feat(core): integrate ternary-graph route module — RoomGraph for room routing, communities & topology analysis

[SuperInstance]

Summary

The RoomGraph gives pincher actual pathfinding — rooms aren't just piles of data anymore. This PR integrates the ternary-graph crate (zero-dependency, #![forbid(unsafe_code)]) into pincher-core as the route module.

What's Added

New module: pincher-core/src/route/mod.rs — a RoomGraph wrapper over the ternary-weighted graph substrate:

Pathfinding

• distances_from() — Bellman-Ford shortest paths (handles negative edges)
• all_distances() — all-pairs via Floyd-Warshall
• route_cost() — single-pair shortest path
• next_hop() — cheapest forward-progress neighbor

Community Detection

• detect_communities() — label propagation (positive edges attract, negative repel)
• cluster_rooms() — spectral clustering via power iteration on signed Laplacian
• community_modularity() — signed modularity scoring

Topology Analysis

• trusted_components() — connected components over positive (trusted) edges only
• degree(), adjacency(), laplacian(), normalized_laplacian(), degree_matrix()

Factory

• build_routing_graph() — quick construction from room name slices

Why This Matters

Room relationships in PincherOS are naturally ternary: trusted (+1), adversarial (-1), or neutral (0). The ternary-graph ecosystem models this directly, giving us:

1. Signed shortest paths — route around blocked rooms, prefer trusted corridors
2. Community structure — discover which rooms naturally cluster via label propagation or spectral clustering
3. Modularity scoring — evaluate partition quality numerically
4. Trusted subgraph isolation — identify fully-trusted zones

Build & Test Results

$ cargo check -p pincher-core
    Finished dev profile [unoptimized + debuginfo]

$ cargo test -p pincher-core
    Finished test profile [unoptimized + debuginfo]
    running 140 tests
    test result: ok. 140 passed; 0 failed; 0 ignored; 0 measured

140 tests pass (129 pre-existing + 11 new route module tests). Zero regressions.

Phase 1 Roadmap Progress

This advances the ternary integration roadmap steps:

Step	Status
ternary-graph dependency	✅ Merged
Route module (RoomGraph)	✅ This PR
Community detection	✅ In route module
Spectral clustering	✅ In route module
Graph persistence (serde)	🔜 Next — needs ternary-graph serde support
RPC exposure	🔜 Future

Notes

• Uses directed graphs for blocked edges to avoid automatic negative cycles from undirected Neg edges
• ternary-graph v0.1.0 at commit fdf1355e — zero transitive dependencies, zero risk of version conflicts
• All doc examples use ignore to avoid requiring network access for doctest fetching

[SuperInstance]

This PR is superseded by #7 (integrate-ternary-types) which takes a more aligned approach: using ternary-types as the lightweight shim crate rather than the full ternary-graph external dependency. The route module in #7 provides the same RoomGraph, pathfinding, and community detection functionality inline.

Closing this PR — the functionality is delivered via the superior architecture.

[SuperInstance]

Superseded by PR #7