Enumeration Nine Valid

Abstract

All twenty-six period-nine orbit certificates are valid.

The twenty-six words are the primitive rotation classes among the two hundred forty phase-marked solutions of the period-nine equations. The enumerator was validated against the frozen period-eight data before use: it reproduces one hundred thirty-one phase points and fifteen primitive classes, and those fifteen rotation classes coincide with the committed ones as sets.

Theorem 1.1 (Enumeration Nine Valid).

$$\forall o\in TribonacciCodedOrbit,o\in tribonacciPeriodNineOrbitRepresentatives\Rightarrow \mathrm{tribonacciCodedOrbitValid}\left(o\right)$$

Proof. Machine-checked in Lean as D5/S0/Tower/TribonacciPeriodicNine/EnumerationNineValid.tribonacci_period_nine_representatives_valid (✓ std3). ∎

Source. Repository-derived.

Commentary.

Each certificate carries a low state whose arm lies at or below the champion threshold, so no representative is a strict survivor.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodicNine/EnumerationNineValid.tribonacci_period_nine_representatives_valid
• Dependency: D5/S0/Tower/TribonacciPeriodicEight/EnumerationEight
• Dependency: D5/S0/Tower/TribonacciPeriodicNine/EnumerationNineData