n-cube face counts
Theorem.n-cube face counts — f_k(n-cube) = C(n,k)·2^{n−k} — the tesseract counts 16, 32, 24, 8.
Proof.C(n,k)·2^(n−k) — the tesseract counts 16-32-24-8.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/cosmos/index.ts#hypercubeFaces
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"n-cube face counts" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation hypercubeFaces.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (hypercubeFaces @ src/water/cosmos) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes hypercubeFaces (src/water/cosmos/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.