Irreducibles of Delta^n and Omega^n yield classical and quantum propositional logics

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• Quantum theory reveals discreteness of atomic/molecular states with energy levels and quantized transitions.finding0.735
  Foundational quantum-mechanical fact that Schrödinger leverages to explain why molecular configurations are stable against small thermal perturbations.
• Quantum Logic (Birkhoff–von Neumann)framework0.732
  Lattice of subspaces of Hilbert space as logic of quantum propositions.
• Does the multi-directional nature of truth imply an underlying nonlinear representation, or is it compatible with linear separability?question0.728
  Theoretical open question about the geometry of truth in LLMs raised in Discussion
• Omega^n of quantum states with spectral order is a domain and von Neumann entropy is a measurementfinding0.726
  Quantum density operators, ordered by common observable's classical Bayesian order, form a dcpo with max elements pure states; von Neumann entropy is a measurement.
• Quantum theory permits both long-term structural stability and discrete discontinuous changes—both required for genetic inheritance and mutation.finding0.725
• Bell's theorem: experiments by Aspect, Clauser, and Freedman show instantaneous correlations between distant quantum particles, violating local realism.finding0.720
  A foundational empirical result undermining mechanistic separability, cited as evidence that the whole influences local events.
• Elephant programs themselves can be represented as sentences of logic. Their extensional properties follow from this representation without an intervening theory of programming or anything like Hoare axioms.claim0.719
  Fourth abstract claim.
• X → X[′′] on G and M are closure operators satisfying extensivity, idempotence, and monotonicity.finding0.711