The Mass Plane and Its Closures: Stratification, Quantisation and Thermodynamics of the Weyl Orbit

Volume I of this review separated the identities of Patrick B. Reynaud's letter on Souriau's moment map with a dilatation from the readings of his companion series. The identities stand. For a massive spinning body the coadjoint orbit of the Weyl, or similitude, algebra is ten-dimensional, labelled by the dimensionless spin alone; mass is a coordinate conjugate to the dilatation charge D = x·p; the world-line parameter re-enters because D is not conserved; a null momentum makes the dilatation redundant with a boost; and no Gibbs density on the Weyl orbit normalises at non-zero dilatation multiplier. Volume II does not re-prove that arithmetic. It closes the orbit. The closures are six: a Darboux chart for the mass plane; a stratification by causal type of momentum and the Pauli–Lubański vector; geometric quantisation that integrates the spin sphere and refuses an integer on the mass plane; the Liouville measure and the Gibbs divergence restated as unboundedness of a Hamiltonian; Tulczyjew's condition as a reduction; and an anatomisation of the companion series against these closures. A public verification script is still owed. KSCCN review article (Volume II), 5 October 2026. Continues Mamun (2026), https://doi.org/10.5281/zenodo.23164930. Dr. Syed Muntasir Mamun, ORCID 0000-0001-6845-2853. The views expressed are those of the author.