The famous vacuum-energy discrepancy is not a number but a function of an assumption: against the observed 2.24 meV scale it is 10^120.7 at a Planck cutoff, 10^108.4 at GUT, 10^56.4 at 1 TeV, 10^41.6 at QCD, and exactly 1 at the observed scale by construction — four decades of exponent per decade of cutoff, with the loop-factor convention alone shifting every row by 2.2 dex.

e vacuum couples to gravity.
  Everything QFT computes is a DIFFERENCE of vacuum energies, and
  differences are all it has ever been tested on.  The absolute
  value has never been measured by anything except the expansion of
  the universe -- one number, once.

==============================================================================
PART I -- BONUS: THE LEADING NON-EXOTIC EXPLANATION, COMPUTED
          (Weinberg 1987 anthropic bound; Efstathiou 1995;
           Martel-Shapiro-Weinberg 1998)
==============================================================================
  Derivation done here from scratch, spherical top-hat, exact:
    A top-hat of mass M, radius R, in a background with vacuum
    energy rho_V obeys (dR/dt)^2 = 2GM/R + (8 pi G/3) rho_V R^2 - Kc.
    Turnaround requires the RHS to vanish somewhere.  The RHS has a
    minimum at R_*^3 = 3M/(8 pi rho_V), where its value is 3GM/R_*.
    A perturbation that would have turned around at R_ta with
    rho_V = 0 has Kc = 2GM/R_ta, so collapse survives iff
        2/R_ta > 3/R_*  =>  R_* > (3/2) R_ta  =>  rho_V < (4/27) rho_ta
    where rho_ta = 3M/(4 pi R_ta^3) is the perturbation's own
    density at turnaround.  COEFFICIENT 4/27 = 0.148148.

  Chaining the standard EdS top-hat relations
    rho_ta = (9 pi^2/16) rho_m(z_ta),  (1+z_ta) = 2^(2/3) (1+z_c)
  gives  rho_V < (pi^2/3) rho_m0 (1+z_c)^3 = 3.2899 rho_m0 (1+z_c)^3.

    z_c    bound/rho_m0    bound/rho_Lambda,obs   observed is ...
  --------------------------------------------------------------------
    0.0            3.29                     1.5   0.2 decades below ceiling
    1.0           26.32                    12.1   1.1 decades below ceiling
    2.0           88.83                    40.8   1.6 decades below ceiling
    4.0          411.23                   189.1   2.3 decades below ceiling
   10.0         4378.81                  2013.6   3.3 decades below ceiling
  --------------------------------------------------------------------

  RECONCILIATION NOTE (honesty): Weinberg (1987) quotes the
  coefficient (500/729) pi^2 = 6.7693 in terms of rho_m0 (1+z_c)^3,
  a factor 2.06 above the 3.2899 derived above.  I have NOT reconciled
  the definitional difference (his z_c and reference density are
  defined differently).  Both are reported; the O(1) factor does not
  affect any conclusion, because the conclusion is about decades.

  WHAT THIS BUYS AND WHAT IT COSTS:
    BUYS: a selection argument reduces the puzzle from ~10^121 to
      ~10^1-10^3.  That is by far the largest single reduction any
      idea on the market achieves, and it was made BEFORE the
      measurement (Weinberg 1987, Efstathiou 1995, MSW 1998, all
      pre-1998-supernovae or contemporaneous).
    COSTS: it requires an ensemble in which rho_V varies and is not
      otherwise predicted.  That ensemble is not observed and this
      script does not test it.  A bound is not a mechanism.  Also
      note the bound is an UPPER bound only: it explains why rho_V
      is not enormous, and says nothing about why it is not zero,
      nor why it is comparable to rho_m TODAY of all epochs.

==============================================================================
VERDICT
==============================================================================
  *** NOTHING IN THIS FILE SOLVES THE COSMOLOGICAL CONSTANT
  *** PROBLEM.  NOTHING IN THIS FILE IS NEW.  What it does is turn
  *** a slogan into a table with its assumptions attached.

  THE TARGET (computed from Omega_L = 0.685, H0 = 67.4):
    rho_Lambda,obs = 5.8450e-27 kg/m^3 = 5.2532e-10 J/m^3 = 2.5193e-47 GeV^4
    rho^(1/4)      = 2.240 meV

  THE DISCREPANCY IS NOT ONE NUMBER, IT IS A FUNCTION OF A CHOICE:
    Planck cutoff : 10^120.7 (loop factor) .. 10^122.9 (raw M^4)
    TeV cutoff    : 10^56.4 .. 10^58.6
    observed-scale cutoff : 10^0, exactly, by construction.
    Anyone quoting '10^120' with no cutoff attached is quoting an
    assumption as a measurement.  That is the single most useful
    thing in this file.

  BUT THE PROBLEM DOES NOT NEED THE CUTOFF (PART E):
    the electron alone overshoots by 10^31; the Higgs potential's
    own minimum by 10^55.  Those masses are measured.  There is no
    version of 'distrust high energies' that removes the problem.

  SUSY (PART F): required M_s = 2.75e-12 GeV = 2.75 meV, versus an
    experimental floor of 1e3 GeV.  At 1 TeV it misses by 10^58.0,
    with the wrong sign.  Best idea on offer; total failure.

  FINE-TUNING (PART G): ~121 decimal places of cancellation at a
    Planck cutoff -- 9.3 times more digits than the most precise
    measurement ever made.  And that count is itself an artefact of
    the hard-cutoff scheme; in dim reg there is nothing to cancel.

  WHY THIS IS NOT A 'MISSING LINK WE CAN DO'.  Every quantity above
  was computable in under a second on a laptop.  The problem is not
  that the arithmetic is hard.  The obstacle is that we do not know
  WHETHER ZERO-POINT ENERGY GRAVITATES.  Nothing here decides it:
    * QFT is tested only on DIFFERENCES of vacuum energy (Casimir,
      Lamb shift, g-2).  Every one of those works perfectly.  The
      absolute zero point has never been measured.
    * General relativity says the absolute value sources curvature,
      but GR was never tested in a regime where that mattered.
    * A hard cutoff does not even produce w = -1 (PART D), so the
      standard calculation is not computing a cosmological constant.
  Deciding this needs either a new principle (why the vacuum does
  not weigh what it appears to), or a measurement nobody knows how
  to make (the absolute vacuum energy of a laboratory system, in a
  gravitational sense).  Neither is a computation.  A larger
  simulation, a finer grid, more digits: all useless here.

  WHAT WOULD MOVE THIS SEAM (falsifiable, not done here):
    * a sub-millimetre gravity experiment finding that vacuum
      fluctuation energy does NOT gravitate as m/c^2 -- the length
      scale hbar c/rho^(1/4) computed in PART A is 0.08 mm, which
      is why that is the relevant experiment;
    * a laboratory system whose vacuum energy is CHANGED by a known
      amount and whose weight is then measured;
    * the equation of state.  The hard-cutoff mode sum predicts
      w = +1/3 (PART D); observation constrains w to within a few
      percent of -1 (QUOTED).  That is already a hard fact against
      naive mode-summing, already in the data.  Whether w EVOLVES is
      a separate live question and this file takes no position on it.

  STATUS: REPRODUCED, NOT DISCOVERED (Zel'dovich 1967; Weinberg
  1987/1989; Efstathiou 1995; Martel-Shapiro-Weinberg 1998; Koksma
  & Prokopec 2011).  Contribution of this file: one consistent
  scheme, two conventions carried in parallel so the scheme
  dependence is visible, and a cutoff-free floor (PART E) that
  survives every objection to the famous exponent.
==============================================================================

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