Period lengths (chemistry)

2 + 8 + 8 + 18 + 18 + 32 + 32 + 2 = 120

Prediction	120
Measured	120 (periodic table)
Residual	0
Status	hit
Source paper	DCT-FND-V2 · 10.5281/zenodo.20032839

Mechanism

Sum of period lengths Σ 2d² for d = 1, 2, 3, 4 on the periodic table totals 120 = number of 600-cell vertices. Each period closes a coordination shell of the polytope.

Derivation

Sum of period lengths Σ 2d² for d = 1, 2, 3, 4 on the periodic table totals 120 = number of 600-cell vertices. Each period closes a coordination shell of the polytope.

The closed-form prediction is

$$ \text{predicted} = 120 $$

against the measurement 120 (periodic table), 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 (Periodic table; CRC Handbook.).

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.

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

No external references for this entry — theorem or internal derivation.
Source paper: DCT-FND-V2 · 10.5281/zenodo.20032839

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