The vacuum-energy problem splits cleanly along Lorentz invariance. Lorentz-VIOLATING regulators (hard 3-momentum cutoff, spatial lattice) give w = +1/3 AND a quartic divergence; Lorentz-INVARIANT regulators (Pauli–Villars, dimensional regularisation) give w = −1 exactly AND no power divergence at all. The two columns are the same fact: a K⁴ term has no m⁴ to carry it, so it must be built from a regulator scale — and a Lorentz-invariant regulator has no preferred frame to build one from.

              125.25    1    -8.338342e+05      52.52
     top quark                   172.5   12    +2.523186e+07      54.00
     ------------------------------------------------------------------
     SIGNED TOTAL                              +2.228655e+07      53.95
     sum of |rho_i|                            +2.817716e+07      54.05
     ------------------------------------------------------------------
     largest single term: top quark, |rho| = 2.5232e+07 GeV^4 = 10^54.00 rho_obs

  *** THE SURVIVING DISCREPANCY ***
    at mu = 1 GeV      : |signed total| / rho_obs = 10^54.74
    at mu = m_top      : |signed total| / rho_obs = 10^53.95
    change in the discrepancy across 2.24 decades of mu : 0.80 decades

    THAT IS THE WHOLE mu-SENSITIVITY.  Moving the renormalisation
    scale by two and a bit decades moves the answer by LESS THAN
    ONE decade, against a discrepancy of 55 decades.  There is no
    choice of mu -- none, not even an absurd one -- that brings the
    measured-mass contributions anywhere near rho_obs.

    ADVERSARIAL BEST CASE, COMPUTED RATHER THAN ASSERTED.  Choose
    mu by hand to make the LARGEST term vanish exactly: set
    ln(m_top^2/mu^2) = 3/2, i.e. mu* = m_top exp(-3/4).
      mu*                                = 81.4832 GeV
      top-quark term at mu*              = 3.735e-09 GeV^4 (zeroed)
      signed total of everything else    = -1.273623e+06 GeV^4
      that residue / rho_obs             = 10^52.70
      sum of |terms| at mu*              = 10^52.70 x rho_obs
    Killing the single biggest contribution by fiat buys 2.0
    decades out of 55.  And it cannot be done for two particles
    at once: one mu, seven masses.

    Stated as running instead of as a value, which is the
    scheme-independent way to say it (PART F):
      d rho_Lambda / d ln mu = -sum_i (-1)^(2s) n_i m_i^4/(32 pi^2)
                             = +3.141356e+07 GeV^4 per e-fold
                             = 1.25e+54 x rho_obs per e-fold
    The renormalised cosmological constant moves by 10^54 times
    the entire observed dark-energy density when you shift the
    renormalisation scale by ONE e-fold.  No regulator choice
    touches this: it is the log coefficient, and PART F showed all
    three schemes agree on it.

  HONESTY, EXPLICIT:  this is a NATURALNESS statement, not an
  inconsistency.  The bare cosmological constant is a free
  parameter and can absorb any finite number, so nothing above is a
  failed PREDICTION of the Standard Model.  What it is: the
  observed value requires a cancellation to ~55 decimal places
  between the bare parameter and terms computed from masses we have
  measured in laboratories, and that cancellation has to be redone
  by hand at every mass threshold.  That is the problem, and PARTS
  A-F establish that it is the ONLY part of the problem that
  survives an honest regulator.

==============================================================================
VERDICT -- WHICH PART OF '10^120' IS A REGULATOR ARTEFACT
==============================================================================
  *** NOTHING IN THIS FILE SOLVES THE COSMOLOGICAL CONSTANT
  *** PROBLEM.  NOTHING IN THIS FILE IS NEW.  Every result is a
  *** recomputation of Zel'dovich / Pauli-Villars / 't Hooft-
  *** Veltman / Coleman-Weinberg / Akhmedov / Koksma-Prokopec.

  ARTEFACT -- delete these and lose nothing:
    1. THE QUARTIC DIVERGENCE.  Present in both Lorentz-violating
       regulators (hard cutoff: 0.006333 K^4; lattice: 1.193801/a^4)
       and in NEITHER Lorentz-invariant one.  The two Lorentz-
       violating schemes do not even agree with each other on the
       coefficient -- they differ by a factor of 1.94.
    2. THE HEADLINE NUMBER ITSELF.  '10^120' is (cutoff)^4 divided
       by rho_obs.  Both the cutoff and the quartic power are
       supplied by the scheme.  In dim reg there is no such term to
       compute, so there is no 10^120 and, correspondingly, no
       '120 digits of cancellation' to explain.  The famous
       fine-tuning COUNT is a property of a bad regulator.
    3. THE OBJECT ITSELF.  The hard-cutoff mode sum returns
       w = +0.333333 -- a radiation bath.  It is not a cosmological
       constant at all.  A calculation whose answer has the wrong
       equation of state has not computed the quantity in dispute.

  PHYSICAL -- no regulator choice removes these:
    1. THE m^4 LOG TERM.  Its coefficient, -1/(32 pi^2) per e-fold,
       is identical in hard cutoff, Pauli-Villars and dimensional
       regularisation (PART F, verified to ~1e-15 relative).  It is
       an RG running, and runnings are scheme independent.
    2. THE MEASURED-MASS RESIDUAL.  Evaluated in the clean scheme
       for the electron, muon, tau, W, Z, Higgs and top, it
       overshoots rho_obs by 10^54.7 (mu = 1 GeV) or 10^53.9
       (mu = m_top).  Two decades of mu move it by 0.8 decades.
       Equivalently: the renormalised Lambda moves by 1e+54 times
       rho_obs per e-fold of mu.  Nothing here is assumed about
       physics above the electroweak scale.  There is no cutoff in
       PART G at all.

  SO THE SUMMARY SENTENCE IS:  fixing the regulator deletes the
  famous number and leaves the problem.  The vacuum-energy problem
  is not 'why is 10^120 not 1'; it is 'why does a sum of terms of
  order m_top^4/(16 pi^2) -- computed from measured masses, in a
  scheme with no arbitrary cutoff, with the right equation of state
  -- come out 55 orders of magnitude smaller than each of its
  own terms'.  That question is smaller, sharper, and completely
  unsolved.

  WHAT THIS DOES NOT ESTABLISH (stated because the temptation is
  real):
    * It does NOT show the vacuum energy is small, or zero, or
      calculable.  It shows the standard estimate of its SIZE is
      scheme-dependent, and then computes a scheme-INdependent
      lower bound on the tuning that is still 55 decades.
    * It does NOT show that zero-point energy gravitates.  That is
      the actual open question (wave 3, VERDICT) and no computation
      decides it.
    * The w = -1 results here are properties of a REGULATOR, not
      measurements of nature.  Whether the dark energy actually has
      w = -1 is an empirical question handled in Test 15
      (is_the_vacuum_constant.py), not here.
    * No number in this file is a significance.  Every small
      residual quoted (1e-16, 1e-24, 1e-51) is either a truncation
      of a physical limit or a floor of the arithmetic, and each
      one is laddered in the output so the reader can see which.
      None of them measures how well nature obeys anything.
    * The four-regulator table is about SCHEMES, i.e. about our
      bookkeeping.  It is not a survey of candidate physics.  The
      only part of this file that touches nature is PART G, and
      PART G is where the problem is.

  STATUS: REPRODUCED, NOT DISCOVERED.  SOLVES NOTHING.
==============================================================================

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