Notation Reference

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

ε — The break. The minimal asymmetry. The unique unpaired element of Axiom B.

σ — The involution of Axiom S; in AP09 identified with complex conjugation.

ν — The valuation on the record algebra; ν(ε) = 1 is the minimum nonzero value.

Z₂ — The two-element group {0, 1}. The minimal classification.

π₁(SO(3)) — Fundamental group of SO(3) in three spatial dimensions; equal to Z₂.

SU(2) — Double cover of SO(3); pre-break weak gauge group; carries spin-½ representations.

U(1)_Y — Hypercharge gauge group; the phase freedom of the complex Hilbert space.

U(1)_em — Electromagnetic gauge group; the post-breaking surviving symmetry (AP15).

T₃ — Third component of weak isospin (Pauli matrix σ₃ representation).

Y — Hypercharge generator.

Q — Electromagnetic charge; Q = T₃ + Y/2.

W¹, W², W³ — Pre-break SU(2) gauge bosons.

W⁺, W⁻, Z⁰ — Post-break massive weak gauge bosons (physical mass eigenstates).

B — Pre-break U(1)_Y gauge boson.

A — Post-break electromagnetic gauge boson (the photon, AP15).

θ_W — Weinberg angle; mixes W³ and B to produce the post-break Z⁰ and A.

α_em — Fine-structure constant; α_em ≈ 1/137.036; coupling of ε to the connection.

v — Vacuum expectation value of the Higgs field; v ≈ 246 GeV (electroweak scale).

m_e — Electron mass; structurally the minimum self-coupling of ε.

m_W, m_Z, m_H — Masses of W, Z, and Higgs bosons; numerical values are open programme (Gap A, Gap B).

g, g′ — Coupling constants of SU(2) and U(1)_Y; appear in mass formulas m_W = gv/2 and m_Z = gv/(2cosθ_W).

ℏ, c — Reduced Planck constant (AP12); speed of light (Axiom C).

α, β — Substrate stiffnesses (AP06); paired with α_em in the six-face structure.

κ — Einstein’s constant; relates curvature to stress-energy in the field equations (AP08).

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 AP16

Title The Break — Electroweak

Subtitle Forces and Constants

Medium Physics

Artist G

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