Observable detail · SPECTRAL
S(β=0.966) = ln(31), N_eff = 31.005
| Prediction | ln(31) = 3.4341, N_eff = 31.005 |
|---|---|
| Measured | exact (theorem) |
| Residual | 0 |
| Status | hit |
| Source paper | DCT-SPI-01 · 10.5281/zenodo.20032750 |
Mechanism
Partition function with Casimir-invariant correction C_j on the binary-icosahedral group: S(β = 0.966) = ln(31) and effective state count N_eff = f_v + z − 1 = 20 + 12 − 1 = 31.005. Exact to numerical precision.
Derivation
Partition function with Casimir-invariant correction C_j on the binary-icosahedral group: S(β = 0.966) = ln(31) and effective state count N_eff = f_v + z − 1 = 20 + 12 − 1 = 31.005. Exact to numerical precision.
The closed-form prediction is
$$ \text{predicted} = ln(31) = 3.4341, N_eff = 31.005 $$against the measurement exact (theorem), giving residual 0.
Python verification
The verification script for this observable is partition_function_verification.py. Run it with python3 partition_function_verification.py to reproduce the canonical DCT result against the public-archive measurement source listed above (Theorem; verifies numerically.).
Methodology
| Domain | Polytope / structural identity (STRUCT) |
|---|---|
| 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: master-identity · f-p0-5d-kk.
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-SPI-01) is the canonical source of the derivation chain.
References
- No external references for this entry — theorem or internal derivation.
- Source paper: DCT-SPI-01 · 10.5281/zenodo.20032750
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