Z₉ CHY Amplitude at the PTRH Locus: Localisation, Explicit Evaluation, and Resolution of Paper 22 Conjecture 1 under the PTRH Sector-State Prescription

PTRH Paper 26. We complete the resolution of Paper 22 Conjecture 1 in the PTRH framework. Paper 25 established that the nine-point configuration z_n = zeta_9^n is an exact saddle of the CHY scattering equations for all Z_9-symmetric massless kinematics and computed the Parke-Taylor factor and circulant-matrix structure of the CHY measure. The present paper supplies the amplitude half. A lemma classifies the 720 CHY saddles of M0,9 by Z_9 orbit structure, identifying a unique Z_9-invariant fixed point. The PTRH encoding isometry (Paper 24) identifies sector-state external conditions with the Z_9-symmetric moduli locus, pinning each leg to z_i = zeta_9^i; the CHY integral therefore reduces to the residue at the Z_9-invariant saddle. The explicit reduced bi-adjoint scalar amplitude is derived: AZ_9 = -1/(Delta_min^18 * det'Phi_tilde), where Delta_min = 2 sin(pi/9) is the PTRH spectral gap and det'Phi_tilde is the reduced determinant of the Z_9-circulant CHY matrix of Paper 25. The structural form of AZ_9 is shown to be analogous to the N=9 instance of the Guevara-Hu celestial qudit-chain construction. A corollary establishes BCFW bootstrap exactness: the full nine-particle amplitude is uniquely determined by recursion from the three-particle seed, and Paper 23 non-renormalization implies the tree-level sector-resolved structure is exact. Conjecture 1 is thereby resolved under the PTRH sector-state prescription.