hexbit receipt beats rebuild
Theorem.hexbit receipt beats rebuild — rebuild(n) = 2^n − 1 merges, verify(n) = n merges, ratio (2^n − 1)/n — combinatorial, so it carries no machine.
Proof.on the 2^n-leaf lattice a full rebuild costs 2^n − 1 merges and replaying a receipt costs n, both COUNTED not derived, agreeing with the sealed merkleFold at every rung and for an even and an odd leaf; at n = 6 that is 63 against 6, and at n = 1 there is no advantage at all.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/earth/iching/index.ts#hexbitVerifyBeatsRecompute
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
"hexbit receipt beats rebuild" 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 hexbitVerifyBeatsRecompute.
- 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 (hexbitVerifyBeatsRecompute @ src/earth/iching) 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 hexbitVerifyBeatsRecompute (src/earth/iching/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.