X72-28: Lock-Manifold Stability and the Dual-Strain Saddle

Continuing from Round 27's angular-phase-locking gap (STOP-C31), this round performs a genuine linearization of the leading-order dynamics under frozen strain: it proves that the vorticity-direction flow ξ'=P_ξ⊥Sξ is a Rayleigh ascent and the quotient-direction flow n'=-P_n⊥Sn is a Rayleigh descent, each attracted, under a simple spectrum, to opposite eigendirections e₃ and e₁ respectively. The core result is the Common-Lock Saddle Theorem: when ξ=n=e_i lock together, the linearization exponents of any transverse eigenmode come in pairs ±|λ_j-λ_i|, so the leading-order dynamics of frozen strain can never asymptotically attract a common lock by itself — a genuinely stable lock must rely on additional frame mechanics (pressure, viscosity, vorticity, gauge) to actually overcome this unstable strain gap. The route halts at STOP-C32 (dual-strain-saddle / lock-stabilization-forcing gap), passing the baton to the next round to quantify, as a 'lock work,' whether the additional dynamics have enough budget to sustain this unstable lock over time.