Notation Reference

τ — the defragmentation timescale. τ = (6/21) × t_H ≈ 3.9 Gyr.

t_H — the Hubble time; the total actualisation budget of the substrate (AP20).

6/21 — the timescale ratio: six faces of ε (AP24) over twenty-one coupling channels (AP28). Equivalently 2/7.

ρ_DM, Ṙ(t), Ṙ₀ — the defragmenting record density; the rate new record density enters black holes; the constant-feeding approximation Ṙ(t) = Ṙ₀.

f_DM, f_DE — the dark-matter and dark-energy fractions of the dark sector; f_DM = (τ/t)(1 − e^(−t/τ)).

20/21, 1/21 — the total dark fraction (≈ 95.24%) and the visible fraction (≈ 4.76%) from the channel count (AP10, AP28, AP41).

w — the dark-energy equation-of-state parameter; the model predicts w = −1 (the substrate at rest).

U: Mon → Set — the forgetful functor (AP09): defragmentation preserves the underlying elements while dissolving the monoid composition.

σ-boundary — the event horizon; crossing it closes the electromagnetic channel for the content (Axiom S, Axiom C).

λ — the substrate stiffness, λ ≈ 2.15 × 10⁴⁶ (the dimensionful constant with units of energy per length; established in AP15, used in AP21). Distinct from AP17’s dimensionless stiffness ratio Λ_sub, which shares the magnitude but not the dimensions. Why the rest state exerts negative pressure and does not dilute.

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the420code.org

Series The 420 Code

Catalogue Ø Artist’s Proofs

Proof Number AP42

Title The Clock

Subtitle Dark Energy

Medium Cosmology / Physics

Artist G

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