A Primordial-Clock Candidate for de Sitter-MOND Gravity: Explicit Covariant Action, Derived Field Equations, a Dust-like Expanding Background, and an Obstruction to Instantaneous MOND on Expanding Initial Data

We record the exact current state of a candidate relativistic completion of MOND built on a primordial-clock foliation. Established: an explicit covariant action (clock scalar τ, dynamical scalar χ, cubic coupling γ X □χ, matter minimally coupled to one metric); the varied field equations (metric, exactly conserved χ-current, clock constraint, matter conservation); a reconstructed expanding FLRW background on which the clock sector is exactly pressureless dust; positive, luminal tensor modes (cT2 = 1); a finite-wavelength scalar velocity matrix of rank one, with selected positivity results carrying Lean 4 certificates. Not established, stated with equal weight: the coefficient functions were reconstructed to produce a chosen background, not selected from first principles (a correction to earlier statements); the complete nonlinear constraint count is open; the recombination history is incomplete; exact galactic MOND, the measured GN, the full PPN sector, nonlinear lensing, clusters and the CMB are open; a0 = (1/2) c sqrt(G ρΛ) has not been derived. Obstruction: on the solved spherical initial-data family the background-subtracted acceleration is bounded by C(r)ε, and 1 − e−x ≤ x then shows the exact exponential MOND law cannot hold instantaneously on that family (Lean certificate assuming the force bound). The latest evolution-refinement test fails numerical convergence (momentum-constraint residual 7.41e-6 to 1.77e-5 from 129 to 257 points). A section relates this candidate to an independent gate analysis in the same repository (necessity certificate: a dark fraction rising with host mass, f ~ M0.16; every computed mechanism for it so far fails on the forest, small-scale shear or Neff; the framework's own nonlinear P(k) baseline is being computed). This is a status report with named failures, not a claim that the theory is established. AI-assisted research programme; not peer reviewed.