Bug: community hierarchy is inverted (fine partition has fewer clusters than coarse)

[raphasouthall]

Summary

`vault_stats` reports `communities_coarse=12` and `communities_fine=8`. Textbook Hopfield dynamics (low β = broad basins, few clusters; high β = narrow basins, many clusters) says fine should be greater than coarse. On a 458-note vault, the fine partition has 2 giant (≥100-note) clusters and zero small ones, while the coarse partition has 1 giant and 2 tiny ones.

level	count	min	max	mean	giants ≥100
0 β=0.5 ('coarse')	12	3	121	38	1
1 β=2.0 ('fine')	8	11	123	57	2

Root cause

Three compounding issues in `src/neurostack/attractor.py`:

1. Shared top-K sparsification (`TOP_K_NEIGHBORS=50`, line 61; applied at L237-238). At high β, softmax concentrates on the largest neighbour, and identical top-K neighbour sets funnel notes into a handful of hub-attractors. Raising β counter-intuitively helps hubs monopolise basins.
2. Singleton merging (`_assign_communities`, L296-315) merges every 1-note basin into its nearest non-singleton. At β=2.0 many notes converge to their own attractor and then get absorbed — fine level has 0 singletons pre-merge.
3. Only β differs between levels. Same similarity matrix, same initial state (`np.eye`, L244), same sparsification.

`communities_summarized: 20` is not a third count — it's `12+8` concatenated (rows from both levels live in the same table). See `tools/search_tools.py:400-402` and `community.py:183-190`.

Proposed fix

1. Per-level top-K. Add `TOP_K_COARSE=80` and `TOP_K_FINE=20` in `attractor.py:61`; thread through `_attractor_convergence`.
2. Gate singleton-merge at fine level. Add `merge_singletons: bool = True` arg to `_assign_communities`; call with `False` at β=2.0 or only merge if similarity to a non-singleton exceeds a threshold.
3. Report sizes + modularity in stats. `search_tools.py:394-402` — add `min/max/mean_size` and modularity per level so regressions are visible.
4. Modularity sanity check after assignment in `attractor.py` — warn if `Q(fine) <= Q(coarse)`.
5. Naming. If tuning can't reliably deliver `n_fine > n_coarse` on all vaults, rename `coarse`/`fine` → `broad`/`narrow` (describes attractor width, not partition-size). Update `BETA_COARSE`/`BETA_FINE` constants, stats keys, and `vault_communities` docstring.

Expected effect

Fine partition retains narrow basins. Hierarchy is either truly hierarchical or honestly named. Stats surface the size distribution so anomalies are obvious.

Key files

• `src/neurostack/attractor.py:42-50, 61, 237-238, 273-325, 417-441`
• `src/neurostack/tools/search_tools.py:394-402`
• `src/neurostack/community.py:183-190`

[raphasouthall]

Acceptance criteria

One of:

• Option A (fix hierarchy): `communities_fine > communities_coarse` on the working vault after tuning; max cluster size at fine level < max at coarse
• Option B (rename): keys renamed to `communities_broad` / `communities_narrow`; constants `BETA_BROAD` / `BETA_NARROW`; `vault_communities` docstring updated

Plus (either option):

• `vault_stats` reports per-level `min_size`, `max_size`, `mean_size`, `modularity_Q`
• Per-level `TOP_K` configurable (e.g., `TOP_K_COARSE=80`, `TOP_K_FINE=20`)
• `_assign_communities` singleton-merge gated by a threshold OR disabled at fine level
• Index-time warning fires if `Q(fine) <= Q(coarse)` (Option A) or equivalent sanity assertion (Option B)
• `neurostack doctor` surfaces any hierarchy inversion

Dependencies

• Depends on: Improvement: co-occurrence table is 62% of DB and 82% noise #34 (NPMI changes the similarity matrix feeding the attractor — tuning community clustering on current weights is wasted effort).
• Blocks: nothing downstream; isolated subsystem.

Sequencing

Phase 4 (rework). Hold until #34 is merged.