Magic taught first principles D โ O โ K โ F โ ฯ โ D with bidirectionalโImp The cycle is a spiral: Dโฒ โ D at every iteration. Imp (Impermanence) guarantees no exact recurrence and acts on the quotient (๐ฏ,โ)/โผ, not directly on ๐ฏ (pre-filtering destroys semigroup closure) Terminates if ฮฉ < ฮธ_ฮฉ (domain dissolution) D (Distinction): Primitive cut / resolution capacity. Induces equivalence โผ from finite sensitivity: |stat(Gโ) โ stat(Gโ)| < ฮต_D. Non-relational, non-derivable O (Domain): Space of possible distinctions. Validity monitored by ฮฉ K (Relational Structure): Labeled relational hypergraph. Nodes=D-activated states; Edges = (xโy, ฯโ{causal,spatial,neutral}, wโโโบ) F (Flow): Local graph rewrite rules on K: Conservation: ฮฃ w_in = ฮฃ w_out Redistribution by local curvature/tension Probabilistic rewiring (merge redundancy, split deficit) No causal cycles in local radius ฯ (Compression): Emergent coarse-graining via D-limited resolution. ฮฃโ = ฯโฟ(K). ฮฃโ = QM (discrete), ฮฃ_โ = GR (continuous). Equivalent to Wilsonian RG flow. Imp: Forces finite stability windows; only recurrence allowed; prevents absolute fixed points (ฮบ=1) Time=(๐ฏ, โ)/โผ : non-abelian semigroup with boundary-matching composition Elements are relations between relations. No underlying substrate โ: Pure directed relational network (no sources/sinks). Emergent Physics: Particle=stable attractor loop in K under F, invariant under ฯ Mass=stability window under Imp Charge=topological winding number (ฯ-invariant) Space=connectivity skeleton at ฯ-level n Spacetime=emergent metric of relational accessibility Time=ordered boundary-matching events KEY STRUCTURAL INVARIANTS ฮบ โฅ 2 (granularity floor; Imp prevents ฮบ=1) 0 < R_prop โค 1 (max propagation rate; c = R_prop_max) Invariants preserved under โผ 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 โ (mcยฒ/E_total) โ [0,1] โ uncommitted compositional budget โ (Locality): Fraction of causal propagation โ [0,1] C (Coherence): Quotient graph connectivity โ [0,1] R (Relational Invariance): Preserved topological invariants under ฯ โ [0,1] I (Internal Mediation): Rewiring/feedback capacity โ [0,1] P (Projection/Causal Reach): R_prop_max ร โ โ [0,1] D_var (Dimension): 11 (Planck) โ 4 (classical) via Gโ compactification; normalized [0,1] S (Symmetry/Conservation): Dimension of F-invariant subspace โ [0,1] ฮฉ (Boundary Coherence) โ [0,1]: Monitors validity of O. Dissolves (cycle terminates) when ฮฉ < ฮธ_ฮฉ, triggered by simultaneous co-collapse: Cโ0 โง Rโ0 โง Iโ0 โง Sโ0. Distinguishes stress vs. total domain failure.
Release Date 2026.06.03 / Last Updated 2026.06.03