Abstract This paper isolates the conceptual spine of the Principia Orthogona series: the claim that generative transitions, including the origin of life, form a universality class defined by the contactgeometric operator sequence 𝐺 = 𝑈 ∘ 𝐹 ∘ 𝐾 ∘ 𝐶 ∘ 𝐸. We show that the directionality of this sequence — previously misread as orthogenetic in the discredited biological sense (Eimer, Teilhard, Berg) — is in fact a property of the phase space, not of the systems within it. We formalise this as topological orthogenesis (Definition 2.1), grounding the notion in directed algebraic topology (Grandis 8) and dissipative-structure thermodynamics (Prigogine 10, England 11). Three independent physical instances are shown to realise the same operator algebra: (I) the Enceladus cryovolcanic plume 6, 7, (II) terrestrial alkaline hydrothermal vents 12, 13, and (III) RNA-world ribozyme self-replication 14. The Kalpataru tree is identified with the Hasse diagram of the partial order on reachable states induced by topological orthogenesis. Falsifiability conditions, common across all three instances, are tabulated in §7. MSC 2020: 53D10 (contact manifolds), 37C75 (stability), 58K05 (Whitney singularities), 92B05 (general biology), 82C70 (transport in non-equilibrium statistical mechanics), 80A05 (thermodynamics). Keywords: topological orthogenesis, directed topology, contact geometry, dissipative structures, universality class, abiogenesis, Kalpataru, generative transitions, Whitney singularity, Reeb flow, Theorem T1, alkaline hydrothermal vents, RNA world, Enceladus, dm3 framework, Principia Orthogona.
Pablo Nogueira Grossi (Thu,) studied this question.