# Republish AP31 — The Alignment — FINAL v3 · dated notes 23 September 2026

The locked body is untouched. A Dated notes section is added on its own page after "What This Establishes and What Remains Open" and before "Claim Summary": four matters of record dated 23 September 2026. The contents page gains the entry and two page numbers move. 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 page numbers stripped; the paper's own Contents block is set aside, as the test of record provides.

The document's metadata author read `python-docx`; it is set to **Studio G**, as the procedure requires. Rendered in the house typeface, embedded. No decorative glyph anywhere.

## The notes, in one line each

1. **Debt 20 — paid at the structural register**, on the author's ruling of 23 September 2026: DERIVED-CONDITIONAL, the class of KS-COUP.1. The definition of the bias the proof stands on, the author's two rulings, the five premises, the result, and the three pieces owed at the formal register. The derivation and its check: `Debt_20_the_stability_proof_for_epsilon_2026-09-23.pdf` and `debt20_corridor_check.py`, beside this note.
2. **KS-31.2** — the claim sharpened to what is proved at the structural register; the test bounded to a wider coupled corridor sustained over three drift-times of the organism (D113). Status unchanged, LIVE — STRUCTURAL.
3. **KS-31.7** — the reading adopted: "structurally coherent" is judged before the outcome, by the load-bearing test; a system that passed and then destabilises fires the switch; it is not reclassified after the fact. Status unchanged, LIVE — EMPIRICAL.
4. **Debts 21, 22 and 23** — where they stand: 21 open with a floor; 22 folded into 21 (D116); 23 paid at the structural register by AP02 Theorem VI.2 (KS-COUP.1).

The full text of the notes: `DATED_NOTES_2026-09-23.md`, beside this note, and the paper itself from page 38.

## The published files, all kept

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

| | file | sha256 | pages |
|---|---|---|---|
| **published to 23 Sep 2026 (no notes)** | `proofs/instruments/AP31/AP31_The_Alignment_FINAL_v3_published_to_2026-09-23.pdf` | `0bfc7103b14164938ffc752faf1ec27b5de8b06ed289f6da8083b0c09921a8c7` | 42 |
| **published from 23 Sep 2026** | `/AP31_The_Alignment.pdf` — dated copy `proofs/instruments/AP31/AP31_The_Alignment_FINAL_v3_notes_1to4_published_2026-09-23.pdf` | `8bcc0e17f5772608f2b9e18921b288aeb87531b264f712eed494b8ef7a663086` | 43 |
| **source of record, before** | `proofs/instruments/AP31/AP31_The_Alignment_FINAL_v3.docx` | `4bf597715fc0c331e8b66aff3f543d883cec89477491d1b91b144444c90fee6a` | — |
| **source of record, from 23 Sep 2026** | `proofs/instruments/AP31/AP31_The_Alignment_FINAL_v3_dated_notes_2026-09-23.docx` | `0f8df0985cc9e3c2f72f50044fed2ad300cffda8f4e275b8cdced058c96f41c1` | — |

**The outgoing digest is cited by:** `proofs/instruments/AP31/SOURCE_OF_RECORD.md` as it stood to 23 September 2026. The preserved file above resolves it at a stable path.

## The registry

Two descriptions change by these notes — KS-31.2 and KS-31.7 — and the registry moves to v5.36 · 23 September 2026. No status moves. No count moves: 604 switches, 584 live, two fired. The debts table is unchanged; Debts 20 to 23 are this paper's own.

Listing line: **AP31 · The Alignment · FINAL v3 · dated notes 23 September 2026**

Ruled by G, 23 September 2026 (the chat of that date; "I think it closes").

*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.*