The Holographic Circlette: Part 16 — The DESI Anomaly and the Lattice Equation of State: A Structural Derivation of w0=-0.75

Audit note. This paper predates the framework's methodology audit of 2026-05-30. The w_0 = -3/4 derivation via R-rule averaging is now read in conjunction with the canonical refinement at ANCHOR §15 item 118: under the same Δ_1 = 1/28 spectral-gap structure, the refined value is w_0 = -n_s = -27/28 = -0.9643 matching Planck CMB-only at ~\!0.45σ. The R-rule averaging argument of this paper sits at Proposition tier and is consistent with the structural mechanism (the matter-anchored R4 sector contributing dilution); the precise -3/4 value reflects the simpler 3:1 weighting model, while item 118 supplies the spectral-gap-corrected value. §16.3 search-space audit: the precision-match should be read at Proposition tier; the structural mechanism (parity-check averaging producing w ≠ -1) survives as substrate-level explanation. The Ollivier-Ricci linearity dependency (§15 item 52) remains o Three of the four parity checks are purely structural (w=-1) and one is matter-anchored (w=0). The macroscopic average is structurally locked at w0=-3/4, matching DESI DR2 (w0=-0.752+/-0.071) within 1 sigma. Strict topological linearity connects this to local Ollivier-Ricci curvature. v2.0 (2026-06-12): an in-PDF dated status/erratum note has been added reflecting the June 2026 canon audit (DRIFT/ANCHOR ledger); see the paper's status note for the specific corrections, supersessions, or upgrades. 2026-06-20 legacy canon revision: This is a canon-reconciled legacy version. Dark-energy equation-of-state status changed The paper retains its historical derivation trail but carries a 2026-06-20 canon revision note identifying current status and superseded claims. 2026-06-21 canon refresh: This version incorporates the 2026-06-21 ANCHOR/DRIFT/PTMS canon refresh and rebuilt local PDF.