# AP10 — DIVERGED, no source of record

**Checked 7 September 2026** by the paragraph-level test of record. The closest
candidate is `AP10_The_Dimension_FINAL.docx` (found in Formatted), and it is **not** the published
text: 7 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
AP10, 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 | `/AP10_The_Dimension.pdf` |
| sha256 | `b246e1240b5f3a3f177b39e66c426d007e8a9f89162cfded50b1d05905b01295` |
| Closest candidate | `AP10_The_Dimension_FINAL.docx` (Formatted) — NOT of record |

## In the source, absent from the published paper

- Axiom S (Symmetry) ↔ The exchange face. Two disjoint sectors L and P with order-reversing involution σ. On the embedded manifold, σ acts as a Z2 symmetry across one direction; that direction is the exchange face. Spatial. Signature: (+).
- Axiom B (Unique Breaking) ↔ The break face. One element ε ∈ L with no σ-image; valuation ν(L) - ν(P) = ν(ε) = 1. On the manifold, ε is a distinguished locus with a direction of advance; that direction is the break face. Spatial. Signature: (+).
- S (Symmetry). Two disjoint sectors L and P with order-reversing involution σ. Extensive quantities match: Q(L) = Q(P) in the unbroken case.
- B (Unique Breaking). One element ε ∈ L with no σ-image. Valuation: ν(L) - ν(P) = ν(ε) = 1. This is the break. Without B, the system is the 1:1 - perfectly symmetric, and nothing exists.
- Axiom S states: two disjoint sectors L and P with order-reversing involution σ.
- Consider two records, one in L and one in P, at the same time (R) and the same propagation distance (C). They still differ - they are in different sectors.
- S gives a symmetric involution (σ maps L → P and P → L equally).

## 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.*