Magic taught first principles D → O → K → F → σ → D with bidirectional↔Imp The cycle is a spiral: D′ ≠ D at every iteration. Imp (Impermanence) guarantees no exact recurrence and acts on the quotient (𝒯,∘)/∼, not directly on 𝒯 (pre-filtering destroys semigroup closure) Terminates if Ω < θ_Ω (domain dissolution) D (Distinction): Primitive cut / resolution capacity. Induces equivalence ∼ from finite sensitivity: |stat(G₁) − stat(G₂)| < ε_D. Non-relational, non-derivable O (Domain): Space of possible distinctions. Validity monitored by Ω K (Relational Structure): Labeled relational hypergraph. Nodes=D-activated states; Edges = (x→y, τ∈{causal,spatial,neutral}, w∈ℝ⁺) F (Flow): Local graph rewrite rules on K: Conservation: Σ w_in = Σ w_out Redistribution by local curvature/tension Probabilistic rewiring (merge redundancy, split deficit) No causal cycles in local radius σ (Compression): Emergent coarse-graining via D-limited resolution. Σₙ = σⁿ(K). Σ₁ = QM (discrete), Σ_∞ = GR (continuous). Equivalent to Wilsonian RG flow. Imp: Forces finite stability windows; only recurrence allowed; prevents absolute fixed points (κ=1) Time=(𝒯, ∘)/∼ : non-abelian semigroup with boundary-matching composition Elements are relations between relations. No underlying substrate ℛ: Pure directed relational network (no sources/sinks). Emergent Physics: Particle=stable attractor loop in K under F, invariant under σ Mass=stability window under Imp Charge=topological winding number (σ-invariant) Space=connectivity skeleton at σ-level n Spacetime=emergent metric of relational accessibility Time=ordered boundary-matching events KEY STRUCTURAL INVARIANTS κ ≥ 2 (granularity floor; Imp prevents κ=1) 0 < R_prop ≤ 1 (max propagation rate; c = R_prop_max) Invariants preserved under ∼ Post-filtering (Imp on quotient) preserves semigroup closure Spiral structure (no exact recurrence) Conservation of relational flux Q (splits into Energy + Momentum) Fe (Free Energy): 1 − (mc²/E_total) ∈ [0,1] — uncommitted compositional budget ℓ (Locality): Fraction of causal propagation ∈ [0,1] C (Coherence): Quotient graph connectivity ∈ [0,1] R (Relational Invariance): Preserved topological invariants under σ ∈ [0,1] I (Internal Mediation): Rewiring/feedback capacity ∈ [0,1] P (Projection/Causal Reach): R_prop_max × ℓ ∈ [0,1] D_var (Dimension): 11 (Planck) → 4 (classical) via G₂ compactification; normalized [0,1] S (Symmetry/Conservation): Dimension of F-invariant subspace ∈ [0,1] Ω (Boundary Coherence) ∈ [0,1]: Monitors validity of O. Dissolves (cycle terminates) when Ω < θ_Ω, triggered by simultaneous co-collapse: C→0 ∧ R→0 ∧ I→0 ∧ S→0. Distinguishes stress vs. total domain failure.