The hard part: not self-replication (engineering), but the GEOMETRY.
Given MachineState M at time t, where IS it on the manifold?
Product manifold decomposition:
- Stack: Δ₇ (7-simplex, Fisher-Rao metric)
- FAMM: ℝ⁴ⁿ (delay-competition metric)
- Scars: M(Δ₇) (pressure-weighted measures)
- Full state: Δ₇ × ℝ⁴ⁿ × M(Δ₇) with block-diagonal metric
Computed coordinates for default quine.py state:
- Stack: (0.5,0,0,0,0,0.5,0,0) on Φ-Σ edge of Δ₇
- FAMM: (1.0,-0.693,2.0,1.0,2.0,0.0,1.0,0.5) in log-delay coords
- Scar: 0.1 point mass at Φ-Σ edge
- Total: 25 coordinates
Key insight: program execution IS geodesic flow on this product
manifold. Boundaries (fuel=0, Gödel boundary) are where the
interesting things happen.
Refs: ChentsovFinite.lean (unique metric), quine.py (state),
UniversalMathEncoding.lean (16D chaos space)
