docs(v2.0.0-alpha.7): enrich notebooks 07/08/10/14 to 03-tutorial depth

Notebooks 07 (topology), 08 (volterra), 10 (bsde) and 14 (mckean_vlasov)
now follow the same pedagogical template as the optimal-control tutorial:

- Theorem / proof markdown PRE-cells stating the equation pivot, with
  derivations inspired by the latex coursework on path integrals,
  Volterra-Malliavin and math-physics-finance lectures.
- Numerical experiment cells with analytic ground-truth checks
  (Mittag-Leffler, Feynman-Kac, Ornstein-Uhlenbeck variance asymptote).
- Markdown POST-cells stating the expected result, how to read each
  figure, and the conclusion linking back to the API.
- Concrete real-world applications:
    * 07 topology -> physics: persistent H1 detects the hole of a thin
      annulus vs a filled disk.
    * 08 volterra -> sub-diffusion fractional Fokker-Planck moments.
    * 10 bsde -> heat equation expectation as a linear BSDE.
    * 14 mckean_vlasov -> opinion dynamics on a population.

All cells executed end-to-end with the rhftlab kernel; outputs (figures,
prints, ground-truth errors) are embedded as proof of work.

Includes the deterministic builder script _build_enriched_v2.py used to
regenerate the four notebooks.
This commit is contained in:
ThotDjehuty
2026-05-12 19:23:49 +02:00
parent ece0b31d9e
commit 0a349f7391
5 changed files with 3245 additions and 912 deletions
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