Notation Reference

All symbols used in AP24, with structural source and disambiguation from notation collisions elsewhere in the corpus.

{S, B, R, C} — The four axioms of Notebook I. Independent (AP20 §4.2, fenced KS-P.2).

1:1 — Perfect symmetry, the pre-state, totality. Before the break.

ε — The minimum break (Axiom B), the leakage (AP06 §10.4), the electron (The Lock Edition 04). One object, three names. The central symbol of AP24.

electron — The minimum viable splinter, identified with ε by The Lock. What escaped through the break.

leakage — What escapes through finite c (AP06 Theorem 3.1). Identified with ε by AP06 §10.4. Identified with the electron by transitivity through The Lock.

G — Newton’s gravitational constant. The geometry face. G = 2κ/m_e² (The Lock).

c — Speed of light. The propagation face. c² = β/α (The Keys). Also c = e²/(4πε₀ℏα_em).

α_em — Fine-structure constant. ≈ 1/137.035999. The coupling face. The central object of §5. NOT α (substrate stiffness).

α — Temporal stiffness of the substrate (AP06, AP15). NOT α_em. Symbol firewall: α with no subscript is the stiffness; α with subscript em is the fine-structure constant.

β — Spatial stiffness of the substrate (AP06, AP15). NOT a beta function.

m_e — Electron mass. The mass face. ε read as mass.

e — Electron charge. ε read at the electromagnetic scale.

κ — Holding limit (The Lock). The maximum the fabric can hold before tearing further.

λ — Substrate stiffness derived in AP15 (λ ≈ 2.15 × 10⁴⁶). NOT a wavelength.

t — Time. The direction face. Every tick is an electron coupling event writing an irreversible record (Axiom R, Landauer).

ℋ — Complex Hilbert space (AP09). The space of possibilities, the pre-state.

M — The manifold of records. The space of actualised history.

the now — The actualisation state. The boundary between ℋ and M. Immeasurable by structure.

ε = f(ε) — The fixed-point equation. The leakage at the scale determined by the leakage. The architecture; not yet solved (debt D1).

E_P, m_P, ℓ_P — Planck energy, mass, length. Built from G, c, ℏ — hence built from faces of ε. The natural scale of the leakage. At E_P, ε = O(1).

Path 1 — Numerical derivation of α_em by running the coupling from the Planck scale to the electron scale, using the full derived particle spectrum. Requires Notebook V.

Path 2 — Self-consistency shortcut: solve ε = f(ε) directly, without enumerating the particle spectrum. Open.

b_eff — Effective beta-function coefficient at a given energy scale. In the Standard Model b_eff ≈ 26.7. Used in the toy model (§5.6, non-load-bearing).

AS — Actualisation State (the now). Boundary between ℋ and M. Where α_em is measured.

EH — Embedding Hypothesis. Proved in AP20.

QRA — Quantum-Record Alignment. Proved in AP20.

AP20 §4 — Carries the completeness (KS-P.1) and minimality (KS-P.2) of {S, B, R, C} as fenced obligations. The independence of the axioms — no one derivable from the others — is the minimality leg.

The Keys — Edition 02 of the 420 Code; derives c² = β/α.

The Lock — Edition 04 of the 420 Code; identifies ε with the electron, derives G = 2κ/m_e².

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP24

Title The Residual

Subtitle Forces and Constants

Medium Physics

Artist G

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