Tribonacci Period-Eight Orbit Data

Abstract

Fifteen exact primitive cycles supply the new Tribonacci period-eight data.

Theorem 1.1 (Fifteen new primitive period-eight orbits).

$$\mathrm{length}\left(tribonacciPeriodicOrbitRepresentativesExactlyEight\right)=15$$

Proof. Machine-checked in Lean as D5/S0/Tower/TribonacciPeriodicEight/EnumerationEightData.tribonacci_new_periodic_orbit_count_eight (✓ std3). ∎

Source. Repository-derived.

Commentary.

Rotation reduction of the one hundred twenty new phase states gives fifteen representatives, each with eight transitions.

Theorem 1.2 (All fifteen new period-eight orbits are valid).

$$\mathrm{Forall}\left(tribonacciPeriodicOrbitRepresentativesExactlyEight,tribonacciCodedOrbitValid\right)$$

Proof. Machine-checked in Lean as D5/S0/Tower/TribonacciPeriodicEight/EnumerationEightData.tribonacci_new_periodic_orbit_representatives_valid_eight (✓ std3). ∎

Source. Repository-derived.

Commentary.

Eight bounded exact proof groups certify branch choices, gap bounds, closure, and phase distinctness under the default limits.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodicEight/EnumerationEightData.tribonacci_new_periodic_orbit_count_eight
• Truth anchor: D5/S0/Tower/TribonacciPeriodicEight/EnumerationEightData.tribonacci_new_periodic_orbit_representatives_valid_eight
• Dependency: D5/S0/Tower/TribonacciPeriodic/EnumerationSeven