The anthropic bound on the vacuum energy explains far less than advertised: a four-way-validated linear growth ODE gives collapsed fractions 0.561, 0.210, 7×10⁻³, 6×10⁻⁹ as Λ grows ×1, ×10, ×100, ×1000, placing the ceiling at 6.4×, 35.5×, 108× the observed value at 50%, 10%, 1% thresholds. Granting a multiverse ensemble removes ~118.6 of 120.1 orders, leaving ~1.55; without granting the ensemble it explains zero.

78           67.74%

  [V7] closed-form median (12.3093) vs trapezoid over numeric F (12.3093):
       relative difference                      = 4.521e-10
  [V8] closed-form normalisation int_0^inf F dlam = 8.118427 vs numeric
       8.118427, relative difference               = 1.734e-13

  PRIMARY SCALE (M = 1e12 h^-1 Msun):
    Weinberg-style flat-prior median  Lambda = 12.3 x observed
    mean                              Lambda = 23.9 x observed
    observed Lambda sits at the 8.2th percentile of the prediction.
    TENSION: the argument predicts a Lambda about 1.09 dex LARGER
    than what we measure.  This is the well-known failure mode of the
    anthropic explanation: it does not merely fail to derive Lambda,
    it mildly MISPREDICTS it, in the direction of too much Lambda.
    Only ~8% of observers in this ensemble would see a Lambda as
    small as ours.  Deliberately NOT converted to a 'sigma': a
    percentile in a made-up ensemble is not evidence strength, and
    this project does not manufacture significance.  It is a mild
    embarrassment for the argument, no more and no less.

==============================================================================
BLOCK 9 -- SIDEBAR: THE BOUND IS TWO-SIDED IN |Lambda| BUT STILL A BOUND
------------------------------------------------------------------------------
  For Lambda < 0 the universe recollapses.  Flat matter + negative
  Lambda has the exact solution a ~ sin^(2/3)(3/2 sqrt(|Om_L|lam) H0 t),
  so the total lifetime is t_crunch = (2pi/3)/(sqrt(lam*Om_L) H0).
  1/H0 = 14.452 Gyr.

    required lifetime   max |Lambda|/Lambda_obs (negative side)
      3.0 Gyr                  147.8
      5.0 Gyr                   53.2
     10.0 Gyr                   13.3
  So habitability confines Lambda to roughly |lam| < 1e1-1e3 on BOTH
  sides.  It still does not explain why Lambda is nonzero: lam = 0 is
  perfectly habitable (in fact MORE structure forms), so the anthropic
  argument gives no reason at all for Lambda != 0.  That half of the
  puzzle -- tiny-but-not-zero -- is completely untouched.

