Magic 101

Characters

Professor McCullough

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.

Intro

Professor McCullough

Hello students