Implement Sophia MVP scaffold (stages 0–3 + topology pivot)

Six-crate Rust workspace (core/sim/llm/store/server/bin) backing a
Three.js + WebGL frontend. Live at http://127.0.0.1:7777 via `cargo run`.

Sim
- Event-driven scheduler with min-heap, per-engram tick, staggered Spawn
  events (40 ms apart) so each engram's flight is visually readable.
- Solid-donut torus topology (replaces original spherical density-driven
  shell, see Topology Pivot in docs/system-analysis.md). Configurable
  major/minor radii in config.toml; live `POST /api/galaxy/:id/resize`.
- Physics: Verlet integration + friction; in-hole pull + galactic spin
  (CCW around +z) for spiral-ejection ejection from the donut centre;
  soft tube boundary with velocity-reflecting wall.
- Cosine-weighted gravity (kiddo k-NN within radius 25, threshold 0.50)
  and synapse formation (threshold 0.62) gated to inside-the-tube only.
- LM Studio integration via OpenAI-compatible REST: batched embeddings,
  optional Bearer auth, semaphore-bounded parallel ops per §13.5.

Server
- axum HTTP + WebSocket. Routes: /healthz, /api/galaxy CRUD, /seed,
  /ingest, /resize, /engrams/:id, /ws/galaxy/:id/events.
- Binary 12-byte-aligned position frames at ~20 Hz; JSON for sparse
  events (Hello, EngramCreated, SynapseCreated, TorusUpdated).
- Layered config: config.toml (defaults) + config.local.toml (secrets,
  gitignored) merged on startup.

Frontend
- Vite + vanilla TypeScript + three.js 0.169.
- Engrams render as additive bloom-friendly point sprites with a
  per-engram hash-driven hue rotation and breathing pulse.
- Comet-style velocity-aligned trails; additive ribbon synapses whose
  endpoints track engram positions every frame.
- UnrealBloomPass + ACES tone-mapping for the linked-particles look.
- HUD shows torus dims, engram + synapse counts, LM Studio status;
  controls for seed, ingest, and live torus resize.

Docs
- README replaced with docs/IDEA.md; system-analysis.md updated with
  the topology pivot decisions and Galaxy Ejection refinement notes
  (the implementation plan lives in ~/.claude/plans, gitignored).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

crates/sophia-core/src/slate.rs

@@ -0,0 +1,35 @@
+use serde::{Deserialize, Serialize};
+
+/// Universal Slate (per §13.1) — Stage 2 layer 1 only: a dense embedding
+/// vector. The deeper LLM-comparison layer arrives in Stage 4.
+#[derive(Debug, Clone, Serialize, Deserialize)]
+pub struct Slate(pub Vec<f32>);
+
+impl Slate {
+    pub fn dim(&self) -> usize {
+        self.0.len()
+    }
+
+    pub fn norm(&self) -> f32 {
+        self.0.iter().map(|x| x * x).sum::<f32>().sqrt()
+    }
+
+    /// Cosine similarity in `[-1, 1]`. Returns 0 if either vector is zero or
+    /// dimensions disagree (the latter can happen across embedding model
+    /// changes — see §13 risk #3).
+    pub fn cosine(&self, other: &Slate) -> f32 {
+        if self.0.len() != other.0.len() {
+            return 0.0;
+        }
+        let mut dot = 0.0_f32;
+        let mut a2 = 0.0_f32;
+        let mut b2 = 0.0_f32;
+        for (a, b) in self.0.iter().zip(other.0.iter()) {
+            dot += a * b;
+            a2 += a * a;
+            b2 += b * b;
+        }
+        let denom = (a2.sqrt() * b2.sqrt()).max(1e-9);
+        dot / denom
+    }
+}