The Planck Lattice: A Cross-Domain Population Survey of 526 Measurable Quantities
Abstract
We map 526 measurable quantities from 13 scientific domains onto the Planck-unit logarithmic coordinate system defined in Clark (2026a), where a(x) = |log₁₀(x / x_P)|. Overall integer clustering is not statistically significant (mean |residual| = 0.246, p > 0.10, Monte Carlo, 10⁵ simulations). However, address occupancy is non-uniform: the most populated integer address hosts 42 quantities from 5 independent domains, exceeding the null-model expectation of ~11 (p < 10⁻⁵). Domain-specific clustering is significant (p < 0.001) in every category tested. A monotonic emergence gradient (Spearman ρ = 1.0) links biological organisational complexity to lattice position across eight levels. Centesimal sub-address analysis reveals physical entrainment as the mechanism behind within-address clustering: 65% of items at address 48 share a single sub-address locked to Earth's rotation period. All data, code, and the open-source Planck Lattice Mapper tool are provided for independent verification and extension. v3.2 (9 April 2026): Affiliation corrected from Auckland, New Zealand to Warrnambool, Victoria, Australia. Author name standardised to Robert M. Clark. Clark (2026c) driver analysis DOI updated from "Forthcoming" to 10.5281/zenodo.19312940. Forward references to Papers 4 and 5 added. v3.1 (March 2026): First public release. 526 quantities, 13 domains.
Fields of Study & Subjects
Origins and Evolution of Life
Probability and Statistical Research
Data Analysis with R
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 8 April 2026
- Document type
- Preprint