# AP03 — DIVERGED, no source of record

**Checked 7 September 2026** by the paragraph-level test of record. The closest
candidate is `AP03_The_Ratio_FINAL.docx` (found in Formatted), and it is **not** the published
text: 3 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
AP03, 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 | `/AP03_The_Ratio.pdf` |
| sha256 | `b1be754da741b4ccd173637a0ff49a83b653b5098243c00633b6ccc64a554284` |
| Closest candidate | `AP03_The_Ratio_FINAL.docx` (Formatted) — NOT of record |

## In the source, absent from the published paper

- D-AP03.1. The substrate parameters α and β in the kinetic term L = 1⁄2α(∂τφ)2 - 1⁄2β(∇φ)2 - V(φ) are introduced but not derived from a more fundamental theory. Their ratio gives c2 = β/α, but neither α nor β individually is computed from the axioms. This is the deepest open problem in AP03 - distinct from and prior to the G derivation. A truly pre-geometric formulation would derive the distinction
- Postulate E0 - Z2 Minimality. The symmetric pre-state S has Z2 symmetry. The simplest non-trivial symmetry group. Motivated by parsimony but not derived from first principles. Tested via KS-R.2: any falsification of the binary decomposition is also a falsification of Z2 minimality.
- Theorem 3.1 - Z2 Decomposition. The irreducible representations of Z2 are exactly two: the trivial representation and the sign representation. Any representation of Z2 decomposes into copies of these two. There cannot be a third fundamental sector. Proof: section 8.

## 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.*