Tribonacci Period-Six Separation

Abstract

The old and new Tribonacci phase codes form one duplicate-free period-six list.

Theorem 1.1 (Old and new phase codes are disjoint).

$$\mathrm{Disjoint}\left(tribonacciEnumeratedOrbitStatesFiveList,tribonacciEnumeratedOrbitStatesExactlySixList\right)$$

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

Source. Repository-derived.

Commentary.

Three bounded exact comparisons separate each new orbit from the thirty-seven previously certified phase states.

Theorem 1.2 (All period-six phase codes are distinct).

$$\mathrm{Nodup}\left(tribonacciEnumeratedOrbitStatesSixList\right)$$

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

Source. Repository-derived.

Commentary.

Prior distinctness, new distinctness, and old-new separation combine without re-expanding a monolithic comparison.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSixDisjoint.tribonacci_old_new_periodic_orbit_state_codes_disjoint_six
• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSixDisjoint.tribonacci_periodic_orbit_state_codes_nodup_six
• Dependency: D5/S0/Tower/TribonacciPeriodic/EnumerationSixData