sin θ_13

neutrino mixing angle

Prediction	(1 − 1/φ⁴) / 240 = 0.003559
Measured	0.00364 (PDG)
Residual	1.69%
Status	soft
Source paper	DCT-SM-01 · 10.5281/zenodo.20032825

Mechanism

Algebraic ansatz from φ-eigenvalue structure of the binary icosahedral group. 240 = z·f_v = 12·20 is the order of the polytope vertex stabilizer.

Derivation

Algebraic ansatz from φ-eigenvalue structure of the binary icosahedral group. 240 = z·f_v = 12·20 is the order of the polytope vertex stabilizer.

The closed-form prediction is

$$ \text{predicted} = (1 − 1/φ⁴) / 240 = 0.003559 $$

against the measurement 0.00364 (PDG), giving residual 1.69%.

Python verification

The verification script for this observable is particle_physics_tests.py. Run it with python3 particle_physics_tests.py to reproduce the canonical DCT result against the public-archive measurement source listed above (PDG 2024 (Daya Bay + RENO + Double Chooz).).

Methodology

Domain	Standard Model number suite (SM)
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: ckm-s13 · jarlskog-j · inv-alpha.

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-SM-01) is the canonical source of the derivation chain.

References

PDG 2024
Source paper: DCT-SM-01 · 10.5281/zenodo.20032825

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