Notation Reference

1:1 + 1×ε — Axiom L0: one-to-one symmetry broken by an infinitesimal perturbation ε > 0.

ε — the symmetry-breaking parameter; the break. Also identified (Layer 3) with awareness.

g⁺, g⁻ — the metrics on the expanding side (M⁺) and the collapsing side (M⁻) of the transition.

φ, Σ — the transition diffeomorphism φ: M⁻ → M⁺ (φ|Σ = id, normal-reversing) and the non-singular transition hypersurface Σ.

(φ⁻¹)* — the pullback of φ⁻¹, mapping tensors on M⁻ to tensors on M⁺.

h — the perturbation tensor (symmetric 2-tensor) encoding the anisotropy difference, the information content, and the initial conditions; ε·h is the deviation across the transition.

ℤ₂ — the two-element symmetry group; 1:1 ≡ ℤ₂ on Σ (I1), +1×ε ≡ ℤ₂ breaking (I2).

c, ρₚ — the propagation constraint (the speed of light; the null cone) and the compression constraint (the Planck density, ρₚ = c⁵/(ℏG²)).

ℓₚ, tₚ — the Planck length and Planck time; ℓₚ/tₚ = c.

α — the fine-structure constant, α = e²/(4πε₀ℏc) ≈ 1/137; value not derived (D3).

Pₘ(k), n_s — the curvature perturbation spectrum and its measured tilt (n_s ≈ 0.965).

S_vN, S_gen — the von Neumann (fine-grained) entropy and the generalised entropy; S_vN(ρ_total) = const, S_gen non-decreasing.

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP04

Title The Loop Hypothesis

Subtitle Cyclic Cosmology

Medium Cosmology / Physics

Artist G

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