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116 lines
3.9 KiB
Text
116 lines
3.9 KiB
Text
/-
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Domain Intersection Gaps — Cross-Layer Bind Instances
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These are the missing bridges between TTM domain layers.
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Each should eventually become a lawful `bind` instance.
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Citation: Domain intersection analysis, ChatGPT research session, 2026-04-17.
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-/
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namespace MissingProofs.Intersections
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/-! ## Junction α: Compression-Routing-Topology Nexus
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Models: 1-10 (Cognitive Load) ↔ 71-75 (MI Signal) ↔ 16-23 (GWL Coupling)
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Key insight: Information content determines routing policy determines geometric basin.
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-/
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/-- Bind instance: Cognitive Load → Mutual Information Signal. -/
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def bindLoadToMI (load : Float) (miSignal : Type) : Type × Float :=
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-- MI signal extracted from load features
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sorry
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theorem bindLoadToMILawful : True := by sorry -- Cost bounded, information preserved
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/-- Bind instance: MI Signal → GWL Coupling Weight. -/
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def bindMIToGWL (mi : Type) (coupling : Type) : Type × Float :=
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-- Coupling weight derived from MI density
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sorry
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theorem bindMIToGWLLawful : True := by sorry
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/-! ## Junction β: Energy-Control-Encoding Trinity
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Models: 45-48 (Homeostatic) ↔ 54-56 (Landauer) ↔ 89-93 (uSeed)
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Key insight: Thermodynamic constraints shape encoding efficiency.
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-/
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/-- Bind instance: Homeostatic Pressure → Landauer Bound. -/
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def bindControlToEnergy (pressure : Float) (landauer : Type) : Type × Float :=
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-- Pressure as energy demand
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sorry
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theorem bindControlToEnergyLawful : True := by sorry
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/-- Bind instance: Landauer Limit → uSeed Germination Cost. -/
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def bindEnergyToSeed (energy : Type) (seed : Type) : Type × Float :=
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-- Energy budget → activation threshold
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sorry
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theorem bindEnergyToSeedLawful : True := by sorry
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/-! ## Junction γ: Braid-Verification-Lean Convergence
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Models: 79-81 (Braid) ↔ 82-88 (AVMR) ↔ 111-118 (Unified Compression)
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Key insight: Formal verification of compression through braid structure.
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-/
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/-- Bind instance: Bracket Braid Dynamics → AVMR Event. -/
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def bindBraidToAVMR (braid : Type) (event : Type) : Type × Float :=
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-- Braid state classifies as AVMR event
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sorry
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theorem bindBraidToAVMRLawful : True := by sorry
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/-- Bind instance: AVMR Tree → Unified Compression Pulse. -/
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def bindAVMRToCompression (avmr : Type) (pulse : Type) : Type × Float :=
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-- AVMR vector → compression pulse
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sorry
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theorem bindAVMRToCompressionLawful : True := by sorry
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/-! ## Junction δ: Temporal-Dynamics-Signal Intersection
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Models: 24-29 (Temporal) ↔ 122-125 (Dynamics) ↔ 104-109 (Temporal Theorems)
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Key insight: τ-field enables time-aware signal processing.
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-/
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/-- Bind instance: Temporal Dimension → Time Evolution. -/
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def bindTemporalToDynamics (τ : Type) (evolution : Type) : Type × Float :=
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-- Temporal phase drives dynamics
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sorry
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theorem bindTemporalToDynamicsLawful : True := by sorry
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/-- Bind instance: Dynamics → Axial Event Production. -/
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def bindDynamicsToAxial (dynamics : Type) (event : Type) : Type × Float :=
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-- Evolution selects axial generator
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sorry
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theorem bindDynamicsToAxialLawful : True := by sorry
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/-! ## Critical Collapse Lines
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These are single concepts that should unify multiple domains.
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-/
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/-- Q16.16 as universal numeric representation across all domains. -/
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theorem q16UniversalEmbedding : True := by sorry -- Q16.16 embeds into ℝ faithfully
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/-- Shell state as geometric encoding of integers (I ↔ C₁ ↔ H). -/
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theorem shellStateGeometric : True := by sorry -- (n,k,a,b) captures position + state
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/-- Contact detection as closure constraint (C₁ ↔ F ↔ M). -/
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theorem contactAsConstraint : True := by sorry -- κ_A ∧ κ_C is admissibility predicate
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/-- Resonance as spectral/braid/energy degeneracy (C₂ ↔ G ↔ K ↔ M). -/
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theorem resonanceAsDegeneracy : True := by sorry -- Same eigenvalue across representations
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/-- bind() as universal lawful translation (B ↔ E ↔ M). -/
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theorem bindAsUniversal : True := by sorry -- All lawful translations reduce to bind
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end MissingProofs.Intersections
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