Add DynamicSVD demo notebook (Fisher-information validation)

[cweniger]

Implements the notebook part of #114.

What

A new notebooks/ directory with an idealized, self-contained demo of falcon.embeddings.DynamicSVD — n = 100 data bins, 4-parameter models, exact Fisher-information ground truth from autograd (F = Jᵀ C⁻¹ J), no falcon runs and no estimator training. Four sections, each isolating one capability:

1. Basics — linear model + white noise: why variance ranking finds the informative subspace; compression 100 → 8 dims is lossless (information ratio ≈ 1).
2. How many components? — non-linear Gaussian-bump model: information ratio vs. k as a family over prior widths (wider prior ⇒ more components, the static picture of adaptive-round narrowing), multi-fiducial adequacy check, scree plot with unit noise floor, and Wiener shrinkage — explicitly framed as conditioning, not information (Fisher is invariant under it), demonstrated via per-component output variances and reconstruct(). Ends with the σ = 10 case exposing the hard-coded noise floor (DynamicSVD shrinkage assumes unit noise floor; shrinkage=False also disables normalization #113).
3. Streaming & Procrustes — one continuous prior-narrowing sweep, comparing two views of the same run: raw index-ordered components (sign flips and swaps at eigenvalue crossings) vs. the Procrustes-stabilized frame (smooth deformation), plus a basis-jump trace and the coefficients of a fixed observation across updates.
4. Colored noise — same model, noise from a non-trivial PSD (Toeplitz covariance): degraded Fisher ellipses and broken noise floor without whitening; ToeplitzWhitener restores both.

Infrastructure

• notebooks/jupytext.toml pairs every notebook in the directory as ipynb,py:percent. The .py file is the reviewable source of truth; the .ipynb is what GitHub renders and Colab opens.
• The notebook carries an Open in Colab badge and a pure-Python self-bootstrap cell (installs falcon from GitHub when missing; torch/numpy are preinstalled on Colab). All data is synthetic, seeds are fixed, no repo-relative paths.

Not in this PR (deliberately)

• No falcon source changes — the shrinkage noise-floor fix and the shrinkage/normalize flag split remain tracked in DynamicSVD shrinkage assumes unit noise floor; shrinkage=False also disables normalization #113; the notebook documents the current behavior and links there.
• The committed .ipynb has no outputs yet — it has not been executed. CI execution (nbmake), docs rendering (mkdocs-jupyter), and refreshing the stored outputs are tracked in Demo notebook for DynamicSVD (Fisher-information validation) + notebook CI/docs/Colab infrastructure #114.

🤖 Generated with Claude Code

https://claude.ai/code/session_01KUwdQQh7Vr9ArkBE9ahZGG

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 10.33%. Comparing base (d3c33ba) to head (76e0a6a).

Additional details and impacted files

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