Period-Eleven Separation From Earlier Periods

Abstract

The primitive period-eleven states do not collide with any state through ten.

Each new orbit is checked against the frozen period-nine states and the period-ten extension, then the results are recombined.

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

$$\mathrm{Disjoint}\left(\mathrm{flatMap}\left(goldenOrbitStates,goldenPeriodicOrbitRepresentativesTen\right),\mathrm{flatMap}\left(goldenOrbitStates,goldenPeriodicOrbitRepresentativesExactlyEleven\right)\right)$$

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

Source. Repository-derived.

Commentary.

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

References

• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationElevenDisjoint.golden_old_new_periodic_orbit_state_codes_disjoint_eleven
• Dependency: D5/S0/Tower/GoldenPeriodic/EnumerationElevenDistinct