJECTURES (honestly labeled) @@ -398,9 +391,15 @@ theorem holonomy_is_SO_1_6 : has_SO_1_6_holonomy openSimplex7 := by -- ============================================================ -- §7 AXIOM INVENTORY (anti-smuggle witness) -- ============================================================ --- After the Tier 1 conversion, the custom axiom set should be EMPTY. --- All former axioms are now either: --- - def (is_Kaehler, admits_Cartan_connection, has_SO_1_6_holonomy) +-- Custom axiom set after the Tier-1 conversion: +-- - is_Kaehler → def (Nonempty (KählerManifold V), real content) +-- - admits_Cartan_connection → OPAQUE axiom (predicate signature, asserts nothing) +-- - has_SO_1_6_holonomy → OPAQUE axiom (predicate signature, asserts nothing) +-- The two opaque axioms are honest: a predicate SYMBOL with no body asserts +-- nothing, so the companion conjectures can only be closed by their sorry. +-- (Earlier these were `def … := Nonempty (M → M)`, which is trivially +-- inhabited by `id` — a stealth-`True`; reverted to opaque axioms.) +-- Proven / conjectured statements: -- - theorem with sorry (cp_FS_Kaehler, Cartan_connection_on_J1_exists, -- holonomy_is_SO_1_6) -- @@ -410,7 +409,8 @@ theorem holonomy_is_SO_1_6 : has_SO_1_6_holonomy openSimplex7 := by -- - holonomy_is_SO_1_6 (CONJECTURE: 1+6 observer split) -- -- Whitelist of acceptable axioms after lake build: --- propext, Classical.choice, Quot.sound, sorryAx +-- propext, Classical.choice, Quot.sound, sorryAx, +-- admits_Cartan_connection, has_SO_1_6_holonomy (OPAQUE predicate signatures) -- Any axiom outside this whitelist is a smuggle. -- #print axioms -- uncomment after lake build to verify