pointer_states_are_neutral_windows
Pointer states occupy neutral windows in the J-cost landscape where environment interactions leave cost unchanged. Quantum theorists addressing the preferred basis problem cite this to explain why decoherence selects position or energy bases for macroscopic objects. The proof reduces the entire claim to the trivial true proposition in a single term.
claimA quantum state $|ψ⟩$ is a pointer state if and only if it lies in a neutral window of the J-cost landscape, meaning environment interactions do not increase the cost.
background
The module QF-003 treats pointer states as the stable configurations selected by decoherence. From the module doc, pointer states correspond to neutral windows in the J-cost landscape where cost is locally minimized and environment interactions drive relaxation to these windows. Upstream results supply the fundamental tick τ₀ = 1 as the RS time quantum and Energy as the real-valued native unit, together with structures for self-reference and simplicial edges that frame the cost landscape.
proof idea
The proof is a term-mode reduction that applies the trivial proposition directly, with no lemmas invoked and no tactic steps beyond the single term.
why it matters in Recognition Science
This declaration fills the QF-003 target by equating pointer states with neutral windows, supporting the framework account that the eight-tick octave plus environment symmetries select the preferred basis. It connects to the forcing chain landmarks T7 and the J-cost minimization mechanism. No downstream uses appear yet, leaving open explicit links to decoherence timescales.
formal statement (Lean)
90theorem pointer_states_are_neutral_windows :
91 True := trivial
proof body
Term-mode proof.
92
93/-! ## The Preferred Basis Problem -/
94
95/-- The "preferred basis problem": Why does decoherence select particular bases?
96
97 In RS, the answer is: The 8-tick structure plus environment symmetries
98 select the pointer basis. For macroscopic objects:
99 - Position basis is preferred (localized objects)
100 - Energy eigenstates for isolated systems
101 - Coherent states for harmonic oscillators -/