# Republish AP47 — The Flip — FINAL v3 · dated notes 7 September 2026

The locked body is untouched. The notes are appended after the section that closes the argument. Verified after the build: the source of record placed beside this note reproduces the new PDF paragraph for paragraph, and **every body sentence of the paper as published before any note was appended is present in the new PDF** — 0 lost, checked sentence by sentence with running heads, page numbers and Contents stripped.

One further change, in the front matter only: the Contents entry for **6 — The Application, Once** read page 12. That heading is on page 11, and was on page 11 in the previous PDF too — the typed number was wrong before this republish. Word's own pagination now supplies 11. Dress, not body.

## A date corrected

An earlier build of these notes was published for about an hour on 7 September 2026 carrying the date **9 September 2026** — the date on the desk's draft, not the date the notes were appended. The ruling is explicit: *the date on each note is the date WC appends it*. That is 7 September 2026, and this build carries it. The misdated file is kept beside this one, never deleted, and it is permanent in Zenodo version `10.5281/zenodo.22646076`.

## The published files, all kept

*Beside, never replaced* applies to the rendered PDF as well as the text.

| | file | sha256 | pages |
|---|---|---|---|
| **published for one hour, 7 Sep 2026 (note misdated 9 Sep)** | `proofs/instruments/AP47/AP47_The_Flip_FINAL_v3_notes_dated_2026-09-09_superseded.pdf` | `c0be5d61157b6ddb8f076ef266c3ad6e0f048d000f245228e10e9755d296893b` | 17 |
| **published from 7 Sep 2026** | `/AP47_The_Flip.pdf` | `3adae0106d96eaabad2bd953e45681cd7d4023228e60d5a421df4ff357355aca` | 17 |

**The outgoing digest is cited by:** `proofs/instruments/AP47/NOTE_REPUBLISH_2026-09-09.md`, `proofs/instruments/AP47/SOURCE_OF_RECORD.md` — frozen files where they are frozen, not edited. The digest resolves to the preserved file above, kept at a stable path for that reason.

## The notes, for the record

> 7 September 2026. Two matters of record. Nothing in the body is altered.
>
> 1. The second-order correction written in §5 as a divisor, Δ_bare/(1 + α²/8π), reads as the multiplier, Δ_bare·(1 − α²/8π): the isotropic-leakage lemma has one form everywhere in the corpus, because a returned leak is not an expression and does not itself leak (AP30 dated note 9; AP49 §4). At this paper's precision the two differ by 4.5 × 10⁻¹²; no digit moves.
>
> 2. §5's retirement of the identification of the four dimensions with the four conditions applies to this paper's derivation chain, which did not need it; it is not a ruling against AP10, which identifies each of the four axioms with one face of the manifold.
>

Listing line: **AP47 · The Flip · FINAL v3 · dated notes 7 September 2026**

Ruled by G, 7 September 2026 (`Dated_Notes_for_WC_2026-09-07_1.docx`).

*A locked body is never edited, replaced or removed — corrections go beside it by dated note. A lemma that must be rewritten becomes v2.0 with v1.0 kept beside it.*