Period-Eleven Fixed-Point Decomposition

Abstract

The 199 period-eleven fixed equations decompose into eight prefix blocks.

The three 34-equation blocks are each refined into fourth-step subblocks of size twenty-one and thirteen before exact comparison.

Theorem 1.1 (The eight fixed-point blocks have exact sizes).

$$\mathrm{periodElevenFixedBlockLengths}\left(\right)=\mathrm{list}\left(34,21,34,34,21,21,13,21\right)$$

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

Source. Repository-derived.

Commentary.

The block sizes are 34, 21, 34, 34, 21, 21, 13, and 21.

Theorem 1.2 (Every period-eleven fixed point is an enumerated phase).

$$\mathrm{toFinset}\left(\mathrm{goldenFixedPointCodes}\left(11\right)\right)=goldenExpectedPointCodesEleven$$

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

Source. Repository-derived.

Commentary.

The exact fixed-point codes equal the inherited fixed phase and all 198 phases on the primitive eleven-cycles.

References

• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationElevenFixed.golden_fixed_point_block_counts_eleven
• Truth anchor: D5/S0/Tower/GoldenPeriodic/EnumerationElevenFixed.golden_fixed_point_codes_eleven_decompose
• Dependency: D5/S0/Tower/GoldenPeriodic/EnumerationElevenSeparation