Pure Time Theory - Chapter VIII - A Minimal Temporal Grammar with Traceability & Verifiable Examples

This article consolidates Pure Time Theory (PTT) at the L0 layer into a single, minimal temporal grammar and re-expresses earlier results as a non-circular, audit-ready package. The grammar fixes only: (i) pure time with a positive-affine gauge on T_relax; (ii) a unitary, mode-diagonal cadence rho_omega together with the causal recurrence B_{T+1} = rho_omega B_T + S_{T+1}; and (iii) a visibility/fairness rule (plus a zero-bundle four-packet scheduler). Within this L0 setting we give: a static characterization of the Riemann Hypothesis via a phase-injectivity functional E(Z) and a dynamic route that forces E(Z)=0; chart/weight-invariant SAT encodings with a polynomial-time sesquilinear verifier over an exact arithmetic pipeline (Q), and TM↔PTT bridges showing power equivalence (PTT-P = P, PTT-NP = NP) by constructive compilation and exact simulation; a deterministic block-frequency law for the P0 readout that equals the Born weight, together with a modal-diagonal observable calculus under cadence invariances; and a blockwise ledger continuity identity which, after coarse graining and standard diffeomorphism/second-order locality in D=4, yields an Einstein-type balance G + Lambda g = kappa T_mod with kappa fixed by weak-field clock normalization (Helmholtz–Poisson/Yukawa). The manuscript includes a traceability table and four exactly checkable micro-examples, making the results reproducible, verifiable, and ready for audit and reuse.