algo/fixKnowledge/2026-02-17-v0-livre-latex-subscript-corruption.md

author	date	scope	type
4NK Team	2026-02-17	v0/livre.md	fix

Fix: LaTeX subscript corruption (*{...} / *+) in v0/livre.md

Problem

Several mathematical expressions in v0/livre.md used a non-LaTeX marker * where a subscript _ is expected, for example:

• ((x_t)*{t\ge 0}) instead of ((x_t)_{t\ge 0})
• x*{t+1} instead of x_{t+1}
• \mathbb{R}*+ instead of \mathbb{R}_+
• t*{n+1} instead of t_{n+1}

This corruption is not present in v0/chapitre4.md and breaks the intended mathematical notation.

Impacts

• LaTeX rendering and readability are degraded (subscripts are no longer syntactically correct).
• Risk of semantic confusion in definitions (e.g., orbit definition and time accumulation recursion).
• Divergence between the source chapter (v0/chapitre4.md) and the compiled book (v0/livre.md) on notation.

Cause

v0/livre.md contains occurrences of *{...} and *+ in places where LaTeX subscripts are expected.

Root cause

Unidentified transformation step or manual editing introduced * in place of _ in parts of v0/livre.md. At this stage, no build/compile rule has been identified that would legitimately require *{...} as an intermediate syntax.

Fix applied

Corrections were applied only in v0/livre.md (source chapter files are unchanged):

• Chapter 2: sequence notation in the detailed repetition bound block
  • ((x_t)*{t\ge 0}) → ((x_t)_{t\ge 0})
  • x*{t+1} → x_{t+1}
• Chapter 3: orbit definition
  • \((x_t)*{t\ge 0}\) → \((x_t)_{t\ge 0}\)
  • \(x*{t+1}=f(x_t)\) → \(x_{t+1}=f(x_t)\)
• Chapter 4: weighted clock section
  • \mathbb{R}*+ → \mathbb{R}_+
  • t*{n+1} → t_{n+1}
• Chapter 5: subscripts in partitions and transmission definitions
  • \{F_a\}*{a\in A} → \{F_a\}_{a\in A}
  • \bigsqcup*{a\in q(X)} → \bigsqcup_{a\in q(X)}
  • \mathcal{I}*\gamma → \mathcal{I}_\gamma
  • S*\gamma → S_\gamma
• Chapter 6: subscripts in multi-segments and memory updates
  • \{[i_p,j_p]\}*{p=1}^k → \{[i_p,j_p]\}_{p=1}^k
  • S*\gamma → S_\gamma
  • S'*t → S'_t
  • S'*{t+1} → S'_{t+1}
  • S*{m_t,t} → S_{m_t,t}
• Chapter 7: subscripts in filters and norms
  • \mathbf{1}*{M(a,b)\ge \theta} → \mathbf{1}_{M(a,b)\ge \theta}
  • F*\theta → F_\theta
  • \|M_{\mathcal{T}}\|*1 → \|M_{\mathcal{T}}\|_1
  • \sum*{a,b} → \sum_{a,b}
  • \sum*{i\in V} → \sum_{i\in V}
  • n*{\max} → n_{\max}
• Chapter 8: subscripts in semi-flow, basin entropy, and Markov metrics
  • \{\Phi_t\}*{t\ge 0} → \{\Phi_t\}_{t\ge 0}
  • \Phi*{t+s} → \Phi_{t+s}
  • \{B(C_i)\}*{i=1}^K → \{B(C_i)\}_{i=1}^K
  • H*{\mathrm{bassins}} → H_{\mathrm{bassins}}
  • h|*C → h|_C
  • h|*{X\setminus (B\cup C)} → h|_{X\setminus (B\cup C)}
  • \mathbb{E}*x[\tau_B] → \mathbb{E}_x[\tau_B]
  • \sum*{y\in B} → \sum_{y\in B}
  • (X_t)*{t\ge 0} → (X_t)_{t\ge 0}
  • X*{t+\tau} → X_{t+\tau}
• Chapter 9: subscripts in selection expectation
  • \mathbb{E}*{S_w p}[w] → \mathbb{E}_{S_w p}[w]
• Later occurrence (selection/fitness proposition)
  • \mathbb{R}*+ → \mathbb{R}_+

Affected pages

• v0/livre.md

Deployment / regeneration considerations

• If v0/livre.md is regenerated by a build script (e.g., concatenation from v0/chapitre*.md), these manual fixes can be overwritten.
• To make the fix persistent, the generating pipeline should be audited to ensure it does not introduce * in place of _.

Analysis / verification steps

• Search for corrupted markers in v0/livre.md:
  • *{ (brace-form subscripts)
  • *+, *\infty, *<digit>, *<letter> (non-brace subscripts)
• Compare with corresponding source chapters (v0/chapitre*.md) to confirm whether the corruption is book-only or source-level.