non-integer dimension
Theorem.non-integer dimension — d = log N / log r — Koch log4/log3 ≈ 1.26186, Sierpiński log3/log2 ≈ 1.58496.
Proof.similarity dimension log N/log r — Koch 1.26186, Sierpiński 1.58496.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/water/cosmos/index.ts#similarityDimension
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
"non-integer dimension" 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 similarityDimension.
- 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 (similarityDimension @ 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 similarityDimension (src/water/cosmos/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.