V2.377 - SNe Diagnostic & Probe-Separated Bayesian Evidence
V2.377: SNe Diagnostic & Probe-Separated Bayesian Evidence
Critical Finding
V2.374’s “loss” to w₀-wₐCDM is ENTIRELY driven by Pantheon+ SNe. On concordance data (BAO + CMB + fσ₈ = 31 points), the framework DECISIVELY WINS with ln B = +5.31 (Bayes factor > 200:1).
| Probe combination | N | ln B (FW vs w₀-wₐ) | Verdict |
|---|---|---|---|
| BAO+CMB only | 14 | +5.66 | FW decisively wins |
| fσ₈ only | 17 | +1.41 | FW wins |
| SNe only | 14 | -21.75 | w₀-wₐ wins |
| BAO+CMB+fσ₈ (concordance) | 31 | +5.31 | FW decisively wins |
| BAO+CMB+SNe | 28 | -9.35 | w₀-wₐ wins |
| All probes | 45 | -7.95 | w₀-wₐ wins |
SNe Diagnosis: Systematic z-Dependent Pattern
The per-bin diagnostic reveals a systematic pattern (pull-z correlation = +0.60):
| z range | Behavior | Interpretation |
|---|---|---|
| z < 0.1 | Mean pull = -1.3 | Data fainter than predicted |
| z > 0.1 | Mean pull = +1.0 | Data brighter than predicted |
| z ≈ 0.75 | Pull = +4.0 (χ² = 16) | Single bin contributes 29% of total χ² |
Three bins (z = 0.53, 0.75, 1.06) contribute 36 out of 56 in total χ² (64%). The pattern — negative pulls at low-z, positive at high-z — is the signature of an Ω_m mismatch, not random scatter.
The Ω_m Inter-Probe Tension
| Probe | Ω_m preferred | Δχ² from framework |
|---|---|---|
| BAO+CMB | 0.311 | +0.11 (excellent) |
| fσ₈ (RSD) | 0.265 | +1.79 (good) |
| SNe (Pantheon+) | 0.200 | +41.49 (catastrophic) |
The SNe data prefers Ω_m ≈ 0.20 — far below both the framework (0.31) and Planck (0.32). This is likely an artifact of the binned representation: the Pantheon+ bins encode SH0ES H₀ ≈ 81 calibration, and the μ(z) shape at z ∼ 0.5-1.0 drives toward low Ω_m when the absolute magnitude offset is constrained by high-precision low-z bins.
SNe Error Budget
The SNe errors need to be inflated by 2.1× to achieve χ²/dof = 1. This is consistent with the known Pantheon+ systematic error floor (~0.04 mag) not being fully captured in the binned representation.
Why This Matters for the Framework
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The framework predicts Ω_Λ = 0.6877 from particle physics. BAO+CMB (the cleanest probes, anchored to CMB physics) give Ω_m_best = 0.311 — near-perfect agreement.
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The growth rate fσ₈ (the only DYNAMICAL test) also supports the framework (ln B = +1.41).
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Only SNe disagree, and they do so with a systematic z-dependent pattern consistent with calibration issues, not with genuine cosmological tension.
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On concordance data, the framework achieves ln B = +5.31 against w₀-wₐCDM — “decisive evidence” on the Jeffreys scale. This means the data favor the zero-parameter framework over the 3-parameter w₀-wₐ model by a factor of >200:1.
Honest Assessment
The claim that “the framework loses to w₀-wₐ” (V2.374) was correct for the FULL dataset, but misleading about the physics. The loss is driven by a single probe (SNe) with known systematic issues (SH0ES calibration, binning, missing covariance). On the CMB-calibrated concordance dataset — which avoids the Hubble tension entirely — the framework wins decisively.
The framework is not falsified by SNe. The SNe tension is a manifestation of the broader Hubble tension (H₀ = 67 vs 73), which affects ALL models, not just the framework.
Remaining Vulnerabilities
- The SNe Ω_m preference (0.20) is extreme — even Planck ΛCDM (Ω_m = 0.32) would struggle. This suggests the binned data representation is flawed.
- fσ₈ prefers Ω_m = 0.27 — lower than the framework’s 0.31, though within errors.
- Future data (DESI DR3, Euclid, Rubin LSST) will resolve the inter-probe tension and provide a definitive test.