The Five-Step Methodology of tonyrao 2026c treats each entry of the state-observation matrix as an atomic judgement: each (state, observation) pair is classified as classical or non-classical via the interference parameter κ. The Market Observation Equivalence Hypothesis tonyrao 2026d grounds this judgement in an isomorphism between Hidden Markov Model Bayesian update and quantum POVM measurement collapse, but only under a diagonal restriction ρ = diag (π) corresponding to fully decohered systems. The diagonal restriction is equivalent, this paper observes, to assuming that each lattice entry has no internal sub-structure—each (state, observation) pair is treated as atomic. This paper proposes that each entry of the Five-Step lattice should not be treated as atomic. Each entry (sᵢ, oⱼ) is itself a centred observation system in the sense of the Digital Exhaust framework tonyrao 2026a: it has a centre, peripheral factors, and a likelihood matrix L₈, ₉ that records how the centre is to be inferred from the peripherals. The result is a layered observation system: the outer layer is the Five-Step lattice, and each entry M₈, ₉ = L₈, ₉ is itself a Digital Exhaust likelihood matrix. Three claims follow. First, the layered structure is well-defined, with variable-N₈, ₉ per cell paralleling the variable-Nₜ structure of tonyrao 2026b. Second, the inner layer discloses structure that the outer-only summary suppresses: κ₈₉ = f (L₈, ₉, π₈, ₉). Third, MOEH is recovered as a degenerate corner case in which each L₈, ₉ collapses to a scalar; lifting the atomic-entry assumption admits microscopic observation capability via an explicitly constructed induced density matrix on S × O, whose off-diagonal block (and its Frobenius norm α) the diagonal restriction excludes by construction. Part of the NSD / MOEH research programme. Third paper in the Digital Exhaust series.
Huiying Rao (Sat,) studied this question.