Dependency and Scope

0.1 What this paper does

This paper derives the structural mechanism of baryogenesis from {S, B, R, C}.

The observed matter–antimatter asymmetry arises from topological segregation at the actualisation event: matter propagates outward (the ℒ-sector, 1-poles), antimatter collapses inward (the 𝒫-sector, 0-poles, the interior of event horizons).

The net asymmetry is held open by the break ε, which has no σ-image (Proposition 1, unconditional).

The Horizon Conjugation Theorem (§4) derives the identification of the event horizon as the σ-boundary from the axioms, via algebraic quantum field theory (AQFT) and the Bisognano–Wichmann / Sewell modular conjugation theorem.

The two-sector topology (§4.2) resolves the Kruskal region mismatch. Five tagged gaps remain (§4.4); KS-46 is upgraded from LIVE—HARD to ADDRESSED.

The paper does not derive the numerical value of the baryon asymmetry (η ≈ 6 × 10⁻¹⁰). This debt is tracked across the body of work as KS-60, owned by AP26 (The Surplus).

0.2 Dependencies

The dependency chain: Axiom S (Symmetry — σ-involution, two sectors) → Axiom B (Break — ε has no σ-image) → AP17 (The Room: 0-pole/1-pole structure, the Eye) → AP08 (Einstein field equations, Schwarzschild solution) → this paper (Theorem 1: event horizon = σ-boundary; σ̂ = CPT at the horizon).

Depends on: Axiom S (Symmetry — σ-involution), Axiom B (Break — ε has no σ-image), Axiom R (Record — irreversibility; kills white holes), Axiom C (Constraint; forces fold; microcausality), AP05 (Lorentzian spacetime; Poincaré covariance), AP09 (complex Hilbert space), AP08 (Einstein field equations; Schwarzschild solution), AP17 (the Eye; 1-pole/0-pole), AP20 (AS = manifold), AP21 (Steiner tree; Energy–Measure Bridge).

0.3 Axiom mapping

Axiom S supplies the involution σ (two sectors, ℒ ↔ 𝒫) and, with it, the σ-boundary. Axiom B supplies the break ε, which has no σ-image — the uncancellable entry that keeps the ledger from closing. Axiom R kills the white-hole region (records cannot be unwritten), collapsing the four-region Kruskal structure. Axiom C forces the fold and bounds propagation at c, fixing the causal structure in which the event horizon is defined.

0.4 Epistemic status per section

Epistemic status per section. §1 (Crisis of Asymmetry): historical — summary of the baryogenesis problem and Sakharov conditions. §2 (Involution and the Eye): established — summarises Axiom S and AP17. §3 (Two Kinds of Antimatter): derived — local antimatter from pair production is standard; distinction from net asymmetry follows from σ-structure. §4 (Horizon Conjugation): derived — Theorem 1 proved via Tomita–Takesaki modular theory and the Bisognano–Wichmann / Sewell line, with the two-sector topology resolving the Kruskal region mismatch; five tagged gaps (§4.4), all SMALL or smaller, with Gap 5 CLOSED. §5.1 (Segregation): derived — matter outward / antimatter inward follows from Theorem 1 + AP17. §5.2 (Door Stays Open): derived — ε has no σ-image, from the axiom directly, formalised as Proposition 1, independent of Theorem 1. §5.3 (Ratio): debt — structural reason derived; numerical magnitude owed (tracked as KS-60, AP26). §6 (Formal Mapping): derived — quantum-number balance follows from Theorem 1, formalised as Proposition 2.

0.5 Kill switch summary

Five kill switches engage on this paper. KS-46 (black-hole conjugation) is ADDRESSED, split into KS-46A (boundary identification, DERIVED), KS-46B (AQFT bridge, ADDRESSED — bifurcation tension discharged via Sewell 1982, broader bridge SMALL gaps remaining), and KS-46C (operator identification, ADDRESSED). KS-47 (global baryon number) and KS-53 (Hawking evaporation products) are LIVE — EMPIRICAL: both are quantitative predictions with teeth.

0.6 Structural debts owed

The numerical value of the baryon asymmetry, η ≈ 6 × 10⁻¹⁰, is owed. This paper derives the structural reason for the asymmetry (ε has no σ-image); the magnitude is a calculation, tracked across the body of work as KS-60 and discharged in structural form by AP26 (The Surplus). The mass-balance question — whether the mass inside all horizons can account for the missing antibaryonic content — is carried as KS-47.

0.7 Items held open without claiming debt status

The five gaps tagged in §4.4 (AQFT framework adaptation, anti-linearity construction on the specific algebra, the Hartle–Hawking / σ-invariance identification, rotating black holes, and the bifurcation tension — the last now closed via Sewell 1982). The remaining gaps are all SMALL.

0.8 Structural relationships

AP22 reads after AP17 (the Eye), AP08 (the Schwarzschild horizon), AP21 (the Energy–Measure Bridge and filament fragmentation), and AP20 (AS = manifold). It opens onto AP26 (The Surplus), which reads the same surplus as the energy of the break, η = E(ε); the two papers are complementary — AP22 gives the mechanism (where the antimatter is), AP26 gives the form (how much matter is left), reconciled by the cross-horizon balance: the surplus on our side is matched by an equal and opposite surplus on the other, total exactly zero.