The measured dark-energy drift is NOT the vacuum's renormalisation-group running, for three independent reasons. Magnitude: fitting the running-vacuum form to DESI DR2 + Pantheon+ + CMB gives ν = +0.0015 ± 0.0014 (1.07σ), while the QFT running implies ν ≈ 4×10⁵³ — a ratio of 10^56.4. Shape: w_eff(0) = −1 exactly for EVERY ν, an algebraic identity, against a measured w₀ = −0.849. Form: the irreducible m⁴ running renormalises the additive constant, not the νH² term, so it cannot be ν at any magnitude.

, WHICH MUST BE STATED:
      rho_Lambda^(1/4) (our own fit)      = 2.2656 meV
      rho_Lambda^(1/4) (Wave-3/4 target)  = 2.2403 meV
      m from nu (above)                   = 2.4694 meV
      ratio m / rho_Lambda^(1/4)          = 1.0899
      because m/rho_L^(1/4) = (64 pi^2 nu/Om_L)^(1/4) = 1.0899, and
      64 pi^2 nu ~ 1 when nu ~ 1e-3.  So 'the mass scale that
      reconciles the running with the data' IS the dark-energy scale
      itself, to within 10%.  The reverse question is NOT an
      independent coincidence: it returns rho_Lambda^(1/4) because
      nu is O(1) on a logarithmic scale.  No information is gained.
      (For scale: the lightest known massive particles, the
      neutrinos at sum m_nu ~ 60 meV, are already ~24x heavier;
       the electron is 2.1e+08 times heavier.)

------------------------------------------------------------------------------
  AND THE OTHER REVERSE, promised in PART B3(b): at what EPOCH would
  the fixed m^4 running look like the measured nu?  nu(H) =
  |sum n m^4|/(64 pi^2 rho_c(H)) = nu_data requires
      rho_c(H) = 1.019572e+10 GeV^4  ->  T ~ rho^(1/4) = 3.1776e+02 GeV
      H        = 2.393821e-14 GeV = 1.633e+28 H0
    -> a few hundred GeV: the ELECTROWEAK epoch.  Under the mu = H
       identification the m^4 term reproduces the measured nu only
       there, and is wrong by 10^56 today.  A constant that is
       right at one epoch is not the constant being measured.

==============================================================================
PART B6 -- PRECISION LADDER: ARE THE PART-B NUMBERS CLOSED FORM?
==============================================================================
  Wave 3/4 process rule: prove whether an answer tracks PRECISION or
  tracks a tolerance.  Every PART B number is a closed-form ratio of
  input constants, so it must be precision-INDEPENDENT.  Recompute
  nu_QFT and the reconciling mass at 15/30/60/120 decimal digits,
  from the SAME rho_c0 and the SAME fitted nu used in PARTS B2/B5:

      digits                           nu_QFT            m_reconcile [GeV]
          15           4.1102300646003991e+53         2.46940604108415e-12
          30           4.1102300646003988e+53         2.46940604108415e-12
          60           4.1102300646003988e+53         2.46940604108415e-12
         120           4.1102300646003988e+53         2.46940604108415e-12

    -> IDENTICAL to every digit printed as precision increases by a
       factor of 8, and equal to the float values in PARTS B2/B5.
       These numbers do not track precision and do not track any
       tolerance: they are arithmetic on quoted inputs.  The 53
       orders of magnitude are therefore NOT a numerical artefact.
       They are also NOT a significance -- there is no measurement
       error anywhere in PART B2 or B4.

==============================================================================
VERDICT -- CAN THE MEASURED w(z) DRIFT BE THE QFT RUNNING?
==============================================================================
  NO.  Three independent reasons, in increasing order of finality.

