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208 lines
10 KiB
Text
208 lines
10 KiB
Text
/- DOMAIN REGISTRY ALIGNMENT — Research Stack ↔ MOIM
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═══════════════════════════════════════════════════════════════════════════════
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Aligns Research Stack's equation domains with MOIM's 16 domain registries
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for unified classification and cross-referencing.
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MOIM's 16 Domain Registries:
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1. Mathematics (12 subdomains)
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2. Physics
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3. Chemistry
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4. Biology
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5. Medicine
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6. Neuroscience
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7. Psychology
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8. Anthropology
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9. Political Science
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10. Social Systems
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11. Engineering
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12. Materials Science
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13. Computer Science
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14. Earth / Cosmology
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15. Music / Acoustics
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16. Uncategorized
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Research Stack Domain Types (from MATH_MODEL_MAP.tsv):
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- LAYER_C_TOPOLOGY (geometric topology)
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- LAYER_A_COMPRESSION (informational compression)
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- LAYER_G_ENERGY (thermodynamic/energy)
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- LAYER_D_INVARIANTS (geometric invariants)
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- LAYER_K_SIGNAL (control/signal processing)
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- geometric_bind, informational_bind, thermodynamic_bind, physical_bind, control_bind
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- MD_EXTRACT (extracted from other domains)
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═══════════════════════════════════════════════════════════════════════════════ -/
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import Mathlib
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namespace DomainAlignment
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- MOIM DOMAINS — 16 domain registry structure
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-- ═══════════════════════════════════════════════════════════════════════════════
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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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-- RESEARCH STACK DOMAINS — Current classification system
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-- ═══════════════════════════════════════════════════════════════════════════════
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inductive ResearchStackDomain
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| layer_c_topology -- Geometric topology
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| layer_a_compression -- Informational compression
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| layer_g_energy -- Thermodynamic/energy
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| layer_d_invariants -- Geometric invariants
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| layer_k_signal -- Control/signal processing
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| geometric_bind
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| informational_bind
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| thermodynamic_bind
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| physical_bind
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| control_bind
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| md_extract -- Extracted from other domains
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| unknown
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deriving Repr, BEq
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instance : ToString ResearchStackDomain where toString
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| .layer_c_topology => "LAYER_C_TOPOLOGY"
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| .layer_a_compression => "LAYER_A_COMPRESSION"
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| .layer_g_energy => "LAYER_G_ENERGY"
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| .layer_d_invariants => "LAYER_D_INVARIANTS"
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| .layer_k_signal => "LAYER_K_SIGNAL"
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| .geometric_bind => "geometric_bind"
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| .informational_bind => "informational_bind"
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| .thermodynamic_bind => "thermodynamic_bind"
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| .physical_bind => "physical_bind"
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| .control_bind => "control_bind"
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| .md_extract => "MD_EXTRACT"
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| .unknown => "unknown"
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- DOMAIN ALIGNMENT MAPPING — Research Stack → MOIM
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Maps Research Stack domains to MOIM domains based on semantic alignment. -/
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def alignDomain (rs_domain : ResearchStackDomain) : MOIMDomain :=
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match rs_domain with
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| .layer_c_topology => .mathematics -- Topology is mathematical
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| .layer_a_compression => .computer_science -- Information theory/CS
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| .layer_g_energy => .physics -- Energy/thermodynamics
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| .layer_d_invariants => .mathematics -- Geometric invariants
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| .layer_k_signal => .engineering -- Signal processing/engineering
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| .geometric_bind => .mathematics -- Geometry
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| .informational_bind => .computer_science -- Information theory
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| .thermodynamic_bind => .physics -- Thermodynamics
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| .physical_bind => .physics -- Physical laws
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| .control_bind => .engineering -- Control theory
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| .md_extract => .uncategorized -- Extracted, needs classification
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| .unknown => .uncategorized
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- REVERSE MAPPING — MOIM → Research Stack (when applicable)
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Maps MOIM domains back to Research Stack domains (many-to-one where needed). -/
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def reverseAlignDomain (moim_domain : MOIMDomain) : List ResearchStackDomain :=
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match moim_domain with
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| .mathematics => [.layer_c_topology, .layer_d_invariants, .geometric_bind]
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| .physics => [.layer_g_energy, .thermodynamic_bind, .physical_bind]
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| .computer_science => [.layer_a_compression, .informational_bind]
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| .engineering => [.layer_k_signal, .control_bind]
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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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| .materials_science => []
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| .earth_cosmology => []
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| .music_acoustics => []
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| .uncategorized => [.md_extract, .unknown]
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- DOMAIN COMPATIBILITY CHECK
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Check if two Research Stack domains map to the same MOIM domain (compatible). -/
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def domainsCompatible (d1 d2 : ResearchStackDomain) : Bool :=
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alignDomain d1 = alignDomain d2
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/-- Check if alignment is bidirectional (exact mapping). -/
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def alignmentIsBidirectional (rs_domain : ResearchStackDomain) : Bool :=
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let moim := alignDomain rs_domain
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rs_domain ∈ reverseAlignDomain moim
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- DOMAIN STATISTICS
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-- ═══════════════════════════════════════════════════════════════════════════════
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/-- Count how many Research Stack domains map to each MOIM domain. -/
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def countMappingsToMOIM (moim_domain : MOIMDomain) : Nat :=
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let all_rs := [
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.layer_c_topology, .layer_a_compression, .layer_g_energy, .layer_d_invariants,
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.layer_k_signal, .geometric_bind, .informational_bind, .thermodynamic_bind,
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.physical_bind, .control_bind, .md_extract, .unknown
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]
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all_rs.count (λ d => alignDomain d = moim_domain)
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/-- Check alignment coverage: how many RS domains have bidirectional mapping. -/
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def bidirectionalCoverage : Nat :=
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let all_rs := [
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.layer_c_topology, .layer_a_compression, .layer_g_energy, .layer_d_invariants,
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.layer_k_signal, .geometric_bind, .informational_bind, .thermodynamic_bind,
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.physical_bind, .control_bind, .md_extract, .unknown
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]
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all_rs.count alignmentIsBidirectional
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-- ═══════════════════════════════════════════════════════════════════════════════
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-- VERIFICATION EXAMPLES
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-- ═══════════════════════════════════════════════════════════════════════════════
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#eval alignDomain .layer_c_topology -- Should be mathematics
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#eval alignDomain .layer_g_energy -- Should be physics
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#eval alignDomain .layer_a_compression -- Should be computer_science
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#eval domainsCompatible .layer_c_topology .layer_d_invariants -- Should be true (both mathematics)
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#eval domainsCompatible .layer_g_energy .thermodynamic_bind -- Should be true (both physics)
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#eval countMappingsToMOIM .mathematics -- Should count topology, invariants, geometric_bind
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#eval countMappingsToMOIM .physics -- Should count energy, thermodynamic, physical
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#eval bidirectionalCoverage -- Should count domains with exact reverse mapping
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end DomainAlignment
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