The Equilibrium Reading of the Radial Acceleration Relation: What Is Derived, What Is Measured, What Is Dead

VERSION 2 (2026-09-15). Adds Section 8, an audit of the closure claims the same track made in the day after v1: a temperature 'derived three ways', a dark-energy fraction 'derived from the acceleration scale' (Omega_Lambda = 0.6857, +0.07 per cent of Planck), a Lorentz-invariant completion, and a referee defence declaring the theory complete. None is landed. The dark-energy fraction is the inversion of the definition of a_0 (the registered value was built from Planck's Omega_Lambda and H_0 and the identity returns its input; the advertised agreement is the ratio of two roundings of the same Planck parameters; a galactic a_0 returns Omega_Lambda above unity). The temperature is not derived: hydrostatic balance in the 1/r force gives sigma^2 = C/gamma for every profile slope with a free amplitude, so sigma^2 = C/2 is the assumption that the dust is the r^-2 phantom; the lane cited for the promotion fails eight of its own eleven checks. The double count is quantified: with the phantom-density dust as a source of the same field equation the outer rotation curve rises to 1.72 v_flat at five MOND radii, and the only flat version is a cold-dark-matter halo with no scalar force. The proposed completion inherits the Cassini quadrupole (6.4 to 7.6 times the ceiling) through its own static law, and its defence cites two mutually exclusive constructions as one. All 36 Lean certificate files (474 theorems) are recompiled: the track's certificates compile on the standard axioms and certify algebra; one sibling file does not compile. Version 2 also adds, in Section 5, that the weak-lensing relation's deep-branch slope is an identity of the mass run (the profiles' own power laws predict 0.547 +/- 0.024 against the measured 0.537 +/- 0.026) and that its only gravitational content is the amplitude's scaling with baryonic mass, measured at 0.38 +/- 0.08 against the 0.5 a universal scale requires. Every label of version 1 stands. A status report on a candidate reading of the radial acceleration relation within an AI-assisted research programme on the de Sitter-locked acceleration scale a_0 = (1/2) c sqrt(G rho_Lambda). The reading takes the relation not as a force law but as the hydrostatic equilibrium of a cold dark sector at the virial temperature of its baryonic well, sigma^2 = GM/(2 r_M) with r_M = sqrt(GM/a_0), whose isothermal density is exactly the deep-MOND phantom. Twenty computational lanes and five Lean 4 certificates (43 theorems, zero sorry, standard axioms) are consolidated together with an independent same-day audit that relabelled three rungs of the chain. WHAT IS ESTABLISHED. The identification is an exact identity, credited to Milgrom: the coefficient is one by the definition of the temperature. The complete force-law pincer stands: modified gravity fails the Cassini external-field quadrupole by 6.4-7.6 times, modified inertia is lensing-dead, disformal and vector completions fail the preferred-frame bound, and the bimetric door is closed by a Lean certificate. The cluster residual slope (-1.478 against the certified -1.53) and temperature follow from the isothermal phantom with no parameter. The data select the integer n = 2 in the parameter-free family with nothing fitted. WHAT THE AUDIT RELABELLED. Rung 4, the equilibration at the virial temperature, was labelled derived from an N-body formation run; that run integrates Newtonian gravity in units where the MOND radius is one by definition, a_0 never enters its equations, and its own runs give a relaxed radius equal to 0.53 of the initial radius for every start, i.e. no attractor. The rung is postulated. The Milky Way check of the external-field cap is a recorded failure in its own lane (mass 17 times short within 100 kpc), so the cap is a prediction for Gaia DR4, not a confirmation, and the rescue outside the cap is a cold dark matter halo carrying 94 per cent of the dark mass. The 0.064 dex scatter floor is obtained with a free stellar mass-to-light ratio per galaxy and is a measurement with a nuisance, not a confirmed prediction. Five lane checks that pass on a literal true are identified and discounted. Every Lean theorem is an algebraic identity of the static problem; none certifies dynamics. WHAT REMAINS, AND THE TEST THAT DECIDED IT. A companion lane exhibits a covariant, non-barotropic constitutive law, p = P(a) with a the medium's own proper acceleration, from which the identification follows and whose deep limit makes the pressure the gravitational field's energy density; it is cold on the cosmological background by construction, but it does not fix the amplitude (a supply-limited edge gives Tully-Fisher exponent 3, excluded at five sigma) and leaves clusters at the known factor-of-two residual. That lane named a decisive test, and a second lane has now run it against the first lane's own candidate. The closed form: if the phantom producing a galaxy's weak-lensing signal is real mass drawn from a finite budget B = M_dark/M_bar, the enclosed mass freezes at r_t = (1+B) r_M, where the baryonic acceleration is a_0/(1+B)^2 -- independent of the galaxy's mass, so every galaxy in a stack must turn at the same acceleration, from log-slope one half to log-slope one, continuously and strictly downward. All four statements are machine-checked. The measurement, against the published KiDS-1000 excess-surface-density profiles of Brouwer et al. (2021) with the full covariance and that paper's own conversion: the log-log slope over the eight bins below 1e-13 m/s^2 is 0.537 plus or minus 0.026, which is 17.6 sigma from the truncated value and 1.4 sigma from one half. The relation has not turned. The comparison against truncation gives Delta chi-squared of +349 at the abundance-matching budget, +970 at the cosmic dark-to-baryon ratio, and +75 even at a stress budget of 100. Inside one megaparsec the enclosed lensing mass already exceeds the galaxies' entire abundance-matching budget by factors 1.5, 4.1 and 8.7. That excess is real mass, the two-halo term of correlated neighbours, but it is not bound to the lens, so this removes our own medium as the source of the lensing signal and with it every reading in which the phantom carrying the lensing is the galaxy's own bounded sector. MOND as a force law is untouched, since no mass is there and no budget applies; the capped equilibrium reading is untouched because its cap sits at 5.8 kpc, below the innermost lensing bin at 35 kpc, so it makes no prediction anywhere the data are and ordinary cold collisionless matter carries all of the measured signal. Two limits are recorded: the parameter-free square-root branch fits these data poorly in absolute terms, so every verdict is a relative comparison, and dropping the seven lowest-acceleration bins removes the regime the test probes. Two further tensions are recorded with their instruments: a 1-3 per cent raise of S_8 inherited through the field equation, opposite in sign to direct lensing, and the cluster amplitude. This document does not state that a theory is closed. AI-assisted research programme; not peer reviewed.