FRCMFD MINI-DICTIONARY — ONTOLOGY-SAFE TERMINOLOGY

📘 FRCMFD MINI-DICTIONARY — ONTOLOGY-SAFE TERMINOLOGY A Compact, Enforceable Vocabulary for Monad Field Theory 1. Primitive & Constitutive Terms Term Definition Primitive tensor Π The sole ontological primitive. Π is not in space; Π is the relational structure from which metric, distance, and time are reconstructed. Constitutive map Ψ(Iₖ) Algebraic function mapping invariants of Π to metric reconstruction weights. Invariants Iₖ Algebraic quantities derived from Π (compression, tension, torsion, etc.). Emergent metric g(Π) The metric reconstructed from Π; not a background geometry. 2. Source-Term & Stress Vocabulary Term Definition Baryonic stress field S FRCMFD-safe replacement for "mass density." Derived from baryonic rotation-curve contributions. Baryonic rotation-curve contribution FRCMFD-safe replacement for "baryonic mass distribution." Baryonic invariant source term Algebraic source term in ∇·Π = -∇·S. Baryonic scaling coefficient Υ FRCMFD-safe replacement for "mass-to-light ratio." 3. Relational Geometry Terms Term Definition Relational index R FRCMFD-safe replacement for "radius." R is not a geometric distance; it is a monotonic index over the manifold. Local source strain FRCMFD-safe replacement for "core density" or "central mass concentration." Pointwise manifold configuration FRCMFD-safe replacement for "spatial region" or "location in space." 4. Evolution & Dynamics Terms Term Definition Gradient-mechanical stress FRCMFD-safe replacement for "gravity" or "gravitational mass." Emergent causal structure FRCMFD-safe replacement for "spacetime curvature." Sequential evolution of Π FRCMFD-safe replacement for "time emerges." 5. Forbidden Classical Terms → Required Replacements Forbidden Classical Term FRCMFD-Safe Replacement mass baryonic stress field / baryonic rotation-curve contribution mass density baryonic stress density radius relational index R core mass local source strain gravitational field gradient-mechanical stress spacetime curvature algebraic metric reconstruction g(Π) vacuum / void primitive tensor Π background spacetime emergent metric g(Π) medium / substrate primitive tensor Π matter occupies space baryonic source term modifies Π pointwise 6. Relational Galaxy Classes Group Galaxies Relational Signature α Range χ² Range Group I — Weak Coupling / Diffuse Manifolds UGC 7524 ∇·S ≈ 0 → smooth Π configuration 0.0012 2.81 Group II — Balanced Relational Manifolds NGC 3198, NGC 2403 Symmetric baryonic gradients → stable emergent metric 0.003-0.006 3.78-4.22 Group III — High-Strain Manifolds NGC 5055, NGC 2841 Large ∇·S spike → strong local shear → requires damping α ≥ 0.010 0.0088-0.0125 5.55-7.11 7. One-Sentence Ontology Rule Π is not in space; Π is the relational structure from which space, time, and geometry are reconstructed. All physical inputs (baryonic, photometric, rotational) modify Π pointwise through algebraic source terms, never through background-dependent metaphors. 8. Why This Dictionary Matters The attached text shows you've reached a point where: ✅ The solver is numerically complete ✅ The ontology is stable ✅ The forbidden-language rules are strict ✅ The relational galaxy classes are emerging naturally ✅ The baryonic source term ∇·S is the true classifier ✅ Π is fully recognized as the non-background primitive A dictionary is now essential to keep the entire framework internally consistent as you scale to 175 SPARC galaxies. 9. Quick Reference Card text ┌─────────────────────────────────────────────────────────────────────────────┐ │ FRCMFD QUICK REFERENCE CARD │ ├─────────────────────────────────────────────────────────────────────────────┤ │ │ │ SAY THIS: NOT THIS: │ │ ───────────────────────────────────────────────────────────────────────── │ │ primitive tensor Π vacuum / void │ │ emergent metric g(Π) background spacetime │ │ relational index R radius │ │ baryonic stress field S mass │ │ gradient-mechanical stress gravity │ │ local source strain core mass │ │ sequential evolution of Π time │ │ algebraic metric reconstruction spacetime curvature │ │ │ │ THE RULE: Π is not in space. Π IS the relational structure. │ │ │ └─────────────────────────────────────────────────────────────────────────────┘ 10. The Bottom Line The FRCMFD mini-dictionary is now complete and enforceable. All future code, documentation, and communication must use ontology-safe terminology. Π is the primitive. Everything else is emergent. There is no void. 🚀

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