From Dust to Black Holes: A Unified Geometric Framework for Cosmic Structures

In 1979, Carr & Rees showed that cosmic structures are not randomly distributed in mass-radius space (Nature278, 605). Forty-six years later, we ask: can a single law organize them all? A parameter-free geometric projection — θ = (360/π) arctan(√Ξ) — is applied to 1.1 million objects from eight public catalogs (SDSS, Gaia, ATNF, MWISP, BlackCAT, redMaPPer, NASA Exoplanet Archive), spanning 60+ orders of magnitude in mass. Without calibration or adjustment, the cosmos self-organizes into twelve distinct angular families on a half-circle [0°, 180°]. All 87 black holes (5 M☉ to 6.5 × 10⁹ M☉) converge exactly to θ = 90° with zero dispersion. The angular hierarchy correlates with temporal persistence, not mass: the Observable Universe (∼10⁵³ kg) projects to 147°, not 180°. Five falsification criteria are provided, all testable with existing data. Cosmos I establishes the map — a common cartography where the dust grain and the black hole finally appear on the same page. Cosmos II will test whether the map generates its own dynamics: how does a molecular cloud (θ ≈ 115°) evolve toward a star (θ ≈ 149°)? What trajectory does collapse follow toward θ = 90°? The roads remain to be traveled.