The exact weighted cycle for the Frid digit family

Abstract

The exact weighted cycle for the Frid digit family

Theorem 1.1 (a_seed_cycle).

$$\forall k\in \mathbb{N},\forall z\in \mathbb{N},chunkScore\left(rankA,append\left(append\left(replicate\left(z,0\right),replicate\left(k,36\right)\right),singleton\left(37\right)\right)\right)=2\cdot int\left(k\right)+3$$

Proof. Machine-checked in Lean as D5/S1/Words/Palindromes/FridPrefix/RankCyclesA.a_seed_cycle (✓ std3). ∎

Source. Repository-derived.

Commentary.

Numeric chunks 36 and 37 are the six-bit words 100100 and 100101. Initial zero chunks have zero weight. The repeated 36 cycle supplies weight two per repetition; the final chunk supplies the offset three.

References

• Truth anchor: D5/S1/Words/Palindromes/FridPrefix/RankCyclesA.a_seed_cycle
• Dependency: D5/S1/Words/Palindromes/FridPrefix/RankA