Tribonacci Period-Seven Orbit Data

Abstract

Ten exact primitive cycles supply the new Tribonacci period-seven data.

Theorem 1.1 (Ten new primitive period-seven orbits).

$$\mathrm{length}\left(tribonacciPeriodicOrbitRepresentativesExactlySeven\right)=10$$

Proof. Machine-checked in Lean as D5/S0/Tower/TribonacciPeriodic/EnumerationSevenData.tribonacci_new_periodic_orbit_count_seven (✓ std3). ∎

Source. Repository-derived.

Commentary.

Rotation reduction of the seventy new phase states gives ten representatives, each with seven transitions.

Theorem 1.2 (All ten new period-seven orbits are valid).

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

Proof. Machine-checked in Lean as D5/S0/Tower/TribonacciPeriodic/EnumerationSevenData.tribonacci_new_periodic_orbit_representatives_valid_seven (✓ std3). ∎

Source. Repository-derived.

Commentary.

Five bounded exact proof groups certify branch choices, gap bounds, and closure under the default resource limits.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSevenData.tribonacci_new_periodic_orbit_count_seven
• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSevenData.tribonacci_new_periodic_orbit_representatives_valid_seven
• Dependency: D5/S0/Tower/TribonacciPeriodic/EnumerationSix