Everpresent Λ — causal-set theory's fluctuating cosmological 'constant' — splits cleanly. Its magnitude prediction is real: Λ_rms = 1/√V₄ evaluates to 1.39× the observed Λ with this registry's own fitted H₀ (the only advance prediction of Λ's size in physics), and it tracks H² at every epoch, dissolving the why-now coincidence. But its dynamics are excluded by this registry's own pipeline: 0 of 2000 wandering-Λ realizations fit DESI DR2 + Pantheon+ + CMB better than ΛCDM (ensemble-typical Δχ² ≈ +3000; best single draw +260), 14% recollapse before reaching us, and 97% flip the sign of ρ_Λ inside z ≤ 2.5 — so w(z) is typically not even definable, the wrong shape for the registry's smooth 2.16σ descent.

   required -- we observe the CMB, so a crash before it is fatal
    with or without the R prior in the fit.

  B6 -- DOES WANDERING LAMBDA PRODUCE THE REGISTRY'S BINNED w(z)?
        (USR-2026-0004: -0.920, -1.078, -1.537 across
        bins 0.0-0.4 / 0.4-1.0 / 1.0-2.5; at each realization's own
        best fit; w_bin = -1 + (1/3) dln rho_L / dln(1+z) over the
        bin; undefined if rho_Lambda changes sign inside the range.)
    among the 1720 viable realizations:
      w defined in the whole data range (no sign change, z<=2.5):   53  (0.0308)
      monotone DESCENT w1 > w2 > w3:                      10  (0.0058 of viable)
      descent AND crossing -1 (w1 > -1 > w3):              2  (0.0012)
      ALL THREE bins within 2 sigma of USR-2026-0004:      0  (0.0000)
      best realization: rho_Lambda changes sign inside z<=2.5 --
      its w(z) is not even definable across the data range.
    registry bins for reference: -0.920+/-0.040 / -1.078+/-0.093 / -1.537+/-0.282

==============================================================================
PART C -- WHAT WOULD DISTINGUISH EVERPRESENT LAMBDA FROM BOTH LCDM
          AND SMOOTH QUINTESSENCE (the project's sharpest tool)
==============================================================================
  (i) NON-MONOTONIC w(z) WANDERING WITH HUBBLE-SCALE COHERENCE.
      Smooth quintessence and CPL give monotone or slowly-turning w(z);
      everpresent Lambda predicts w(z) that wanders, with coherence length
      Delta ln V ~ 1 (Delta z ~ 0.3 at low z) and sign changes of rho_Lambda
      (raw-ensemble probability of a sign change inside z <= 2.5: 0.97,
      amplitude-independent).  CURRENT REACH: the registry's own binned w(z)
      (USR-2026-0004) has THREE bins -- it can see a descent but cannot tell
      wandering from monotone descent.  DESI DR3 + Euclid BAO/SN will support
      ~8-10 independent w bins at sigma_w ~ 0.05-0.15 to z ~ 2: enough to see
      one full coherence oscillation if its amplitude is >~ 0.1 in w.  A
      reconstruction that goes DOWN, then UP, then DOWN with Delta z ~ 0.3-1
      coherence would kill both LCDM and smooth quintessence while being
      everpresent Lambda's native shape.

  (ii) ISOTROPY STRESS -- THE KNOWN OBJECTION, STATED REGARDLESS.
      Lambda built from the local causal past is a spacetime FUNCTION:
      causally disconnected patches at recombination had independent
      fluctuations, so naively Delta Lambda / Lambda ~ O(1) between sky
      patches, wildly violating the observed 1e-5 CMB isotropy.  Ahmed et
      al. acknowledge this; no covariant local formulation that fixes it
      exists (this is the model's kinematical gap, analogous to our
      USR-2026-0070 finding for the emergent-gravity wing).  Any everpresent
      Lambda that survives must correlate super-horizon patches -- which is
      exactly the kind of nonlocal bookkeeping a COMPUTED universe performs
      cheaply and a local dynamical law does not.  CURRENT REACH: CMB
      isotropy already constrains the naive version fatally; the surviving
      formulations predict small residual anisotropy -- the place to look is
      hemispherical power asymmetry (the ~2-sigma large-angle sector already
      in this registry, cosmic-variance capped) and anisotropy of H0/BAO
      across sky patches, where DESI DR3 and Euclid will reach sub-percent
      per-patch precision.

