Period-Twelve Five-Step Separation

Abstract

The period-twelve phases admit a five-step partition and low-arm witnesses.

Twenty-one legal five-step prefixes partition every inherited and new phase fixed by the twelfth iterate.

Theorem 1.1 (Period-twelve low arms obey the golden bound).

$$\forall O\in goldenPeriodicOrbitRepresentativesExactlyTwelve,\mathrm{goldenStateArm}\left(\mathrm{decodeGoldenState}\left(\mathrm{lowState}\left(O\right)\right)\right)\le goldenThreshold$$

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveSeparation.golden_new_periodic_orbit_low_arms_bounded_twelve (✓ std3). ∎

Source. Repository-derived.

Commentary.

Each primitive twelve-cycle has an explicit phase whose arm is at most the exact golden threshold.

References

• Truth anchor: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveSeparation.golden_new_periodic_orbit_low_arms_bounded_twelve
• Dependency: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveDisjointB