Research focus · Lane–Seifert
How strongly do supernova data support timescape, and how much does that conclusion depend on the analysis? Our four-stage programme connects reproduction and controlled Pantheon+ comparisons to a planned prediction test on DES-Dovekie.
Published finding
In the preregistered Strand 2 comparison, switching from our Lane-type hierarchical likelihood (H) to the Seifert-type Tripp likelihood (T) increases ln B by approximately 1.89 nat. The P+1690 data at zCMB ≥ 0.075 and the common β prior [0,4] remain fixed.
The architecture switch changes the relative model preference with the data held fixed. Which individual assumption generates this shift is the open question for Strand 3.
| Implementation | β prior | ln B |
|---|---|---|
| H · hierarchical | [0,4] | 0.38 |
| T · Tripp | [0,4] | 2.27 |
ln B = ln Z(timescape) − ln Z(spatially flat ΛCDM). Positive values favour timescape. Values rounded to two decimal places; architecture contrast from unrounded values: 1.8931 nat.
One programme · Four connected stages
The four-stage framework was designed from the outset: reproduce, compare, understand, then test on further data. Each detailed study builds on the completed preceding results. The aim is to establish how strongly supernova data support timescape and how much that conclusion depends on the analysis, whatever the outcome.
Completed · STOP documented
Strand 1 · Reproduce
The baseline evidence test at zmin = 0.040 did not meet its prespecified reproduction tolerance and ended at STOP. A subsequent maximum-likelihood check reproduced the published best-fit values at zCMB ≥ 0.033 (fv0 = 0.675, ΩM0 = 0.433). This limits our reproduction claim; it does not establish an error in the published calculation.
Completed · Results published
Strand 2 · Compare
On identical P+1690 data at zCMB ≥ 0.075 and common priors with β in [0,4], the implemented Lane-type and Seifert-type likelihoods give ln B ≈ 0.38 and 2.27. Their paired difference is 1.8931 nat. Terminal Record v1.5 was published on 27 October 2026. Reconstruction of the exact historical analyses remains a separate question.
Preregistered · 31 October 2026
Strand 3 · Understand
Strand 3 separates two mean maps and three covariance treatments, with β in [0,4] and [0,7], on P+1690 (full and zCMB ≥ 0.075) and P+580. It adds a false-positive control on ΛCDM-generated data, subject to registered generator checks, and a bias-correction test. Analysis and decision rules are preregistered. No results yet.
Plan published · 1 November 2026
Strand 4 · Test
Strand 4 is planned as a predictive transfer test on DES-Dovekie. Shared supernovae form a paired pipeline bridge; objects also present in P+1690 are excluded from the prediction sample. A quantitative prediction learned from Strand 3 and its interpretation will be fixed publicly before the DES prediction test. Absolute Bayes factors will be assessed alongside calibration under known truth. The final test specification is not yet registered. No results yet.
Agreement on DES would support the predictive model’s transfer to further data. It would not, by itself, establish which cosmology is correct. A mismatch would challenge the predictive model as a whole, including population modelling and the pipeline transfer. Statements about timescape and ΛCDM will use the absolute Bayes factors together with the known-truth calibration.
The programme follows one question across four stages. It first checks reproduction, measures the effect of changing the analysis, investigates the assumptions responsible, and then tests a prediction on further data. This makes the strength and the limits of the supernova evidence more explicit.
Sources & evidence
Dated results records, registered protocols and the public programme outline make the four stages traceable. The Strand-4 record also publicly binds the detailed planning state by its SHA-256 hash.
Strand 3 will publish its prediction register before results from the main phase are unsealed. The checks specified in the registration remain prerequisites.
Strand 1: author and scientific responsibility Harald Zierhut; technical execution and numerical checking Thomas Schwarz. Strands 2–4: Harald Zierhut and Thomas Schwarz as co-authors; scientific design and decisions Harald Zierhut; computing and technical execution Thomas Schwarz.
Page updated: 1 November 2026. The links point to dated versions.
