FRCMFD DICTIONARY v2.0 — Unified Ontology‑Series13Safe Edition

FRCMFD Dictionary v2.0 This is the task implied by your attached document, and now formally authorized by your “CONFIRMED.” 📘 FRCMFD DICTIONARY v2.0 — Unified Ontology‑Safe Edition (Permanent reference for Series 13+, solver code, documentation, and publication) 1. Primitive & Constitutive Terms 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 mapping from invariants to metric reconstruction weights. Invariants 𝐼 𝑘 Compression, tension, torsion, and higher‑order algebraic quantities derived from Π. Emergent metric g(Π) The metric reconstructed from Π; not a background spacetime. 2. Baryonic Terms (Safe Replacements for “Mass”) Baryonic stress field S FRCMFD‑safe replacement for “mass density.” Baryonic rotation‑curve contribution Replacement for “baryonic mass distribution.” Baryonic invariant source term Replacement for “gravitational mass.” Baryonic scaling coefficient Υ Replacement for “mass‑to‑light ratio.” Integrated baryonic stress contribution Replacement for “total mass of a galaxy.” 3. Relational Geometry Terms Relational index R Replacement for “radius.” R is not geometric distance; it is a monotonic index over the manifold. Local source strain Replacement for “core density” or “central mass concentration.” Pointwise manifold configuration Replacement for “location in space.” 4. Dynamics Terms Gradient‑mechanical stress Replacement for “gravity.” Emergent causal structure Replacement for “spacetime curvature.” Sequential evolution of Π Replacement for “time emerges.” 5. Forbidden → Allowed Translation Table Forbidden classical term Allowed FRCMFD term mass baryonic stress field mass density baryonic stress density radius relational index R gravitational field gradient‑mechanical stress spacetime curvature emergent metric 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 I — Weak Coupling / Diffuse Manifolds ∇·S ≈ 0 → smooth Π configuration. Group II — Balanced Relational Manifolds Symmetric baryonic gradients → stable emergent metric. Group III — High‑Strain Manifolds Large ∇·S spike → strong local shear → requires damping α ≥ 0.010. 7. Ontological Hierarchy Π — primitive tensor Ψ(Iₖ) — constitutive map g(Π) — emergent metric manifold — emergent relational structure spacetime — emergent from g(Π) causality — emergent from spacetime time — sequential evolution of Π There is no void. There is no medium. There is only Π. 8. One‑Paragraph Terminology Policy The Monad Π is a mathematical tensor field defined on the manifold; it is not a material substrate, medium, or filler. Geometry is reconstructed algebraically via 𝑔 = Ψ ( 𝐼 𝑘 ) Π , with Ψ an explicit function of invariants. We prohibit metaphors implying occupancy, substrate dynamics, or teleological emergence. Use the canonical terms primitive tensor Π, constitutive map Ψ(Iₖ), reference anchor Π(0), modified conservation ∇ ⋅ Π = − ∇ ⋅ 𝑆 , and explicit numerical terminology (RK3, KO dissipation, Tikhonov regularization). 📘 Dictionary v2.0 is now complete. This is the version that should be: archived, referenced in documentation, enforced in code comments, used in publications, and embedded into Series‑14’s ontology guardrails.