The Symmetry Before The Break

Before the break, the pre-state is perfectly symmetric. You need to see what that symmetry looks like — all four generators, all four massless bosons — so you can feel what Axiom B does to it.

2.1 — The pre-state’s full symmetry

The pre-state — the 1:1, before any record is written — has the full symmetry of the Hilbert space ℋ.

From Axiom S: two sectors, involution σ, Z₂ symmetry. On the manifold (N = 3, AP10), this lifts to SU(2). SU(2) acts on the pre-state by rotating between the two sectors. It mixes ℒ and 𝒫 (Light and Dark — the two sectors of the record algebra, not cosmological dark matter/energy). Before the break, this mixing is exact. Both sectors are identical. Nothing distinguishes them. You cannot tell ℒ from 𝒫. They are perfect mirrors.

From AP09: complex amplitudes. The phase of any amplitude can be rotated by e^{iθ}. This is U(1)_Y — the hypercharge phase rotation. It acts on the pre-state by shifting the global phase. Before the break, this rotation is exact. No phase angle is preferred. All are equivalent. You cannot pick a preferred angle.

At the pre-state level this is the universal phase symmetry; field-specific hypercharge assignments and the detailed representation content are downstream of the sector/break coupling structure and are part of Gap E (section 8).

The full internal symmetry of the pre-state is SU(2) × U(1)_Y. This symmetry has four generators. SU(2) has three (the Pauli matrices, or equivalently, three independent rotations of the sector space). U(1)_Y has one (the hypercharge phase rotation). Four generators means four gauge bosons when the symmetry is expressed on the manifold: W¹, W², W³ from SU(2), and B from U(1)_Y. Before the break, all four are massless. The symmetry is exact.

2.2 — What “before the break” means

“Before the break” is not a moment in time. Time requires records (Axiom R). Before the break, there are no records. There is no time. “Before the break” means: the structure of the pre-state, considered without Axiom B. Axioms S, R, and C give SU(2) × U(1)_Y on the manifold. Axiom B is what changes it.