# AP16 — DIVERGED, no source of record

**Checked 7 September 2026** by the paragraph-level test of record. The closest
candidate is `AP16_The_Break_Electroweak_v2.docx` (found in Formatted), and it is **not** the published
text: 6 paragraph(s) in the source are absent from the
published PDF, and 0 published sentence(s) are absent from
the source.

**Until a matching source is produced, the published PDF's text is the source for
AP16, and the AP30 republish procedure is not available to it.** No file is
copied into this folder, so nothing here can be harvested by mistake.

| | |
|---|---|
| Published PDF | `/AP16_The_Break_Electroweak.pdf` |
| sha256 | `d361386650e20b8ce988f2b201d8cffc3b9b13e7e2d0d41a4b09706ee5d44cda` |
| Closest candidate | `AP16_The_Break_Electroweak_v2.docx` (Formatted) — NOT of record |

## In the source, absent from the published paper

- L and P are the two sectors of Axiom S, connected by the involution σ: L ↔ P. ε is the break - the unique unpaired element of Axiom B. ν is the valuation; ν(ε) = 1 is the minimum nonzero value. Z2 is the two-element group; π1(SO(3)) = Z2 is the fundamental group of SO(3) in three spatial dimensions.
- Axiom S (two sectors / involution). The two sectors L and P give the Z2 classification that lifts to SU(2) on the manifold (via Z2 = π1(SO(3)) in N = 3, AP10; double cover SU(2) → SO(3), AP11). Load-bearing for the pre-break symmetry.
- Axiom B: one element ε ∈ L with no σ-image in P. Valuation ν(ε) = 1. The minimum viable splinter.
- Axiom B → ε ∈ L, no σ-image in P → sectors no longer interchangeable → SU(2) broken → U(1)em survives → SU(2) × U(1)Y → U(1)em. Electroweak symmetry breaking.
- Claim. The derivation maps the two sectors (L, P) to the SU(2) weak isospin doublet. The two-component structure of weak isospin matches the two-sector structure of Axiom S.
- 3 (The Break). DERIVED. Axiom B places ε in L with no σ-image in P. SU(2) × U(1)Y → U(1)em. Three generators broken (W+, W-, Z0 acquire mass via coupling to ε). One generator survives (the photon stays massless). The Higgs field = ε as background condition. The electron = ε as localised excitation. The Higgs mechanism = Axiom B.

## In the published paper, absent from the source

*(none)*

*Each item is either a pre-publication draft difference, which is nothing, or a paragraph G edited after publication, which becomes a dated note. That is G's reading to make.*