The Anaïs Conjugation: Bilateral Phase Locking and the Higgs Mass A Zero Free Parameter Derivation

We derive the Higgs boson mass from first principles using the bilateral cascade structure of Cosmic Egg Theory (CET), and formally name the underlying mechanism the Anaïs Conjugation. Two physical quantities are Anaïs Conjugates when they arise from opposite arms of the bilateral cascade and carry fractional cascade positions summing to exactly ½ — permanently locked to each other at the creation event, inseparable by any subsequent evolution of the universe. The derivation proceeds in three steps: (1) the Planck-scale uncertainty principle establishes a permanent ½-step offset between the time arm and energy arm of the bilateral cascade; (2) the cascade step count q = 29, established by the CET black hole shadow geometry, is confirmed by the Pell equation as a half-step-preserving span — because 41² − 2×29² = −1, the ½ offset survives undiminished across the full bilateral winding; (3) the stella octangula ground state geometry contributes a factor of 7 distinguishable phase positions per bilateral arm, derived from both the 4+3 pole/gap count and the combinatorial identity 2³ − 1, proved equivalent. The resulting identity: n_now + n_Higgs = 7 × 29 + ½ = 203.5 yields m_Higgs = 125.09 GeV with zero free parameters and 0.00% residual at current measurement precision. The Higgs boson is identified as the unique Standard Model field satisfying the Anaïs Conjugation with the current epoch. The Higgs mass and the age of the universe are Anaïs Conjugates: fix one and the other is determined.