Primitive Golden Period-Eleven Certificates

Abstract

Eighteen exact primitive period-eleven orbit certificates extend the golden table.

The period-eleven branch words and quadratic coordinates are stated exactly over Q(phi).

Theorem 1.1 (Eighteen primitive period-eleven orbits).

$$\mathrm{length}\left(goldenPeriodicOrbitRepresentativesExactlyEleven\right)=18$$

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

Source. Repository-derived.

Commentary.

Each representative carries an eleven-step closed itinerary.

Theorem 1.2 (The period-eleven representatives are valid).

$$\forall O\in goldenPeriodicOrbitRepresentativesExactlyEleven,\mathrm{goldenCodedOrbitValid}\left(O\right)$$

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

Source. Repository-derived.

Commentary.

Every displayed code follows its source, target, and affine branch rules and closes after eleven steps.

References

• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationElevenData.golden_new_periodic_orbit_count_eleven
• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationElevenData.golden_new_periodic_orbit_representatives_valid_eleven
• Dependency: D5/S0/Tower/GoldenPeriodic/EnumerationTen