Tribonacci Period-Six Fixed Points

Abstract

Thirty-nine period-six equations reduce to inherited phases and five new cycles.

Theorem 1.1 (Thirty-nine period-six fixed-point equations).

$$\mathrm{length}\left(\mathrm{tribonacciFixedPointCodes}\left(6\right)\right)=39$$

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

Source. Repository-derived.

Commentary.

The three-letter transition graph has thirty-nine closed, phase-marked words of length six.

Theorem 1.2 (Period-six equations decompose into certified orbits).

$$\mathrm{toFinset}\left(\mathrm{tribonacciFixedPointCodes}\left(6\right)\right)=tribonacciExpectedPointCodesSix$$

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

Source. Repository-derived.

Commentary.

Independent large, small, and combined gap checks identify all fixed codes with the inherited phases and thirty new phases.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSixFixed.tribonacci_fixed_point_code_count_exactly_six
• Truth anchor: D5/S0/Tower/TribonacciPeriodic/EnumerationSixFixed.tribonacci_fixed_point_codes_six_decompose
• Dependency: D5/S0/Tower/TribonacciPeriodic/EnumerationSixDisjoint