The Net Asymmetry

5.1 — The segregation

By Theorem 1 (§4), the event horizon is the σ-boundary, and σ̂ = CPT at the horizon. The 1-pole/0-pole topology of the Eye (AP17) then implies the following segregation:

At the actualisation event — the origin of the expanding manifold (AP20) — the 1:1 broke via the splinter (Axiom B). The tension field formed (AP17).

The topology of the Eye emerged: 1-poles (propagation, outward, light, matter) and 0-poles (fold, inward, gravity, antimatter). The σ-involution maps one to the other.

But the two sides of the Eye are not equivalent: one propagates outward (visible), the other collapses inward (hidden behind horizons).

The structural argument for segregation: The 1-pole is the condition of propagation — outward expansion, light, the ℒ-sector. The 0-pole is the condition of collapse — inward folding, gravity, the 𝒫-sector.

By Theorem 1, the event horizon is the boundary between these two conditions. Matter (σ-even content) propagates in the ℒ-sector. Antimatter (σ-odd content, the σ-images) resides in the 𝒫-sector — inside the horizons.

From one Eye to many: The primordial actualisation creates one Eye topology with one 0-pole. As the tension field evolves, it forms filaments via the Steiner tree mechanism (AP21, Proposition 2).

At filament intersections, energy density exceeds the compactification threshold. The primordial 0-pole fragments into individual direct vacuums — primordial SMBHs. Each SMBH is a local 0-pole, a local expression of the 𝒫-sector.

Additional 0-poles form throughout cosmic history: stellar black holes (from collapse of massive stars), primordial black holes (from density fluctuations), and any other structure where Axiom C forces compactification.

The visible universe is the white of the Eye. The black holes — all of them: supermassive, stellar, primordial — are the black of the Eye.

The net baryon surplus in the visible universe is balanced by the net antibaryon content inside the horizons.

You are standing on the matter side of a ledger whose other half is hidden behind every black hole in the universe. The books balance. You just cannot see the other page.

5.2 — Why the door stays open

If the ledger is exactly 1:1, why doesn’t everything annihilate? Why is there a visible universe at all?

Because of Axiom B.

Proposition 1 (Uncancellable entry). In the axiom structure 1:1 + 1×ε @ AS, the element ε has no σ-image. The ledger has exactly one entry that cannot be cancelled by the involution.

Proof. The involution σ maps ℒ ↔ 𝒫. The notation “1:1” denotes a bijection: every element in ℒ has exactly one image in 𝒫, and every element in 𝒫 has exactly one pre-image in ℒ.

The 1:1 exhausts σ — the bijection accounts for all paired elements. The “+1×ε” is the remainder: one additional element, the splinter, that does not participate in the bijection.

Therefore ε is not in the domain of σ. Therefore ε has no σ-image.

Note: Proposition 1 is independent of Theorem 1. It depends only on Axioms S and B. Whether or not the event horizon is the σ-boundary, ε has no σ-image.

The existence of an irreducible asymmetry is unconditional.

Because ε has no reflection in the 𝒫-sector, the 1:1 cannot perfectly close. The splinter holds the door open. Matter remains outside the horizon and antimatter remains inside, held apart by the structural geometry.

The visible universe exists because ε exists.

You exist because the axiom has a remainder. One uncancellable entry. One splinter that the mirror cannot reflect. That is you. That is everything you have ever seen.

5.3 — The ratio

The observed baryon asymmetry parameter is η ≈ 6 × 10⁻¹⁰. Approximately one extra baryon per billion photons.

The value debt (tracked across the body of work as KS-60, owned by AP26). The argument provides the structural reason for the asymmetry (ε has no σ-image, Proposition 1) but does not yet derive the ratio. Proposition 1 says the asymmetry must exist.

The magnitude requires a calculation: the ratio η may be derivable from the information content of the minimum viable splinter (ε) relative to the total degrees of freedom available at the epoch of segregation.

This calculation is owed.