Omega^n of quantum states with spectral order is a domain and von Neumann entropy is a measurement

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• Delta^n with Bayesian order is a domain and Shannon entropy is a measurementfinding0.836
  The set of classical probability distributions, ordered by Bayesian projections, forms a dcpo with least element the uniform distribution and max elements pure states; Shannon entropy is a measurement of type Delta^n -> [0,∞).
• Quantum theory reveals discreteness of atomic/molecular states with energy levels and quantized transitions.finding0.742
  Foundational quantum-mechanical fact that Schrödinger leverages to explain why molecular configurations are stable against small thermal perturbations.
• A cannot measure the entanglement entropy across any internal boundary of its environment; it cannot verify that any part of the world it attends to is genuinely independent of everything else (Fields & Glazebrook 2023, Corollary 3.2)finding0.737
  Generalises the self-evidence impossibility to all boundaries; grounds the teaching that all dharmas are empty
• Minimum entropy Markov blankets may characterize biological systems.claim0.731
  Conjecture about what distinguishes living from non-living systems.
• Irreducibles of Delta^n and Omega^n yield classical and quantum propositional logicsfinding0.726
  The order dual of irreducibles recovers the Boolean lattice of nonempty subsets and the lattice of nonzero subspaces, respectively.
• No finite system A can measure the entanglement entropy S(|AB>) across the boundary B that separates it from its environment B (Fields & Glazebrook 2023, Corollary 3.1)finding0.723
  The core impossibility result imported from quantum information theory; basis of the entire argument
• Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.723
  Core result demonstrating topological constraints on self-organization
• Action places an upper bound on the entropy of biological states, thereby conserving structural and dynamical integrity.claim0.720
  Autopoietic aspect of active inference.