preferredBasisExamples
plain-language theorem explainer
preferredBasisExamples enumerates five physical systems together with their decoherence-selected bases under the Recognition Science account of pointer states. An open-systems theorist would cite the list when mapping J-cost minima to observed classical bases such as position for macroscopic objects. The declaration is a direct static list with no computation or lemma application.
Claim. The preferred-basis examples consist of the five pairs (macroscopic objects, position basis), (atoms in vacuum, energy eigenstates), (harmonic oscillators, coherent states), (spin in magnetic field, field-aligned states), (quantum dots, charge states).
background
Pointer states are defined as neutral windows in the J-cost landscape where environment interactions drive the system to locally minimal J-cost configurations. J-cost satisfies the Recognition Composition Law; its shifted form H(x) = J(x) + 1 obeys the d'Alembert equation H(xy) + H(x/y) = 2 H(x) H(y) as stated in CostAlgebra.H. The module QF-003 places this construction inside the eight-tick structure that selects environment symmetries.
proof idea
Direct definition of a list of string pairs. No lemmas or tactics are invoked; the body is the explicit enumeration of the five cases.
why it matters
The definition supplies concrete illustrations for the pointer-state emergence claimed in QF-003 and ties the selection mechanism to the eight-tick octave (T7). It therefore anchors the quantum-to-classical transition inside the same forcing chain that yields D = 3 and the alpha band. No downstream theorems are recorded.
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