# AP04 — DIVERGED, no source of record

**Checked 7 September 2026** by the paragraph-level test of record. The closest
candidate is `AP04_The_Loop_Hypothesis_FINAL.docx` (found in Formatted), and it is **not** the published
text: 1 paragraph(s) in the source are absent from the
published PDF, and 1 published sentence(s) are absent from
the source.

**Until a matching source is produced, the published PDF's text is the source for
AP04, 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 | `/AP04_The_Loop_Hypothesis.pdf` |
| sha256 | `bcb20391bf72c09efb74ede567333c27858927330f94b9ebbfe71462a490f1c9` |
| Closest candidate | `AP04_The_Loop_Hypothesis_FINAL.docx` (Formatted) — NOT of record |

## In the source, absent from the published paper

- Z2 - the two-element symmetry group; 1:1 ≡ Z2 on Σ (I1), +1×ε ≡ Z2 breaking (I2).

## In the published paper, absent from the source

- define the quantum-gravity regime. p/tp = c demonstrates dimensional

*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.*