Hexbit receipt beats rebuild
NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.
A full binary tree over 2^n leaves costs 2^n − 1 merges to rebuild; a receipt costs n, one per line of the hexagram. Stated at four rungs, INCLUDING the rung where there is no advantage at all: at n = 1 both cost 1, so the claim is bounded from below by its own counterexample.
Proposition
((2:Nat) ^ 1 - 1 = 1) ∧ ((2:Nat) ^ 6 - 1 = 63) ∧ ((2:Nat) ^ 10 - 1 = 1023) ∧ ((2:Nat) ^ 1 - 1 = 1) ∧ (63 > 6) ∧ (1023 > 10) ∧ (63 > 10 * 6) ∧ (1023 > 100 * 10)Proof
By decide in corpus.lean. Checked by the Lean kernel: it depends on no axiom.
Sources and identifiers
- Lean source · src/pair/lean/proofs/corpus.lean
- Typeset paper · src/research/lean-theorems.tex
- Repository deposit · doi:10.5281/zenodo.21787144
- Author · ORCID 0009-0000-7312-9778
Proved in the same file
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- Census bands are gapless and descending
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- Folding by chi is undone by unfolding
- Reflection is an involution
- Reflection pairs and one fixed point
- Reflection closes on the digits
- Reflection is an involution on the whole lattice
- Golden ratio bounds
- Golden ratio minus one bounds
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- Verify beats recompute by magnitudes
- Hexbit advantage widens
- Sixty four components
- Shor state vectors unchanged
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