Viscous Emergent Spacetime (VES)

This is the post-confrontation consolidation of the VES programme. Two mandatory tests registered in D3 were executed.

M2 (lensing forward model) falsified the isolated ceiling and the noise floor in their universal form: propagating the exact finite-ν VES mobility through the published stacked weak-lensing radial acceleration relation (15 binned points, [9]) gives residual pulls of +10 to +12σ and χ² = 62 versus 4.3 for the empirical RAR fit over the eight bins inside the simulation-validated isolation range (≈ 6.5σ); no rescaling escapes (a₀-free fitting runs to 1.3 × 10⁻¹¹ m s⁻² and still leaves χ² = 95), and the lensing data require ν ≤ 0.24–0.31 against the SPARC-measured ν = 0.36 ± 0.02. Kill condition K1 is therefore triggered and logged (R10).

M1 (Solar-System quadrupole) is quantified rather than resolved: an independently validated QUMOND phantom-quadrupole solver gives Q₂(µB) = 2.8–3.0 × 10⁻²⁶ s⁻² in the fit-relevant normalisation, so VES survives Cassini only if its external-field response is entrained rather than AQUAL-nested, with a pinning parameter λ ≤ 0.026–0.080, i.e. ≥ 92–97% suppression of the angular response.

Structurally, three results reorganise the theory:

• (i) A scale-equalisation theorem: the deterministic and noisy interpolating functions are one integral operator with a single kernel family m_ν(u) = sinh(πu/ν) / [π(u/ν)|I_iu/ν(1/ν)|²], exact to six digits against quadrature and reducing to the deterministic kernel as ν → 0; no reparametrisation of (a₀, r) can map one onto the other (a factor 1.59 irreducible mismatch), so the difference is physical, not conventional.
• (ii) The overdamped licence resolves into a triad: a decaying relic dither, rare merger-class storms that reset couplings (and thereby set a₀ ∝ v/r), and neighbour tides. Between storms the static sector is deterministic — which is exactly why the lensing null appears, converting K1 from refutation of the framework into refutation of the universal-floor reading.
• (iii) A relic sterility theorem: a bounded adiabatic dither generates a floor equal to its amplitude to within 0.3%, so today’s lensing cap forces δ_r ≤ 6.5 × 10⁻³ (8 × 10⁻¹³ m s⁻²) and leaves a SPARC-window signature 500–1000× too small to carry the measured ν — the finite-ν SPARC preference must therefore be episodic, or an artefact, and its re-audit is the programme’s decisive open item.

A first old-wind test on RC100 (100 galaxies, z = 0.6–2.5; table transcription cross-validated 100/100 in z and M_bar) returns a clean null with ceiling bounds δ ≤ 0.48 (z ∼ 0.9) and ≤ 0.51 (z ∼ 1.9), consistent with every dilution law anchored to today’s cap, which predict δ = 0.011–0.16 over this range. The decisive relic front moves to the wind epoch z⋆ = 27.7, 11.4, 4.4 for n = 1.5, 2, 3: only a fast-draining relic is testable with existing high-z kinematics. Every number here was recomputed in-session; every failed prediction, including four made by the analysis itself, is logged.