  (iii) SIGN CHANGES OF LAMBDA IN THE PAST.
      A wandering Lambda was NEGATIVE for O(half) of its history.  A past
      negative-Lambda episode at z ~ 2-4 depresses H(z) locally and is
      visible as rho_DE(z) crossing zero in expansion-history
      reconstructions.  Intriguingly, the registry's own binned w descent
      (w = -1.54 in the 1.0-2.5 bin) corresponds to rho_DE FALLING toward
      higher z -- the direction of a zero crossing just beyond the data.
      CURRENT REACH: background data constrain rho_DE(z)/rho_c0 to ~ +/-0.15
      out to z ~ 1.5 but only ~ +/-0.3-1 at z > 2; a crossing at z >~ 3 is
      essentially unconstrained today.  DESI DR3 Lyman-alpha BAO and Euclid
      push few-percent H(z) to z ~ 3.5: a detected rho_DE(z) zero crossing
      would eliminate LCDM and every non-phantom smooth quintessence in one
      stroke, and is everpresent Lambda's most falsifiable near-term
      signature.

  DISCRIMINATOR VERDICT FOR THE PROJECT.  Everpresent Lambda is the one
  discreteness theory whose signature lives in the dynamics -- precisely
  where this registry's live cracks are.  It is Lorentz-invariant (causal
  sets dodge every frame-dependent seam this project has already closed),
  and its distinguishing predictions (i) and (iii) are testable THIS decade.
  But PART B shows what it must survive to get there, and (ii) is a standing
  kinematical objection that no amount of background fitting removes.

==============================================================================
HEADLINES
==============================================================================
  A. MAGNITUDE (REPRODUCED -- Sorkin's prediction, our H0):
     V_4(past light cone) = 5.923e+242 l_p^4 ; V_4(causal diamond) = 5.725e+242 l_p^4
     Lambda_rms/Lambda_obs = 1.387 (light cone) ; 1.411 (diamond)
     with the 8pi action normalisation: 34.87 ; 35.47 -- the bracket
     IS the prediction: right magnitude out of 122 orders, loose
     to ~1 order in the volume/normalisation conventions.
     TRACKING: Lambda_rms(z) ~ H(z)^2 at every epoch (table in
     PART A) -- the 'why now' problem does not arise.
  B. SHAPE CONFRONTATION (THIS FILE'S CONTRIBUTION):
     crashed universes (recollapse before z=0): 280/2000 = 14.0%
     ensemble Delta chi^2 vs LCDM, viable realizations, quartiles:
       with CMB   :   +2236.34 /   +3027.05 /   +3759.66
       without CMB:   +1029.09 /   +1536.53 /   +2002.82
     fraction beating LCDM: 0.0000 (with CMB), 0.0000 (without);
       beating the CPL best fit: 0.0000 ; MC floor 5.0e-04
     best single realization: Delta chi^2 = +259.79 vs LCDM
       (CPL: -6.97) -- best of 2000 noise draws, NOT the model.
     'as LCDM-like as our data' (Delta chi^2 <= 6.97): 0.0000
     binned-w shape (USR-2026-0004 descent -0.92/-1.08/-1.54):
       monotone descent: 10/1720 viable ; descent crossing -1: 2 ;
       all 3 bins within 2 sigma of the registry: 0  (fraction 0.0000)
  C. DISCRIMINATORS: (i) wandering w(z), Hubble coherence -- DESI
     DR3/Euclid can see it; (ii) patch-to-patch Lambda variance --
     already fatally constrained in the naive version (the honest
     objection); (iii) past sign changes of rho_DE -- open at z>3,
     DESI DR3 Lya + Euclid reach it.  Raw sign-change probability
     in z<=2.5: 0.97 (amplitude-independent).

  INTERPRETATION IN ONE LINE: the magnitude coincidence is real and
  reproduced; pushed through this project's own likelihood, the
  wandering-Lambda ENSEMBLE is judged by the numbers above --
  ensemble-typical fit quality, not the best draw, is the model.

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