The Discrete Extramental Clock as Bayesian Optimal Accumulator: Large Deviations, Renormalization, and Strong Optimality under Purely Ordinal Observability

We present a unified theoretical framework that connects the deductive reduction of ordinal dynamics to Feigenbaum universality with the theories of large deviations, topological pressure, and sequential Bayesian inference. The setting is deliberately minimal and robust: a finite space X of ordinal configuration vectors (rank orderings of N components observed in sliding windows of length n). On this space we work with the Systemic Tau observable τₛ(k), defined as the average Kendall rank correlation across all pairs of components. This observable requires no knowledge of absolute values, is invariant under monotonic transformations, and is remarkably robust to noise. Under generic assumptions on the underlying flow (transversal quadratic critical surfaces), the foundational result known as Teorema v24 shows that the first-return map reconstructed purely from ordinal data on a suitable coherence phase coordinate is of class C³, unimodal, and possesses a non-degenerate quadratic critical point, with all constants controlled explicitly by the geometry of the flow. Consequently the classical Feigenbaum--Coullet--Tresser renormalization theory applies, providing the universal scaling constant δ ≈ 4.6692016091 and a combinatorial lemma on the expected absolute value of τₛ in periodic orbits of period 2ᵏ. We construct a bounded coherence potential φ_τ whose associated rate function I(ν) arises from the variational principle for topological pressure on the finite space. A combined proposition establishes that entropy-plus-potential quantities rescale by δ⁻¹ across renormalization levels of the filtration ᵣ\ and that large-deviation rates for atypical values of τₛ decay geometrically as δ⁻ʳ. We prove three main results that form a single coherent package. First, the Discrete Extramental Clock (RECD)---whose increments are given exactly by the renormalization-scaled law Δ t(k) := δ⁻ᵏ · |τₛ(k)| · (Δ t₀ / n)---emerges canonically as the accumulation process of the log-posterior for the critical-proximity parameter under sequential Bayesian updating with purely ordinal observations. Second, the empirical measures on X satisfy a large-deviation principle with good rate function I(ν); the probability of atypical values of the systemic tau observable decays geometrically near criticality at a universal rate governed by the renormalization hierarchy. Third, within the natural class of accumulation schemes that depend on τₛ only through potentials of the same form, the RECD is strongly optimal simultaneously in exponential growth rate of the log-posterior, in the minimax sense over adversarial sequences of renormalization levels, and in the long-run accumulation rate of ordinal Kullback--Leibler divergence. The optimality is information-theoretically equivalent to weighting by the Feigenbaum eigenvalue δ itself. The development remains symbolic and combinatorial on the finite space X whenever possible. While the mathematical arguments are fully rigorous, we have made special effort to provide conceptual motivation, intuitive pictures, and step-by-step explanations before technical details, so that the ideas are accessible to a scientific reader with solid mathematical background but not necessarily expert in renormalization or large-deviation theory. Diagrams are used to make the hierarchical structures and dynamical processes visually intuitive. The framework supplies a universal, model-independent language for detecting critical transitions under the weakest possible observational assumptions and is consistent with (and supplies an information-theoretic foundation for) the broader four-level ontological hierarchy of extramental time.