A Common Dimensional Structure for Particle Masses, Spin, Color and Charge

A particle-mass prescription based on cumulative simplex counts assigns the observed families to spatial depths 2, 3, 4, 5, 6 and 10. An apparently different calculation gives exactly the same set: within ten spatial dimensions, a single minimal real rotation spinor admits a nondegenerate, rotation-invariant first-order clock precisely at those depths. Two further complete-channel calculations single out depths three and four, the quark assignments, through exceptional three-component responses. A spatial spinor profile realizes spin one-half and has finite bound-direction norm above depth two. A six-normal-direction exterior construction supplies relative charge weights 0, −1, 2/3, −1/3, with color singlets and two triplets of the same type; a separate depth-five construction connects neutrality with a handed kinetic sign. We present these results together because they constrain different aspects of the same proposed dimensional organization. The mass formula, its electron-referenced scale prescription, numerical inputs, geometric calculations and compatibility conditions are given explicitly. Their shared premises can reduce the number of unrelated choices, although the results are not statistically independent. The charge weights do not yet uniquely assign every particle to a depth, and no common interacting action has been shown to select all occupied counts and reproduce all properties. The contribution is a reproducible convergence of conditional mathematical structures, together with concrete bridges needed to turn it into a physical theory. It is not a claim of experimental confirmation or a completed derivation of the Standard Model spectrum.