Primitive Golden Period-Twelve Certificates

Abstract

Twenty-five exact primitive period-twelve orbit certificates extend the golden table.

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

Theorem 1.1 (Twenty-five primitive period-twelve orbits).

$$\mathrm{length}\left(goldenPeriodicOrbitRepresentativesExactlyTwelve\right)=25$$

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

Source. Repository-derived.

Commentary.

Each representative carries a twelve-step closed itinerary.

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

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

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

Source. Repository-derived.

Commentary.

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

References

• Truth anchor: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveData.golden_new_periodic_orbit_count_twelve
• Truth anchor: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveData.golden_new_periodic_orbit_representatives_valid_twelve
• Dependency: D5/S0/Tower/GoldenPeriodic/EnumerationEleven