The distance to the target round trips on the record

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.

The distance to the target round-trips on the record: adding the target back to what remains returns every recorded count. That holds exactly when a count is at or above the target, so the record is read through the inverse of `remaining` instead of being compared to a literal.

Proposition

∀ n ∈ recorded, remaining n + 123 = n

Proof

By decide in wave-57-extraction-verified.lean. Checked by the Lean kernel: it depends on no axiom.

Sources and identifiers

• Lean source · src/pair/lean/proofs/wave-57-extraction-verified.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

• First descent is six
• Descent target is the census
• The descent is strictly monotone
• Remaining falls with the count
• Merging strictly decreases
• Line ceiling is fibonacci

All machine-checked theorems