Mass as a Coordinate, Spin as a Label: An Anatomical Review of Reynaud's Dilatation of Souriau's Moment Map

This review anatomises Patrick B. Reynaud's letter Symplectic geometry at eleven parameters: Souriau's moment map with a dilatation (Reynaud, 2026a). The letter's algebraic core is narrow and, in outline, correct. The eleven quantities of a classical body — position, momentum and a Pauli–Lubański vector orthogonal to momentum — are read as the value of a moment map. For the Poincaré group that value lies on an eight-dimensional coadjoint orbit labelled by two Casimirs, with the world-line parameter quotiented out, so that 11 = 8 + 2 + 1. Adjoining the dilatation D = x·p changes the stabiliser. For a massive spinning body the coadjoint orbit of the Weyl, or similitude, algebra is ten-dimensional, labelled by the dimensionless spin alone: 11 = 10 + 1. Mass, a Poincaré Casimir, becomes a coordinate conjugate to D, and the world-line parameter re-enters because D is not conserved along free massive motion. The conformal completion in so(2,4) places the same body on a twelve-dimensional orbit whose invariants are functions of spin. A massless body gains nothing from the dilatation, and the conformally invariant massless spinning body is identified with Penrose's twistor. On the thermodynamic side, no normalisable Gibbs density on the Weyl orbit admits a non-zero dilatation multiplier. The review separates identities of the algebra from readings imposed by an unpublished companion series and from records of other authors. The identities are the contribution; the readings are not established in the letter. Ontologically the letter shifts mass from label to coordinate and spin from vector to invariant. KSCCN review article, 5 October 2026. Dr. Syed Muntasir Mamun, ORCID 0000-0001-6845-2853. The views expressed are those of the author.