  1. MAGNITUDE.  Fitting the standard running-vacuum model to DESI
     DR2 BAO (13 pts) + Pantheon+ (1590 SNe, full cov) + a compressed
     CMB prior gives
         nu = +0.001541 +/- 0.001433     (Delta chi^2 = 1.15, 1.07 sigma)
     -- consistent with zero.  The QFT m^4 running, under the
     running-vacuum programme's own identification mu = H, would
     require
         nu_QFT = 4.110e+53 ,  a ratio of 10^56.4 .
     Even against the loosest bound this data can produce (BAO+SN
     only, |nu| < 0.060) the ratio is 10^54.8.
     (that fit's own best value is nu = +0.0405 -- still 10^55.0
     below nu_QFT, and it is the CMB lever arm that removes it.)
     Running vacuum does NOT dissolve the vacuum-energy fine-tuning.
     It RELOCATES it, from 'why is rho_Lambda 10^54 times smaller
     than its own running' to 'why is nu 10^56 times smaller than
     its own estimate'.  The same tuning, restated in one
     dimensionless number instead of 120 decimal places.

  2. SHAPE.  The model cannot make the measurement even if nu were
     free.  w_eff(0) = -1 EXACTLY for every nu (PART A3), while the
     registry's CPL fit has w0 = -0.849.  At its own best fit the
     model's tilt is wa_eff = -0.00203 against a measured wa = -0.548,
     i.e. 0.37% of it.  Reproducing the measured wa needs nu = 0.415,
     which the same data reject at Delta chi^2 = +66929.
     The registry's 2.16 sigma is not a measurement of nu.

  3. FORM.  The decisive one, and the contribution of this file.
     The irreducible QFT running has a coefficient with NO scale in
     it (m^4), so under mu = H it is a running of the ADDITIVE
     CONSTANT c0, not of the nu H^2 term.  Its implied 'nu' would
     scale as 1/H^2 -- not a constant, so not nu, at any magnitude.
     The running-vacuum literature knows this and drops the m^4 term
     by fiat.  Do the literature's own m^2 mu^2 term honestly with
     Standard Model masses and you get
         nu(m^2 mu^2) = 9.883e-35 ,  which is 10^31 times TOO SMALL.
     The two available identifications straddle the measurement by
     10^56 and 10^31 IN OPPOSITE DIRECTIONS.  The published
     nu ~ 1e-3 is obtained by inserting M = 2.08e+18 GeV by hand.

  SO: DO RUNNING-VACUUM MODELS EXPLAIN ANYTHING?
     On this data combination, no.  Delta AIC(RVM - LCDM) = +0.85
     (disfavoured), Delta AIC(RVM - CPL) = +3.82 (CPL preferred),
     and the model captures 17% of CPL's chi^2 improvement for one
     parameter.  It is a RE-PARAMETRISATION of the tuning that also
     fits the data worse than the phenomenological form it hoped to
     explain.  The one thing it does do is make the tuning explicit
     and dimensionless, which is worth something: nu is a single
     number, and 56 orders is easier to state than 120.

  THE COINCIDENCE THAT WILL NOT GO AWAY, AND ITS DEFLATION.  The
  mass scale that would make the m^4 running produce the observed
  nu is 2.47 meV -- the dark-energy scale, yet again.  But PART B5
  shows WHY: m/rho_Lambda^(1/4) = (64 pi^2 nu/Om_L)^(1/4), and
  64 pi^2 nu ~ 1 for nu ~ 1e-3.  The question 'what mass gives the
  observed nu' is the question 'what mass gives the observed
  rho_Lambda' wearing a hat.  It is the same coincidence, not a new
  one, and this file has not explained it.

  WHAT IS NOT EVIDENCE HERE.  sigma(nu) is a profile-likelihood fit
  error.  The 1e-13 residuals in PART A2 are integrator floors that
  track tolerance (shown).  The PART B numbers are closed-form and
  precision-independent (shown, PART B6).  No Monte Carlo, no RNG.

  STATUS: REPRODUCED, NOT DISCOVERED.  SOLVES NOTHING.  The models,
  the fit and the running are all standard; the confrontation of the
  two magnitudes in one variable, and the observation that they are
  not even the same TERM, is what this file adds.
==============================================================================

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