Expand description
A general d-dimensional cubical-homology engine — one engine, every rung of the ladder.
progress_complex produced π₁ (2 processes) and π₂ (3 processes) with hand-built 2D and 3D
complexes. Rather than write a 4D one, then a 5D one, this is the lift: a single cubical complex in
any dimension, computing the full Betti vector (β₀, β₁, …, β_d) over GF(2). Then the ladder is
literal — d processes → a (d−1)-sphere void → π_{d−1} ≠ 0 — and walking it toward the
∞-groupoid is just “one more process, one more dimension,” handled by the same code.
An elementary cube is a Cube: a minimal corner plus the set of free axes it extends along (its
dimension). Its boundary is the 2k faces obtained by pinning each free axis low or high. From a set
of filled top cells we take the downward closure, build the boundary matrices ∂_k, and read
β_k = #C_k − rank ∂_k − rank ∂_{k+1} — homology with no shortcuts, in arbitrary dimension.
Structs§
- Cube
- An elementary cube: the minimal corner, and the sorted set of axes it extends along (each by one unit). The dimension is the number of free axes; fixed axes hold the corner’s value.
- Cubical
Complex - A cubical complex, stored as the cells of each dimension
0..=dim.