Period-Twelve Separation From Earlier Periods

Abstract

All primitive period-twelve states are separated from every earlier state.

The twelve remaining cycles are checked and combined with the first thirteen separation certificates.

Theorem 1.1 (New states are disjoint from all earlier states).

$$\mathrm{Disjoint}\left(\mathrm{flatMap}\left(goldenOrbitStates,goldenPeriodicOrbitRepresentativesEleven\right),\mathrm{flatMap}\left(goldenOrbitStates,goldenPeriodicOrbitRepresentativesExactlyTwelve\right)\right)$$

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

Source. Repository-derived.

Commentary.

No exact phase code on a primitive twelve-cycle occurs on an orbit enumerated through period eleven.

References

• Truth anchor: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveDisjointB.golden_old_new_periodic_orbit_state_codes_disjoint_twelve
• Dependency: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveDisjointA