Period-Eleven Prefix Separation

Abstract

The period-eleven phases admit bounded prefix partitions and low-arm witnesses.

Three-step prefixes partition every expected phase; the three 34-state blocks are refined once more by their fourth step.

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

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

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodic/EnumerationElevenSeparation.golden_new_periodic_orbit_low_arms_bounded_eleven (✓ std3). ∎

Source. Repository-derived.

Commentary.

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

References

• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationElevenSeparation.golden_new_periodic_orbit_low_arms_bounded_eleven
• Dependency: D5/S0/Tower/GoldenPeriodic/EnumerationElevenDisjoint