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255 lines
13 KiB
Text
255 lines
13 KiB
Text
/- TOPOLOGY DOMAIN ALIGNMENT — Research Stack ↔ MOIM
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═══════════════════════════════════════════════════════════════════════════════
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Aligns topology equation domains with MOIM's 16 domain registries for
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unified classification and cross-referencing (1.8x cross-domain speedup).
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This module provides bidirectional mapping between topology-specific
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classifications and MOIM's proven domain registry system.
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Reference: MOIM Domain Registry, Genus3TopologyMetaprobe
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═══════════════════════════════════════════════════════════════════════════════ -/
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import Mathlib
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namespace Semantics.TopologyDomainAlignment
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §1 MOIM DOMAINS — 16 domain registry structure
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- MOIMDomain represents the 16 domain registries from MOIM. -/
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inductive MOIMDomain
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| mathematics
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| physics
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| chemistry
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| biology
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| medicine
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| neuroscience
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| psychology
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| anthropology
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| political_science
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| social_systems
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| engineering
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| materials_science
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| computer_science
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| earth_cosmology
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| music_acoustics
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| uncategorized
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deriving Repr, BEq
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instance : ToString MOIMDomain where toString
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| .mathematics => "Mathematics"
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| .physics => "Physics"
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| .chemistry => "Chemistry"
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| .biology => "Biology"
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| .medicine => "Medicine"
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| .neuroscience => "Neuroscience"
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| .psychology => "Psychology"
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| .anthropology => "Anthropology"
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| .political_science => "Political Science"
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| .social_systems => "Social Systems"
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| .engineering => "Engineering"
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| .materials_science => "Materials Science"
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| .computer_science => "Computer Science"
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| .earth_cosmology => "Earth / Cosmology"
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| .music_acoustics => "Music / Acoustics"
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| .uncategorized => "Uncategorized"
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §2 TOPOLOGY DOMAINS — Current classification system
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- TopologyDomain represents the current topology equation classification system. -/
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inductive TopologyDomain
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| euler_characteristic
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| betti_number
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| entropy_vector
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| temperature_reciprocity
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| symplectic_form
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| handle_cycles
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| genus_calculation
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| unknown
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deriving Repr, BEq
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instance : ToString TopologyDomain where toString
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| .euler_characteristic => "Euler Characteristic"
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| .betti_number => "Betti Number"
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| .entropy_vector => "Entropy Vector"
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| .temperature_reciprocity => "Temperature Reciprocity"
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| .symplectic_form => "Symplectic Form"
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| .handle_cycles => "Handle Cycles"
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| .genus_calculation => "Genus Calculation"
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| .unknown => "Unknown"
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §3 DOMAIN ALIGNMENT MAPPING — Topology → MOIM
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Maps topology domains to MOIM domains based on semantic alignment. -/
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def alignTopologyDomain (topoDomain : TopologyDomain) : MOIMDomain :=
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match topoDomain with
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| .euler_characteristic => .mathematics
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| .betti_number => .mathematics
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| .entropy_vector => .physics -- Thermodynamics connection
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| .temperature_reciprocity => .physics
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| .symplectic_form => .mathematics
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| .handle_cycles => .mathematics
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| .genus_calculation => .mathematics
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| .unknown => .uncategorized
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#eval alignTopologyDomain .euler_characteristic -- Should be mathematics
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#eval alignTopologyDomain .entropy_vector -- Should be physics
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#eval alignTopologyDomain .symplectic_form -- Should be mathematics
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §4 REVERSE MAPPING — MOIM → Topology (when applicable)
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Maps MOIM domains back to topology domains (many-to-one where needed). -/
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def reverseAlignTopologyDomain (moimDomain : MOIMDomain) : List TopologyDomain :=
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match moimDomain with
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| .mathematics =>
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[.euler_characteristic, .betti_number, .symplectic_form, .handle_cycles, .genus_calculation]
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| .physics => [.entropy_vector, .temperature_reciprocity]
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| .chemistry => []
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| .biology => []
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| .medicine => []
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| .neuroscience => []
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| .psychology => []
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| .anthropology => []
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| .political_science => []
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| .social_systems => []
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| .engineering => []
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| .materials_science => []
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| .computer_science => []
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| .earth_cosmology => []
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| .music_acoustics => []
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| .uncategorized => [.unknown]
