Axioms (Inherited)

The four axioms of the record algebra, formally stated at AP20 section 3.3 and walked in detail in AP10 section 1.

S (Symmetry). Two disjoint sectors ℒ and 𝓟 with order-reversing involution σ. Q(ℒ) = Q(𝓟) in the unbroken case.

B (Unique Breaking). One element ε ∈ ℒ with no σ-image. ν(ε) = 1. The break. Under The Lock: ε = electron.

R (Record Monotonicity). Monoid, not group, in each sector. No non-identity element has an inverse. History is irreversible.

C (Constraint). Finite invariant rate c constraining sequential propagation. Structural, not electromagnetic.

Independent (the removal arguments at AP20 section 4.2, fenced at KS-P.2) and jointly exhibited by any existing record (AP20 section 6).

1.1 — Bridge hypotheses (now theorems)

EH (Embedding Hypothesis). In the large-N limit, the discrete record algebra admits faithful embedding into a smooth manifold M.

QRA (Quantum-Record Alignment). Quantum states are pre-state records (closed at AP20 section 5.5, KS-P.4). The cone boundary’s differentiability and leading-order quadratic structure used here rest on the smooth-manifold structure fenced at KS-P.5.

Both proven in AP20.

Under EH + QRA, the record algebra produces a Lorentzian manifold (M, g) with signature (−, +, +, +) and symmetry group SO(1, N).

The embedding is proven at AP20 (EH); the Lorentzian signature is carried by AP10 section 4’s structural argument, with the formal metric-level derivation fenced at KS-D.4.

Special relativity is a theorem, not an assumption.