Notation Reference

ℒ, 𝒫 — The two sectors of Axiom S, connected by the involution σ: ℒ ↔ 𝒫.

ε — The break. The minimal asymmetry. The boundary between sectors; the object that writes records on the manifold.

σ — The involution of Axiom S. In AP22 identified with CPT conjugation on the manifold.

ℋ_EW — Internal electroweak state space of ε. ℋ_EW ≅ ℂ². Distinct from spin space (AP11), colour space (AP19), and overall phase (AP15).

|ℒ⟩, |𝒫⟩ — Basis for ℋ_EW. Abstract internal labels, not spacetime directions.

U(2) — Group of 2×2 unitary matrices. The full gauge group on ℋ_EW before decomposition.

SU(2) — Traceless (relative-orientation) part of U(2). Weak isospin.

U(1)_Y — Determinant part of U(2). Hypercharge.

U(1)_EM — Electromagnetic gauge symmetry (AP15). The post-breaking remnant: Q = T³ + Y/2.

T¹, T², T³ — Weak isospin generators (Pauli matrices σ₁, σ₂, σ₃).

Y — Hypercharge generator.

Q — Electromagnetic charge. Q = T³ + Y/2 (post-breaking).

Chirality — Lorentz-representation property of spinor fields. Left-chiral ψ_L ∈ (½, 0) and right-chiral ψ_R ∈ (0, ½).

γ⁵ — Chirality operator. Eigenvalues ±1 distinguish left-chiral and right-chiral components.

P_L, P_R — Chiral projectors. P_L = ½(1 − γ⁵), P_R = ½(1 + γ⁵).

D_μ — Covariant derivative. For the electroweak connection: D_μ = ∂_μ − igW_μ^a T^a − ig'B_μY/2.

AS — Actualization State. The actualizing now.

EH — Embedding Hypothesis (AP20). The algebraic pre-state structure embeds into the physical manifold.

QRA — Quantum–Records Algebra (AP20). The full algebraic structure that EH embeds.

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP27

Title The Harmonics

Subtitle Forces and Constants

Medium Physics

Artist G

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