Key Findings (v0.1.0)
This page states what the final Protocol 1b run supports, in the order result → interpretation → caveat. The data are 1,590 Pantheon+SH0ES supernovae and 13 DESI DR2 BAO measurements, sampled with 100,000 steps and 96 walkers per model.
None of the findings below is a detection. Each is conditional on a fixed sound horizon, bounded priors and a fixed reference cosmology for the Ξosc time axis (Known Limitations).
Key results
1. ΛCDM is disfavoured by this dataset combination
Result. ΛCDM has ΔAIC = 18.3 relative to the best model, with χ² = 1554.2 against 1531.8 for CPL and 1529.8 for Ξosc.
Interpretation. Both dynamical models fit the combined data markedly better than a constant w = −1 does, even after the AIC penalty for their extra parameters. This suggests that the data prefer something other than w = −1 within this setup — it does not identify which.
Caveat. The BIC, which penalises parameters more heavily, narrows the gap (next section), and r_d is fixed rather than marginalised.
2. CPL and Ξosc are close by AIC; the BIC reorders the three
| Model | χ² | k | AIC | BIC | ΔAIC |
|---|---|---|---|---|---|
| CPL | 1531.824 | 4 | 1539.824 | 1561.343 | 0.000 |
| Ξosc | 1529.763 | 6 | 1541.763 | 1574.041 | 1.939 |
| ΛCDM | 1554.165 | 2 | 1558.165 | 1568.924 | 18.341 |
Result. CPL has the lowest AIC and the lowest BIC. Ξosc has the lowest raw χ² but ΔAIC = 1.94 relative to CPL. Under the BIC, Ξosc (1574.041) falls behind ΛCDM (1568.924).
Interpretation. The extra two parameters of Ξosc buy a small χ² gain that the AIC almost forgives and the BIC does not. The data do not single out the oscillating model.
Caveat. The χ² of each model is the best sampled point of its chain, not an exact minimum; see Model Comparison.
3. A non-zero amplitude is allowed, but it is prior-limited
Result. ε = 0.185 (+0.077, −0.087), i.e. ε/σε ≈ 2.26 with a symmetrised σε.
Interpretation. The posterior prefers ε > 0, but ε is sampled under a one-sided prior (0 < ε < 0.3), and the corner plot shows its distribution rising towards the upper bound. The ratio is a descriptive summary; it is not the significance of a detection.
Caveat. T and φ₀ remain weakly constrained. Details: Ξosc Oscillation Diagnostic.
4. The final chains satisfy the practical convergence criterion
Result. N/50 = 2,000 exceeds the largest autocorrelation time of Ξosc, τmax = 1504 (parameter T).
Caveat. The criterion measures sampling noise, not prior-boundary pile-up or multimodality. See Convergence Diagnostics.
Evidence level
These statements correspond to the ξ entries of the Claims Register: preliminary for the amplitude preference, and not stronger for anything else.