==============================================================================
HEADLINE NUMBERS
------------------------------------------------------------------------------
  [H1]  validation: EdS max |D/a - 1|                 = 3.963e-12
  [H2]  validation: ODE vs quadrature, lam=1 / lam=1e3 = 4.518e-12 / 3.166e-12
  [H3]  validation: ODE vs 2F1, lam=1 / lam=1e3        = 4.518e-12 / 3.165e-12
  [H4]  validation: D_inf lam^-1/3 scaling, max residual = 2.220e-11
  [H5]  validation: D_inf vs analytic, max residual      = 1.054e-10
  [H6]  g(10*Lambda) = 0.464159   vs analytic 10^-1/3 = 0.464159
  [H7]  observed universe: D(a=1) = 0.785555, D_inf/D(1) = 1.403720
  [H8]  Lambda_max/Lambda_obs (M=1e12; 50%/10%/1% of F_obs) = 6.4 / 35.5 / 108.1
  [H9]  full spread over 5 mass scales x 3 thresholds:
        log10 Lambda_max/Lambda_obs in [0.23, 2.98]
  [H10] observed rho_Lambda = 2.553e-47 GeV^4 = (2.248 meV)^4
  [H11] log10(problem): reduced-M_Pl naive = 120.1 | M_Pl naive = 122.9
        M_Pl 1-loop = 120.7 | TeV naive = 58.6 | TeV 1-loop = 56.4
  [H12] ORDERS EXPLAINED (only if a multiverse + smooth measure is
        granted): 118.6 of 120.1 (Planck-cutoff, reduced M_Pl, naive);
        57.0 of 58.6 (TeV cutoff, naive).  ORDERS LEFT OVER = 1.55.
        WITHOUT the ensemble: 0 orders explained.
  [H13] flat-prior median Lambda = 12.3 x observed; mean = 23.9 x;
        observed value sits at the 8.2th percentile (predicts too much
        Lambda by 1.09 dex).
  [H14] negative-Lambda recollapse bound (5 Gyr lifetime):
        |Lambda|/Lambda_obs < 53
  [H15] ceiling sensitivity (M=1e12, 10% threshold) over
        delta_c in [1.60,1.75] x sigma scale [0.95,1.05]:
        Lambda_max in [28.4, 45.9] -- a factor 1.61 spread
  [H16] flat-prior median across mass scales 1e9 -> 3e14:
        Lambda_med/Lambda_obs = 124.1, 30.2, 12.3, 4.2, 0.5
        P(lam<lam_obs)        = 1.0%, 3.8%, 8.2%, 19.5%, 67.7%
==============================================================================
INTERPRETATION (honesty rules apply)
------------------------------------------------------------------------------
  WHAT THIS SHOWS.  The anthropic bound is real and it is
  quantitative.  A universe with Lambda more than ~35 x ours (primary
  calibration, 10% threshold; range 1.7-962 over all 5 mass scales x 3
  thresholds) freezes linear growth before galaxy-scale perturbations
  reach delta_c, and forms essentially no galaxies.  The ceiling sits
  log10 = 0.2-3.0 above the observed value.  Against a naive vacuum-
  energy prediction that is 10^120.1 too large (reduced Planck cutoff,
  no loop factor) or 10^58.6 (TeV cutoff), the ceiling accounts for
  almost all of the gap -- IF you grant a multiverse ensemble and a
  measure smooth on the scale of Lambda_obs.

  WHAT THIS DOES NOT SHOW -- and this is the honest headline:
  (1) IT DOES NOT SOLVE THE COSMOLOGICAL CONSTANT PROBLEM. Nothing
      computable does.  The obstruction is conceptual: we do not know
      whether zero-point energy gravitates at all, or what subtracts
      it.  This script recomputes a bound; it derives no value.
  (2) IT IS AN UPPER BOUND, NOT A PREDICTION.  Turning a bound into a
      prediction requires a prior/measure over an ensemble that is
      unobserved and, at present, unmeasurable.  Without that, zero
      of the ~120 orders are explained.
  (3) WITH THE STANDARD FLAT PRIOR IT MISPREDICTS. The median
      Lambda is 12x observed and we sit at the 8th percentile.
      The argument's own preferred measure wants ~1.1 dex MORE
      Lambda than we see.  Not a refutation -- but not a success
      either, and the residual sits inside the very window the
      argument itself constructs.
  (4) IT SAYS NOTHING ABOUT WHY Lambda != 0.  Lambda = 0 is maximally
      habitable.  The tiny-but-nonzero half of the puzzle is untouched.
  (5) THE CEILING IS SOFT.  Lambda_max ~ sigma^3 delta_c^-3, so the
      sensitivity table above moves it by a factor of several.  Do not
      quote a single Lambda_max; quote the range and the calibration.

  BOTTOM LINE FOR THE SEAM: the vacuum's local effects are verified to
  ~12 digits (electron g-2) while its total gravitating energy is wrong
  by 10^42 (cutoff at the QCD scale, where the condensate contributions
  are actually measured) up to 10^123 (Planck-mass cutoff, no loop
  factor).  The best non-exotic explanation on offer converts that into
  a habitable window only ~0.2-3.0 dex wide above the observed value,
  and then needs a multiverse to say anything at all.  This is a genuine,
  quantified hole in the standard picture -- and it is NOT a hole this
  project can close by computing.  Deflationary result, logged as such.
  STATUS: reproduced-known-result (Weinberg 1987/1989; Efstathiou 1995;
  Martel-Shapiro-Weinberg 1998).  No new claim is made.
==============================================================================

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