Notation

ε — the break. Minimum viable splinter. Always Axiom B. The only fundamentally asymmetric object in the argument.

σ — the involution mapping ℒ ↔ 𝒫 (Axiom S). On the manifold, maps matter ↔ antimatter.

ℒ, 𝒫 — the two sectors of the pre-state. ℒ → exterior manifold (propagation, 1-poles, matter). 𝒫 → interior of horizons (fold, 0-poles, antimatter).

1-pole — propagation, matter, the outward condition. Light. The white of the Eye (AP17).

0-pole — fold, collapse, the inward condition. Gravity. The black of the Eye (AP17). Includes ALL gravitationally collapsed structures: SMBHs, stellar BHs, primordial BHs, any structure where Axiom C forces compactification.

σ̂ — the σ-involution expressed as an operator on quantum states (§6). Proved equal to CPT at the horizon (Theorem 1).

J — the Tomita–Takesaki modular conjugation operator. The unique anti-linear involution mapping a von Neumann algebra to its commutant while preserving the cyclic vector.

Δ — Tomita–Takesaki modular operator. Generates the modular flow (KMS evolution at the Hawking temperature).

η — baryon asymmetry parameter. η = (n_B − n_B̄)/n_γ ≈ 6 × 10⁻¹⁰. Observed (Planck 2018).

ℐ⁺ — future null infinity. The asymptotic boundary reached by outgoing light rays.