Observable detail · STRUCT
McKay correspondence \(2I \to E_8\)
| Prediction / mechanism | McKay correspondence between the binary icosahedral group \(2I\) and the affine Lie algebra \(\widehat{E_8}\); fixes both the three-generation count and the SM gauge group. |
|---|---|
| Measured | Mathematical theorem (McKay 1980). |
| Residual / status | HIT — structural identity |
| Status | HIT |
| Source paper | DCT-SM-01 |
Mechanism
McKay 1980: \(2I\) is the only finite subgroup of \(SU(2)\) whose representation graph reproduces the \(\widehat{E_8}\) Dynkin diagram.
Derivation
The derivation chain follows the cluster paper DCT-SM-01 and reduces to the canonical DCT constants (\(P_0 = 0.851\), \(\omega_0 = 50{,}037\), \(c_{BD} = 138{,}189\), master identity \(2\omega_0 + 3 = c_{BD} \cdot P_0^2 = 100{,}077\)). See the cluster paper for the full multi-line derivation.
Methodology
| Domain | Polytope / structural identity (STRUCT) |
|---|---|
| Input data source | See "References" below for the canonical public-archive citation. |
| Measurement procedure | The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference. |
| Acceptance threshold | HIT: residual within 1σ of measurement. SOFT: directional agreement 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 verdict pill above. |
Python verification
Verification script: partition_function_verification.py. Run with python3 partition_function_verification.py to reproduce the canonical DCT result against the public-archive measurement source listed below.
Cross-references
Related observables: conformal-wall-theorem · master-identity.
Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.
Audit notes
This sub-page is part of the post-build-out of the observable archive (see the observable index). Verdict reflects the corpus-canonical (constant-\(P_0\)) treatment. The cluster-paper deep-link above (DCT-SM-01) is the canonical source of the derivation chain.
References
- McKay 1980
- Source paper: DCT-SM-01
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