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137 lines
5 KiB
Text
137 lines
5 KiB
Text
import Semantics.Path
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namespace Semantics.ENE
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-- ENE Self-Diagnostics
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-- Formalization of the five-condition unified invariant from the
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-- unconventional mathematics specification.
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--
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-- The Five Conditions:
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-- KNIT: Hamiltonian path exists (learning loop covers all points)
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-- RIGID: Stress matrix Ω ⪰ 0, Ωp = 0 (load balanced, structure stable)
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-- CRNT: Deficiency δ = 0 (decision space minimally specified)
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-- FLAVOR: ΔMₛ > 0 (method assignments more coherent than random)
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-- NEURO: |gradient_slope| > τ (gradient mode active)
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/-- Diagnostic report for the ENE graph. Mirrors `ene_diagnostics.py`. -/
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structure DiagnosticReport where
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nPoints : Nat := 0
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-- KNIT condition
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knitPathExists : Bool := false
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knitCoverage : Float := 0.0
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knitPathLength : Nat := 0
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-- RIGID condition
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rigidPsd : Bool := false
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rigidResidual : Float := 0.0
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rigidMinEigen : Float := 0.0
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-- CRNT condition
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crntDeficiency : Nat := 0
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crntComplexes : Nat := 0
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crntLinkage : Nat := 0
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crntStoichDim : Nat := 0
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crntIsZero : Bool := false
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-- FLAVOR condition
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flavorSharing : Float := 0.0
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flavorRandom : Float := 0.0
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flavorBias : Float := 0.0
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flavorPositive : Bool := false
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-- NEURO condition
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neuroSlope : Float := 0.0
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neuroThreshold : Float := 0.3
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neuroOk : Bool := false
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neuroMode : String := "UNKNOWN"
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deriving Repr, BEq
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/-- Count how many conditions passed. -/
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def DiagnosticReport.conditionsPassed (r : DiagnosticReport) : Nat :=
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let checks := [
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r.knitPathExists,
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r.rigidPsd,
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r.crntIsZero,
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r.flavorPositive,
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r.neuroOk
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]
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checks.filter id |>.length
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def DiagnosticReport.conditionsTotal : Nat := 5
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/-- Overall health: all five conditions must pass. -/
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def DiagnosticReport.overallHealthy (r : DiagnosticReport) : Bool :=
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r.conditionsPassed = DiagnosticReport.conditionsTotal
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/-- KNIT condition: a Hamiltonian-like path exists through all MIPoint nodes.
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In the formalization, this is a proposition that a lawful path visits
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all observation nodes in the graph. -/
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def KnitCondition (g : Graph) (p : AtomicPath) : Prop :=
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let miNodes := g.nodes.filter (λ n => match n.type with | NodeType.observation => true | _ => false)
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AtomicPath.isLawful p ∧ AtomicPath.length p = miNodes.length
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/-- RIGID condition: the graph's stress structure is positive semi-definite.
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We formalize this as a predicate on the graph's load profiles. -/
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def RigidCondition (g : Graph) : Prop :=
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-- In the formal model, this requires that for every interpretation node,
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-- the associated load profile is non-negative and finite.
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∀ n ∈ g.nodes,
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(∀ e ∈ g.edges,
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e.target == n ∧ e.type == EdgeType.has_load →
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e.weight ≥ 0.0)
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/-- CRNT (Chemical Reaction Network Theory) condition:
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The decision space is minimally specified — no hidden deficiency.
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In the formal model: the graph has no orphan observation nodes
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(nodes with no outgoing projection edge). -/
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def CrntCondition (g : Graph) : Prop :=
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∀ n ∈ g.nodes,
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n.type == NodeType.observation →
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(∃ e ∈ g.edges, e.source == n ∧ e.type == EdgeType.projects_to)
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/-- FLAVOR condition: method assignments are more coherent than random.
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In the formal model: nodes assigned to the same attractor share
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a common method label more often than not. -/
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def FlavorCondition (g : Graph) : Prop :=
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-- For every attractor, if multiple canonical states are assigned to it,
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-- they should share methods positively.
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∀ a ∈ g.nodes,
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a.type == NodeType.attractor →
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let assigned := g.inEdges a |>.filter (λ e => e.type == EdgeType.assigned_to)
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let methods := assigned.map (λ e => e.source.label)
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methods.length ≤ 1 ∨
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-- There exists some method that appears more than once
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(∃ m, 1 < (methods.filter (λ x => x == m)).length)
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/-- NEURO condition: the graph exhibits gradient structure along a principal axis.
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In the formal model: there exists a path through observations where
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the method labels correlate with position in the path. -/
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def NeuroCondition (_g : Graph) : Prop :=
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-- There exists a non-empty lawful path through observations
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-- with at least 3 nodes, showing structured progression.
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∃ (p : AtomicPath),
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AtomicPath.isLawful p ∧ AtomicPath.length p ≥ 3 ∧
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AtomicPath.staysWithin p (λ n => n.type == NodeType.observation)
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/-- The complete set of five ENE conditions as a single structure. -/
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structure ENEDiagnostics where
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graph : Graph
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knitPath : AtomicPath
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report : DiagnosticReport
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/-- All five conditions hold simultaneously. -/
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def ENEDiagnostics.allConditionsHold (d : ENEDiagnostics) : Prop :=
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KnitCondition (ENEDiagnostics.graph d) (ENEDiagnostics.knitPath d) ∧
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RigidCondition (ENEDiagnostics.graph d) ∧
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CrntCondition (ENEDiagnostics.graph d) ∧
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FlavorCondition (ENEDiagnostics.graph d) ∧
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NeuroCondition (ENEDiagnostics.graph d)
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/-- A graph is healthy if all five diagnostics pass. -/
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def Graph.isHealthy (g : Graph) (p : AtomicPath) : Prop :=
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KnitCondition g p ∧ RigidCondition g ∧ CrntCondition g ∧
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FlavorCondition g ∧ NeuroCondition g
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end Semantics.ENE
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