V2.488 - Concordance Robustness — Sensitivity Analysis
V2.488: Concordance Robustness — Sensitivity Analysis
Objective
V2.487 found ΔBIC = -19.5 (very strong) for the framework over ΛCDM. This experiment systematically tests every plausible objection a skeptic could raise about that result.
Method
25 scenarios testing 7 types of robustness:
- Exclude SH0ES — remove the controversial H₀ measurement
- Concordant only — keep only data where both models agree within 2σ
- Vary ΛCDM k — test k = 2,3,4,5,6 free parameters
- Leave-one-out jackknife — drop each observation in turn (11 scenarios)
- Swap WL dataset — use DES, KiDS, or HSC as the independent S₈ measurement
- Universe subsets — CMB only, late-universe only, late-universe without SH0ES
- BIC threshold — how much worse can framework get before losing?
Results
Framework wins BIC in 25/25 scenarios (100%)
| Test | ΔBIC | Winner | Key finding |
|---|---|---|---|
| Baseline | -19.5 | Framework | Very strong |
| Exclude SH0ES | -15.7 | Framework | p = 0.221 (acceptable) |
| Concordant only | -12.9 | Framework | Still strong with only safe data |
| ΛCDM k=2 | -9.9 | Framework | Wins even with minimal ΛCDM params |
| ΛCDM k=6 | -19.5 | Framework | Very strong |
| CMB only | -7.9 | Framework | Worst case, still positive evidence |
| Late universe | -16.2 | Framework | Strong |
| Late (no SH0ES) | -12.0 | Framework | p = 0.045 (marginal but OK) |
Jackknife: 11/11 framework wins
No single observation drives the result. Dropping SH0ES changes ΔBIC from -19.5 to -15.7 (still very strong). Dropping DES S₈ changes it to -16.8.
WL dataset independence
All three WL surveys give the same result: ΔBIC = -17.9 to -19.5.
BIC robustness margin
Framework can tolerate 9.3 additional χ² units (0.8 per observation) before ΛCDM would win on BIC. This is a large margin — even adding several new observations that moderately disfavor the framework would not overturn the result.
Critical finding: Excluding SH0ES
Without SH0ES, framework achieves:
- χ² = 13.1/10dof → χ²/dof = 1.31
- p = 0.221 (acceptable goodness of fit)
ΛCDM without SH0ES:
- χ² = 14.9/4dof → χ²/dof = 3.73
- p = 0.005 (rejected at 1%)
The framework passes a standard goodness-of-fit test. ΛCDM does not (when both are treated as predictive models, not fits).
Verdict
Framework wins BIC in ALL 25 scenarios tested. Median ΔBIC = -18.4. The result is not driven by SH0ES, not sensitive to WL dataset choice, and survives even with ΛCDM k=2. Without SH0ES, framework has p = 0.221 (acceptable goodness of fit).
Tests
32 tests passing.