IndisputableMonolith.Quantum.Observables
This module defines quantum observables as self-adjoint operators on Hilbert spaces in the Recognition Science QM bridge. It supplies the basic types used by commutation and ILG modules. The content consists of type declarations and sibling definitions for Observable, Projector, and Hamiltonian with no proofs.
claimAn observable is a self-adjoint operator $A$ on Hilbert space $H$ with $A^* = A$. Projectors are idempotent self-adjoint operators and the Hamiltonian is the generator of time evolution.
background
The module sits inside the quantum domain and imports the Hilbert space construction whose doc-comment reads '# Hilbert Space for Recognition Science QM Bridge'. It uses the inner-product and adjoint infrastructure from Mathlib to formalize self-adjointness. Sibling declarations introduce Observable, Projector, and Hamiltonian as the core objects.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the observable definitions that feed the CommutationStructure module (whose doc states 'Structural commutation content: projector algebra is idempotent') and the ILG.Substrate module (whose doc states 'This module connects the ILG framework to the proper Quantum Bridge'). It therefore anchors the quantum side of the Recognition Science bridge to induced lattice gravity.
scope and limits
- Does not derive any commutation relations.
- Does not specify spectra or eigenvalues.
- Does not encode measurement postulates.
- Does not reference the phi-ladder or J-cost.
- Does not treat continuous versus discrete spectra.