D2a — σ₃ and step: The Observable and the Canonical Transition Rule (Triniton Framework, Discrete Regime)

D2a — σ₃^obs and step: The Observable and the Canonical Transition Rule This document establishes the definition and canonical construction of the discrete observable σ₃^obs_T and the transition rule step within the Triniton framework (discrete regime). All imported results are explicitly referenced to D2a-C (evidentiary companion), which reproduces the relevant primary discrete corpus statements. Key results: (I) σ₃^obs_T([x]_T, r) := |B_r^T([x]_T)/≡T| is defined as a globally-dependent observable, with its strict locality explicitly declared open. (II) MP(III) is a structural non-freezing filter with an existential operational representation — not its definition. (III) The information-economy criterion C_PE is logically independent of MP(III); a local adaptation C_PE^loc is introduced as a declared convention whose equivalence with the corpus definition is not established. (IV) The canonical argmax-Φ rule is imported via the four-link chain: Lemme 4 → Thm 34 → §A2 → Thm III.A1(iii). (V) Φ(S,T) := Σ{r=1}^{r_max} σ₃^obs_T([x₀]_T, r) is the decision functional maximised by step. (VI) Φ is non-decreasing under step, using Thm III.A1(ii) together with a declared monotonicity convention. (VII) Rooted-ball locality (Thm III.D1) is established; locality of σ₃^obs_T requires an additional coherence lemma, declared open. Open programs explicitly identified: equivalence C_PE^loc ≡ condition (d) of Thm III.A1(iii); local/global coherence lemma for σ₃^obs_T; full Θ(r^d) bound on Class A; Ω(r^d) general lower bound; quotient interpretation of Ext_loc; horizon rule for r_max; monotonicity of Δσ₃^obs = ΔΦ. No result from the continuous or cosmological corpus is imported. No post-hoc closure of open programs is permitted. Documentary architecture: D2a → D2a-C → Primary discrete corpus. Status labels: [Proved here], [Imported], [Imported w/ reserve], [Convention-D2a], [Open — discrete].