import Mathlib.CategoryTheory.Category.Basic
import FoundationalReformulation.Status

namespace FoundationalReformulation

open CategoryTheory

universe v u w

/-- A physical context is an object of an explicitly supplied Mathlib category. -/
structure PhysicalContext (C : Type u) [Category.{v} C] where
  object : C
  metadata : ClaimRecord

/-- A family of context morphisms into a target, without asserting that it is a cover. -/
structure Cover {C : Type u} [Category.{v} C] (target : C) where
  Index : Type w
  object : Index → C
  inclusion : (i : Index) → object i ⟶ target
  assumptionIds : List String

/-- The seven Paper 1 assumptions, represented as distinct propositions. -/
structure ContextAssumptions where
  p1a01_higherCategoricalComposition : Prop
  p1a02_coverageStableUnderBaseChange : Prop
  p1a03_coefficientAssignment : Prop
  p1a04_effectiveDescentClass : Prop
  p1a05_structurePreservingComparators : Prop
  p1a06_geometryExcludedFromSignature : Prop
  p1a07_nonGeometricModel : Prop

structure P1C01Dependencies (assumptions : ContextAssumptions) : Prop where
  p1a01 : assumptions.p1a01_higherCategoricalComposition
  p1a02 : assumptions.p1a02_coverageStableUnderBaseChange

structure P1C03Dependencies (assumptions : ContextAssumptions) : Prop where
  p1a05 : assumptions.p1a05_structurePreservingComparators
  p1a06 : assumptions.p1a06_geometryExcludedFromSignature

structure P1C04Dependencies (assumptions : ContextAssumptions) : Prop where
  p1a07 : assumptions.p1a07_nonGeometricModel

namespace ContextClaims

def compositionalContexts : ClaimRecord :=
  .openGoal "P1-C01" ["P1-A01", "P1-A02"]

def explicitRealizations : ClaimRecord :=
  .openGoal "P1-C03" ["P1-A05", "P1-A06"]

def geometryNotDetermined : ClaimRecord :=
  .openGoal "P1-C04" ["P1-A07"]

end ContextClaims

end FoundationalReformulation