Notation Reference

U(1) — Group of phase rotations e^{iθ} on the circle S¹. The simplest continuous symmetry.

ℋ — Complex Hilbert space (AP09). Carries complex amplitudes; the Born rule reads its squared magnitudes as probabilities.

M — Lorentzian manifold (AP20). D = 4 (AP10), signature (−, +, +, +).

ψ — State vector in ℋ. ψ = |ψ|e^{iφ} carries magnitude and phase.

σ — Involution of Axiom S; in AP09 identified with complex conjugation on ℋ.

ε — The unique unpaired element of Axiom B. Source of the connection. Identified with the electron at the chemical-biological scale (The Lock).

Aμ — U(1) gauge connection on M. The 1-form that encodes the pre-state’s global phase as read locally.

Fμν — Electromagnetic field tensor. Fμν = ∂μAν − ∂νAμ. The curvature of the connection.

Dμ — Covariant derivative. Dμ = ∂μ − iqAμ.

Jμ — Current. Pushforward to M of the ε-record worldline. Jμ(x) = qδ³(x − x_ε(t)) dx_ε^μ/dt.

q — U(1) charge. Integer in units of e (Theorem 5).

θ — Phase angle. Element of U(1) = S¹.

α_em — Fine-structure constant. ≈ 1/137. Coupling strength of ε to the connection.

c — Speed of light. Finite causal bound of Axiom C.

ℏ — Reduced Planck constant. Quantum cost per record (AP12).

k_B — Boltzmann constant. Appears in the Landauer bound k_B T ln 2 per erased bit.

S(|Ψ⟩) — von Neumann entropy of the pre-state. S(|Ψ⟩) = 0 (pure).

AS — Actualization State. The actualizing now — the surface from which all records are written (AP01).

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

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

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP15

Title The Connection

Subtitle Forces and Constants

Medium Physics

Artist G

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