---
author: 4NK Team
date: 2026-02-17
scope: v0/livre.md (global)
type: fix
related_corrective_chapters:
  - v0/chapitre25.md
---

# Fix: Enforce M0 “memory” disambiguation in `v0/livre.md`

## Problem

`v0/livre.md` uses the terms **mémoire / héritage / dépendance au passé / non‑Markovianité** across multiple chapters, but without a systematic declaration separating:

- **memory-structure**: a transmissible constraint register that constrains reachability; vs
- **memory-state**: apparent non‑Markov behavior induced by a projection / incomplete state (hidden variables).

Additionally, some algorithmic-complexity bullets used “Mémoire: O(…)”, which overloads the word “mémoire” with a computational “space” meaning inside the same book.

## Impacts

- Ambiguity between “non‑Markov because of projection” and “transmissible constraint memory”.
- Risk of importing “memory” as an explanatory primitive instead of tracking it as either a **register** or a **state-completeness** issue.
- Terminological collision between conceptual memory and computational memory (space usage).

## Cause

Memory/heritage sections were introduced and expanded chapter-by-chapter, but the book did not include a global, explicit M0 compliance pass.

## Root cause

No explicit global convention existed to force an **observable/state/projection/Markov-status/type** declaration whenever the “memory” vocabulary is invoked.

## Fix applied

Applied the correction **only** in `v0/livre.md`:

- Added an **M0 rule** and two **standard declarations** in the Introduction’s “Note de méthode (mémoire)”.
- Added an **M1 rule**: when an argument depends on past-dependence / a register \(K\), formulate it first on the minimal closed extended state, then discuss projections.
- Added **local M0 declarations** in sections/chapters where “heritage/memory/non‑Markov” is structural:
  - transmission-structure section (“mémoire des collisions”),
  - Chapter 6 (heritage),
  - Chapter 7 (distributed history),
  - “Héritage sans essence” section,
  - Chapter 13 (projection-induced non‑Markov) and “Dépendance au passé…” section,
  - “Verrouillage induit par héritage” section.
- Added minimal glossary rows for **mémoire transmissible** and **variable cachée** (M0 concepts).
- Replaced algorithmic complexity bullets “Mémoire: O(…)” with **“Espace: O(…)”** to avoid mixing conceptual memory with space complexity.
- Clarified two early “mémoire” mentions with “(au sens M0)”.

## Affected pages

- `v0/livre.md`

## Deployment / regeneration considerations

- If `v0/livre.md` is regenerated from `v0/chapitre*.md`, this fix can be overwritten. In that case, the M0 rule and local declarations should be ported to the corresponding source chapter files (keeping `v0/chapitre<n>.md` as the canonical sources).

## Analysis / verification steps

- In `v0/livre.md`, search for: `mémoire`, `héritage`, `dépendance au passé`, `non‑Markov`, `non-Markov`.
- Verify that sections using these notions include an explicit M0 declaration (observable/state, projection, Markov status, type).
- Verify that computational complexity bullets use `Espace:` (not `Mémoire:`).