# Hierarchical three-layer journal manuscript

This directory is the publication-oriented source for:

> **Sequential Feature Recovery in a Three-Layer Network: Exact Hermite
> Geometry, a Conditional DMFT--RMT--BBP Closure, and Muon Experiments**

## Build

```bash
latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex
```

If `latexmk` is unavailable, the equivalent explicit sequence is:

```bash
pdflatex -interaction=nonstopmode -halt-on-error main.tex
bibtex main
pdflatex -interaction=nonstopmode -halt-on-error main.tex
pdflatex -interaction=nonstopmode -halt-on-error main.tex
```

The output is `main.pdf`.  The source uses only standard TeX Live packages,
BibTeX, and checked-in figures.

## Scientific status

Read `CLAIM_LEDGER.md` before editing theorem language.  The manuscript keeps
four levels separate:

1. exact finite deterministic statements proved in the paper;
2. imported block-Wishart results under bounded-block hypotheses;
3. conditional BBP and DMFT consequences with named missing assumptions;
4. finite empirical observations.

In particular, neither a joint reused-sample DMFT nor a raw polynomial
dynamic-BBP theorem is currently claimed.

`LITERATURE_MAP.md` explains the role and non-role of every research lineage:
hierarchical feature recovery, MSRJD/DMFT, block-Wishart RMT, BBP, Kac--Rice,
cavity/replica/AMP, and Muon.  In particular it distinguishes population,
fresh-sample, same-data trajectory, and critical-point Hessian laws.

The general-link extension is rigorous at the population level: explicit
Hermite-tail norms control risk, gradient, and Hessian truncation.  The
high-dimensional dynamic closure remains conditional on separately listed
DMFT, bulk, local-law, and tail/data-reuse hypotheses.

Muon-\(a\) is treated as an AMP-like nonseparable spectral channel, not
silently renamed AMP.  The manuscript derives its exact Fr\'echet derivative
and states the dynamic-cavity/long-memory Onsager construction that would be
needed for a genuine state evolution.  The replica route is used only as a
static equilibrium and fixed-point consistency target.

## Reproducibility

The scripts and stored results are in:

```text
experiments/brainstorm/resnetl3/
```

`analyze_hierarchical3_confirmatory.py` derives all paired intervals, exact
sign tests, and censored sector-time summaries directly from the stored
trajectory CSV.  The checked-in figures in `figures/` are byte-identical
copies of the reference experiment outputs.
