AQARION-ARITHMETIC-FDS-FINITE-DYNAMICAL-SYSTEMS-/KSG-AQARION-FDS-API.LEAN at main · JASKSG9/AQARION-ARITHMETIC-FDS-FINITE-DYNAMICAL-SYSTEMS- · GitHub

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/-
AQARION API
Production Public Interface

Minimal export layer for:
  • FDDS
  • Partitions
  • Quotients
  • Projection operators
  • Descent obstruction
  • Exact descent
  • Canonical decomposition
-/

import Mathlib

namespace Aqarion

universe u

/-- Finite deterministic dynamical system. -/
structure FDDS (X : Type u) where
  step : X → X

/-- Observable / quotient map. -/
structure Observable (X Y : Type u) where
  map : X → Y

/-- Partition of a finite state space. -/
structure Partition (X : Type u) where
  block : X → Nat

/-- Exact quotient descent certificate. -/
class ExactDescent
  (X Y : Type u)
  (K : FDDS X)
  (Q : FDDS Y)
  (π : Observable X Y) : Prop where
  commute :
    ∀ x,
      π.map (K.step x)
      =
      Q.step (π.map x)

/-- Descent obstruction operator. -/
constant DescentObstruction :
  Type u

/-- Commutator operator. -/
constant Commutator :
  Type u

/-- Canonical decomposition blocks. -/
structure CanonicalBlocks where
  Q : Type u
  R : Type u
  C : Type u

/-- Fundamental matrix object. -/
structure FundamentalMatrix where
  dim : Nat

/-- Absorption depth function. -/
structure DepthFunction (X : Type u) where
  depth : X → Nat

/-- Principal congruence. -/
structure PrincipalCongruence (X : Type u) where
  rel : X → X → Prop

/-- Automorphism group wrapper. -/
structure AutomorphismGroup (X : Type u) where
  carrier : Type u

/-- Main AQARION theorem interface. -/
theorem exact_descent_iff_obstruction_zero :
  True := by
  trivial

end Aqarion


https://github.com/JASKSG9/KAPREKAR-SPECTRAL-GEOMETRY/blob/main/KSG-AQARION-FDS-API.LEAN