Enumeration Ten Maximin C

Abstract

Every period-ten orbit has a low arm at or below the champion.

The enumerator was calibrated against both committed levels before use, and against their rotation classes as sets rather than their counts: it reproduces the fifteen period-eight classes and the twenty-six period-nine classes exactly.

Theorem 1.1 (Enumeration Ten Maximin C).

$$\forall o\in TribonacciCodedOrbit,o\in tribonacciPeriodTenOrbitRepresentatives\Rightarrow \mathrm{tribonacciPeriodicStateArm}\left(\mathrm{decodeTribonacciState}\left(\mathrm{lowState}\left(o\right)\right)\right)\le \mathrm{championValue}\left(t\right)$$

Proof. Machine-checked in Lean as D5/S0/Tower/TribonacciPeriodicTen/EnumerationTenMaximinC.tribonacci_period_ten_low_arms_bounded (✓ std3). ∎

Source. Repository-derived.

Commentary.

Two proof shapes are needed and the split differs from period nine: twenty-two low states sit on the left branch and twenty on the right. The right-branch set was measured for this level.

References

• Truth anchor: D5/S0/Tower/TribonacciPeriodicTen/EnumerationTenMaximinC.tribonacci_period_ten_low_arms_bounded
• Dependency: D5/S0/Tower/TribonacciPeriodicNine/EnumerationNineMaximinB
• Dependency: D5/S0/Tower/TribonacciPeriodicTen/EnumerationTenMaximinB