Golden Periodic Enumeration Through Eleven

Abstract

The exact golden periodic enumeration is complete through period eleven.

The period-ten certificate and eighteen primitive eleven-cycles are combined through a 199-equation exact fixed-point census.

Theorem 1.1 (Four hundred eighty periodic points through eleven).

$$\mathrm{card}\left(goldenPeriodicPointCodesEleven\right)=480$$

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_point_code_count_eleven (✓ std3). ∎

Source. Repository-derived.

Commentary.

The eighteen primitive eleven-cycles add 198 phases to the 282 phases enumerated through period ten.

Theorem 1.2 (Fifty-four disjoint periodic orbits).

$$\mathrm{length}\left(goldenPeriodicOrbitRepresentativesEleven\right)=54\wedge \mathrm{card}\left(goldenEnumeratedOrbitStatesEleven\right)=480$$

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_code_partition_eleven (✓ std3). ∎

Source. Repository-derived.

Commentary.

The 36 prior cycles and eighteen primitive eleven-cycles have no repeated exact phase code.

Theorem 1.3 (The enumeration through period eleven is complete).

$$\forall p\in N,s\in GoldenSurvivorState,\left(\left(p\ge 1\wedge p\le 11\right)\wedge \mathrm{iterate}\left(goldenTransition,p,s\right)=s\right)\Rightarrow s\in decodedRepresentativeOrbitUnionEleven$$

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_orbit_enumeration_complete_eleven (✓ std3). ∎

Source. Repository-derived.

Commentary.

Every real state fixed by a nonzero iterate of period at most eleven lies on one of the fifty-four decoded exact cycles.

Theorem 1.4 (The golden periodic maximin through eleven).

$$\mathrm{IsGreatest}\left(goldenPeriodicOrbitMinimaEleven,goldenThreshold\right)$$

Proof. Machine-checked in Lean as D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_orbit_maximin_eleven (✓ std3). ∎

Source. Repository-derived.

Commentary.

Every new low-arm witness is bounded by the threshold, and the period-three champion continues to attain equality.

References

• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_code_partition_eleven
• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_orbit_enumeration_complete_eleven
• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_orbit_maximin_eleven
• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationEleven.golden_periodic_point_code_count_eleven
• Dependency: D5/S0/Tower/GoldenPeriodic/EnumerationElevenFixed