Observable detail · COSMOLOGY
Spectral index n_s
| Prediction | 1 − 4/120 = 0.9667 |
|---|---|
| Measured | 0.9649 (Planck) |
| Residual | 0.4σ |
| Status | hit |
| Source paper | DCT-CMB-01 |
Mechanism
n_s = 1 − 4/N_vertex with N_vertex = 120 from the 600-cell. The factor 4 = D_spacetime − 0 spacelike directions on the inflationary slow-roll trajectory.
Derivation
n_s = 1 − 4/N_vertex with N_vertex = 120 from the 600-cell. The factor 4 = D_spacetime − 0 spacelike directions on the inflationary slow-roll trajectory.
The closed-form prediction is
$$ \text{predicted} = 1 − 4/120 = 0.9667 $$against the measurement 0.9649 (Planck), giving residual 0.4σ.
Python verification
The verification script for this observable is cmb_analysis.py. Run it with python3 cmb_analysis.py to reproduce the canonical DCT result against the public-archive measurement source listed above (Planck 2018 VI.).
Methodology
| Domain | Cosmology (COS) |
|---|---|
| Input data source | See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction. |
| Measurement procedure | The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied. |
| Acceptance threshold | HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved. |
| Falsification threshold | MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment. |
| Current status | See the verdict pill in the prediction table above. |
Cross-references
Related observables in the same domain: planck-cmb-tt · planck-a-l.
Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.
Audit notes
Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-CMB-01) is the canonical source of the derivation chain.
References
- Planck 2018 VI
- Source paper: DCT-CMB-01
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