A Physical Quantification Framework for Crowd Compression Risk: The P-index System and Its Contact-Mechanical Foundation
Year: 2026
Type: preprint
Abstract: A venue must know whether anyone will be crushed, and the indicator in use is density. Density cannot carry the question, and not because it is imprecise. The plan area of an upright adult places the geometric packing limit near 7 persons/m²; metro systems operate at 6–7 through peak hours with no recorded compressive asphyxia; and the peak local figures reported for crowd-crush incidents lie above that bound, where persons per square metre has ceased to be a well-defined planar measure. The two cannot be placed on a common scale even in principle, and an indicator cannot certify a state it cannot describe. This paper specifies an indicator defined where the deaths occur: on the individual, on force, and on time. The P-index is the cumulative seconds an individual is loaded above the accumulation onset. The C-value is the weight direction places on force — a division by the single-person exertion limit, through which any mechanically describable factor enters and through which nothing else does. Three results follow as arithmetic on stated premises. Compression is structurally collective: an individual committing their full body weight, perfectly aligned, reaches about 62% of the onset, so nobody opens the exposure gate alone. The peak does not kill: impulse is conserved, which bounds any disturbance to a fraction of a second against the minutes asphyxia requires — three orders of magnitude that no stopping distance closes. The window is the operative variable: a fatality is therefore a conjunction of an onset, a load, and a failure to recover within the survival time, and the third is what the P-index measures. The common inference that a fall in a dense crowd is close to sufficient for death does not survive the first two. The framework's discrimination between venues — the ratio of one venue's load to another's — uses no lethal threshold. Thresholds enter only where an absolute line is drawn, and the paper states for each what it rests on and what would displace it: they originate in a single source, by extrapolation, and have not been read in the original. The force-chain residual β is carried without a value. Whether any single channel loses more than 6.55% per contact decides whether routine crowds are absolutely safe at any size or whether every venue is a case, and no measurement of it exists. The framework is a specification. It constrains what a model must output, what it must pass, and what it must disclose, and not how it is built.
Author: Tao, Yixuan
Language: English
Subfield: Ocean Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167717136
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