module module moderate

`IndisputableMonolith.Quantum.PointerStates`

PointerStates module defines basis states and pointer states for quantum mechanics in the Recognition Science framework. It connects these objects to J-cost neutrality and environments using imports from Constants and Cost. Quantum decoherence researchers would cite the module for its predictability sieve and Lindblad eigenstate examples. The module supplies definitions and constructions with no internal proofs.

claimA basis state is an element of Hilbert space $\mathcal{H}$. A pointer state is a neutral window under the $J$-cost that survives the predictability sieve and appears as a Lindblad eigenstate.

background

Recognition Science derives all physics from the single functional equation whose solutions yield the J-cost function and the forcing chain T0-T8. This module imports the RS time quantum $\tau_0 = 1$ tick from Constants and the cost axioms from Cost, then introduces Environment, NeutralWindow, and PointerState to model decoherence. The Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ supplies the algebraic structure used to define neutrality.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the pointer-state objects required by downstream quantum results such as predictability_sieve_selects_pointer_states and macroscopic_decoherence_instant. It realizes the preferred-basis selection implied by J-uniqueness (T5) and the eight-tick octave (T7) inside the quantum domain. No parent theorems are listed in the used_by edges.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (15)

structure BasisState L42
structure PointerState L47
structure Environment L56
def roomEnvironment L63
structure NeutralWindow L76
theorem pointer_states_are_neutral_windows L90
def preferredBasisExamples L102
theorem pointer_states_are_lindblad_eigenstates L118
theorem predictability_sieve_selects_pointer_states L129
theorem neutral_windows_from_jcost L143
def decoherenceTime L159
theorem macroscopic_decoherence_instant L169
def quantumComputingImplications L184
def experimentalEvidence L198
structure PointerStateFalsifier L211