Tribonacci Period-Six Orbit Data

Abstract

Five exact primitive cycles supply the new Tribonacci period-six data.

Theorem 1.1 (Five new primitive period-six orbits).

$$\mathrm{length}\left(tribonacciPeriodicOrbitRepresentativesExactlySix\right)=5$$

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

Source. Repository-derived.

Commentary.

Rotation reduction of the thirty new phase states gives five representatives, each with six transitions.

Theorem 1.2 (All five new orbits are valid).

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

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

Source. Repository-derived.

Commentary.

Exact cubic inequalities certify every branch choice, gap bound, and closing equation without numerical approximation.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSixData.tribonacci_new_periodic_orbit_count_six
• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSixData.tribonacci_new_periodic_orbit_representatives_valid_six
• Dependency: D5/S0/Tower/DBonacciGeneral/TribonacciPeriodicMaximin