# AP19 — DIVERGED, no source of record

**Checked 7 September 2026** by the paragraph-level test of record. The closest
candidate is `AP19_The_Direction_v2.docx` (found in Formatted), and it is **not** the published
text: 4 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
AP19, 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 | `/AP19_The_Direction.pdf` |
| sha256 | `50e6662473f0e074ae98bdc77c5390d2db003da5f312ce711d98a17e1f72d466` |
| Closest candidate | `AP19_The_Direction_v2.docx` (Formatted) — NOT of record |

## In the source, absent from the published paper

- AP09 (The Break - Empty Set). The complex Hilbert space H and the Born rule. Load-bearing for the Lemma in §4.2: the orientation state is in C3 (not R3), which forces SU(3) (not SO(3)).
- Axiom S. The two-sector structure (l, P) and the involution σ. σ acts on the orientation state by complex conjugation, giving antiquarks the conjugate representation C3̄. Provides the paired/unpaired distinction that underwrites the "three faces are interchangeable in spatial expression" claim of §3.4.
- Why the orientation is quantum (C3, not R3). Before collapse, the faces carry no spatial assignment. They exist in superposition across all possible geometric arrangements. The complex amplitudes of C3 describe this superposition. A classical orientation (R3, SO(3)) would describe a manifold that already has a definite spatial arrangement - but that is the post-collapse particle view, not the pre-
- C3 - The complex three-dimensional vector space; the orientation state lives here (Lemma in §4.2).

## 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.*