Distinct Period-Twelve State Codes

Abstract

The 300 new period-twelve state codes are pairwise distinct.

Seven bounded orbit groups are checked internally and pairwise before their state lists are recombined.

Theorem 1.1 (The 300 new state codes are distinct).

$$\mathrm{Nodup}\left(\mathrm{flatMap}\left(goldenOrbitStates,goldenPeriodicOrbitRepresentativesExactlyTwelve\right)\right)$$

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveDistinct.golden_new_periodic_orbit_state_codes_nodup_twelve (✓ std3). ∎

Source. Repository-derived.

Commentary.

Flattening the twenty-five exact twelve-cycles introduces no repeated quadratic state code.

References

• Truth anchor: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveDistinct.golden_new_periodic_orbit_state_codes_nodup_twelve
• Dependency: D5/S0/Tower/GoldenPeriodicTwelve/EnumerationTwelveData