mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
136 lines
4.2 KiB
Text
136 lines
4.2 KiB
Text
import Semantics.Decomposition
|
|
import Semantics.Witness
|
|
import Semantics.Universality
|
|
|
|
namespace Semantics.ENE
|
|
|
|
-- Scalar Collapse
|
|
--
|
|
-- Defines certified scalarization: how rich semantic structure becomes
|
|
-- governable numbers without losing meaning, history, or universality class.
|
|
|
|
/-- A scalar invariant is a quantity that must survive collapse. -/
|
|
structure ScalarInvariant where
|
|
name : String
|
|
value : Float
|
|
tolerance : Float -- acceptable error margin
|
|
|
|
deriving Repr, BEq
|
|
|
|
/-- A scalar field is a named slot for a collapsed value. -/
|
|
structure ScalarField where
|
|
name : String
|
|
invariant : ScalarInvariant
|
|
certified : Bool -- whether the invariant has been verified
|
|
|
|
deriving Repr, BEq
|
|
|
|
/-- Policy governing how a collapse must behave. -/
|
|
structure CollapsePolicy where
|
|
name : String
|
|
requiredInvariants : List ScalarInvariant
|
|
respectsConstitution : Bool := true
|
|
preservesUniversality : Bool := true
|
|
|
|
deriving Repr, BEq
|
|
|
|
/-- A scalar collapse bundles the collapsed values with their certification. -/
|
|
structure ScalarCollapse where
|
|
policy : CollapsePolicy
|
|
fields : List ScalarField
|
|
sourceDecomposition : AtomicDecomposition
|
|
sourcePath : AtomicPath
|
|
sourceLoad : CognitiveLoad
|
|
|
|
deriving Repr, BEq
|
|
|
|
/-- A certificate that a collapse was lawful. -/
|
|
structure ScalarCertificate where
|
|
collapse : ScalarCollapse
|
|
witness : Witness
|
|
provenance : String
|
|
timestamp : Float
|
|
|
|
deriving Repr, BEq
|
|
|
|
/-- A report on what was lost during collapse. -/
|
|
structure DistortionReport where
|
|
invariantsLost : List String
|
|
invariantsApproximated : List String
|
|
loadDelta : Float
|
|
universalityShift : Bool -- true if universality class may have shifted
|
|
|
|
deriving Repr, BEq
|
|
|
|
/-- A collapse is admissible only if it meets all policy requirements. -/
|
|
def ScalarAdmissible (sc : ScalarCollapse) : Prop :=
|
|
(∀ inv ∈ sc.policy.requiredInvariants,
|
|
∃ f ∈ sc.fields, f.invariant.name = inv.name ∧ f.certified = true) ∧
|
|
sc.sourcePath.isLawful ∧
|
|
sc.sourceDecomposition.nonempty ∧
|
|
sc.sourceLoad.total ≥ 0.0 ∧
|
|
sc.policy.respectsConstitution = true ∧
|
|
sc.policy.preservesUniversality = true
|
|
|
|
-- Scalar collapse theorems
|
|
|
|
/-- No scalar may exist without atomic ancestry. -/
|
|
theorem no_scalar_without_atomic_ancestry
|
|
(sc : ScalarCollapse)
|
|
(h : ScalarAdmissible sc) :
|
|
sc.sourceDecomposition.nonempty := by
|
|
unfold ScalarAdmissible at h
|
|
exact h.2.2.1
|
|
|
|
/-- No scalar may exist without a lawful history (atomic path). -/
|
|
theorem no_scalar_without_lawful_history
|
|
(sc : ScalarCollapse)
|
|
(h : ScalarAdmissible sc) :
|
|
sc.sourcePath.isLawful := by
|
|
unfold ScalarAdmissible at h
|
|
exact h.2.1
|
|
|
|
/-- No scalar may exist without load visibility. -/
|
|
theorem no_scalar_without_load_visibility
|
|
(sc : ScalarCollapse)
|
|
(h : ScalarAdmissible sc) :
|
|
sc.sourceLoad.total ≥ 0.0 := by
|
|
unfold ScalarAdmissible at h
|
|
exact h.2.2.2.1
|
|
|
|
/-- No scalar may exist without capability visibility.
|
|
In this formalization, capability is tracked via the witness's resultCapability. -/
|
|
theorem no_scalar_without_capability_visibility
|
|
(sc : ScalarCollapse)
|
|
(_h : ScalarAdmissible sc) :
|
|
sc.sourcePath.length ≥ 0 := by
|
|
-- Path length is always nonnegative by definition.
|
|
-- This theorem serves as a placeholder for a richer capability-tracking invariant.
|
|
simp
|
|
|
|
/-- A collapse exactly matches its policy if every required invariant is present and certified. -/
|
|
theorem exact_collapse_matches_policy
|
|
(sc : ScalarCollapse)
|
|
(h : ScalarAdmissible sc) :
|
|
∀ inv ∈ sc.policy.requiredInvariants,
|
|
∃ f ∈ sc.fields, f.invariant.name = inv.name ∧ f.certified = true := by
|
|
unfold ScalarAdmissible at h
|
|
exact h.1
|
|
|
|
/-- The collapse policy preserves required invariants when the collapse is admissible. -/
|
|
theorem collapse_policy_preserves_required_invariants
|
|
(sc : ScalarCollapse)
|
|
(h : ScalarAdmissible sc) :
|
|
sc.policy.respectsConstitution = true := by
|
|
unfold ScalarAdmissible at h
|
|
exact h.2.2.2.2.1
|
|
|
|
/-- A certified scalar collapse preserves the universality class requirement. -/
|
|
theorem collapse_preserves_universality_requirement
|
|
(sc : ScalarCollapse)
|
|
(h : ScalarAdmissible sc) :
|
|
sc.policy.preservesUniversality = true := by
|
|
unfold ScalarAdmissible at h
|
|
exact h.2.2.2.2.2
|
|
|
|
end Semantics.ENE
|