# AP24 — DIVERGED, no source of record

**Checked 7 September 2026** by the paragraph-level test of record. The closest
candidate is `AP24_The_Residual_v2.docx` (found in Formatted), and it is **not** the published
text: 5 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
AP24, 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 | `/AP24_The_Residual.pdf` |
| sha256 | `3a052367dbbe520415754aff7054c7993f02eebc36074dd7c7907cfbf85b196d` |
| Closest candidate | `AP24_The_Residual_v2.docx` (Formatted) — NOT of record |

## In the source, absent from the published paper

- AP09 (The Break - Empty Set). The complex Hilbert space H. The fixed-point structure of §4.3 uses this complex structure (transcendental fixed points are generically irrational).
- The Planck length. lP = √(ħG/c3). Substitute G = 2κ/me2: lP = √(2ħκ/(me2c3)). The electron mass is under the root.
- the now - The actualisation state. The boundary between H and M. Immeasurable by structure.
- EP, mP, lP - Planck energy, mass, length. Built from G, c, ħ - hence built from faces of ε. The natural scale of the leakage. At EP, ε = O(1).
- AS - Actualisation State (the now). Boundary between H and M. Where αem is measured.

## 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.*