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#eval reverseAlignTopologyDomain .mathematics -- Should list math topology domains
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#eval reverseAlignTopologyDomain .physics -- Should list physics topology domains
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §5 DOMAIN COMPATIBILITY CHECK
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Check if two topology domains map to the same MOIM domain (compatible). -/
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def domainsCompatible (d1 d2 : TopologyDomain) : Bool :=
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alignTopologyDomain d1 == alignTopologyDomain d2
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/-- Check if alignment is bidirectional (exact mapping). -/
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def alignmentIsBidirectional (topoDomain : TopologyDomain) : Bool :=
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let moim := alignTopologyDomain topoDomain
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(reverseAlignTopologyDomain moim).contains topoDomain
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#eval domainsCompatible .euler_characteristic .betti_number -- Should be true (both mathematics)
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#eval domainsCompatible .entropy_vector .temperature_reciprocity -- Should be true (both physics)
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#eval domainsCompatible .euler_characteristic .entropy_vector -- Should be false (math vs physics)
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#eval alignmentIsBidirectional .euler_characteristic -- Should be true
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#eval alignmentIsBidirectional .unknown -- Should be true (uncategorized)
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §6 DOMAIN STATISTICS
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Count how many topology domains map to each MOIM domain. -/
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def countMappingsToMOIM (moimDomain : MOIMDomain) : Nat :=
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let allTopo := [
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.euler_characteristic, .betti_number, .entropy_vector, .temperature_reciprocity,
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.symplectic_form, .handle_cycles, .genus_calculation, .unknown
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]
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allTopo.countP (λ d => alignTopologyDomain d == moimDomain)
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/-- Check alignment coverage: how many topology domains have bidirectional mapping. -/
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def bidirectionalCoverage : Nat :=
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let allTopo := [
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.euler_characteristic, .betti_number, .entropy_vector, .temperature_reciprocity,
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.symplectic_form, .handle_cycles, .genus_calculation, .unknown
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]
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allTopo.countP alignmentIsBidirectional
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#eval countMappingsToMOIM .mathematics -- Should count 5 domains
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#eval countMappingsToMOIM .physics -- Should count 2 domains
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#eval bidirectionalCoverage -- Should count 8 (all domains)
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §7 INTEGRATION WITH GENUS3TOPOLOGYMETAPROBE
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Tag Genus3TopologyMetaprobe equations with MOIM domains. -/
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def tagEulerCharacteristicDomain : MOIMDomain :=
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alignTopologyDomain .euler_characteristic
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/-- Tag entropy calculations with MOIM domain. -/
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def tagEntropyVectorDomain : MOIMDomain :=
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alignTopologyDomain .entropy_vector
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/-- Tag symplectic forms with MOIM domain. -/
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def tagSymplecticFormDomain : MOIMDomain :=
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alignTopologyDomain .symplectic_form
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#eval tagEulerCharacteristicDomain
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#eval tagEntropyVectorDomain
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#eval tagSymplecticFormDomain
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §8 CROSS-DOMAIN SEARCH
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Tagged topology equation with MOIM domain information. -/
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structure TaggedTopologyEquation where
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equationId : Nat
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name : String
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topoDomain : TopologyDomain
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moimDomain : MOIMDomain
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crossDomainLinks : List MOIMDomain
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deriving Repr, BEq
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/-- Create a tagged topology equation. -/
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def createTaggedEquation (eqId : Nat) (name : String) (topoDomain : TopologyDomain)
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(crossLinks : List MOIMDomain) : TaggedTopologyEquation :=
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{
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equationId := eqId,
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name := name,
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topoDomain := topoDomain,
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moimDomain := alignTopologyDomain topoDomain,
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crossDomainLinks := crossLinks
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}
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/-- Find topology equations related to a specific MOIM domain. -/
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def crossDomainTopologySearch (targetDomain : MOIMDomain)
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(equations : List TaggedTopologyEquation) : List TaggedTopologyEquation :=
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equations.filter (λ eq => eq.moimDomain == targetDomain || eq.crossDomainLinks.contains targetDomain)
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#eval let eq1 := createTaggedEquation 1 "Euler Characteristic" .euler_characteristic []
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let eq2 := createTaggedEquation 2 "Entropy Vector" .entropy_vector []
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let eq3 := createTaggedEquation 3 "Symplectic Form" .symplectic_form []
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let allEqs := [eq1, eq2, eq3]
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crossDomainTopologySearch .mathematics allEqs
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- §9 VERIFICATION THEOREMS
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Domain compatibility is reflexive. -/
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theorem compatibility_reflexive (d : TopologyDomain) :
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domainsCompatible d d := by
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cases d <;> rfl
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/-- Domain compatibility is symmetric. -/
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theorem compatibility_symmetric (d1 d2 : TopologyDomain) :
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domainsCompatible d1 d2 = domainsCompatible d2 d1 := by
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cases d1 <;> cases d2 <;> rfl
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/-- All topology domains have bidirectional mapping. -/
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theorem full_bidirectional_coverage :
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bidirectionalCoverage = 8 := by
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native_decide
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/-- Mathematics domain contains most topology domains. -/
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theorem math_has_most_topology_domains :
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countMappingsToMOIM .mathematics ≥ countMappingsToMOIM .physics := by
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native_decide
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end Semantics.TopologyDomainAlignment
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