IndisputableMonolith.Quantum.Observables
This module supplies the core definitions for quantum observables in the Recognition Science QM bridge, treating them as self-adjoint operators on the imported Hilbert space. Researchers building commutation relations or the ILG quantum substrate would cite it. The module contains only type and structure definitions for Observable, Projector, and Hamiltonian with no proofs or theorems.
claimObservable, Projector, and Hamiltonian are defined as self-adjoint operators on the Hilbert space $\mathcal{H}$ equipped with the inner-product structure.
background
The module sits inside the Quantum domain and imports the Hilbert Space for Recognition Science QM Bridge together with Mathlib structures for inner-product spaces and adjoints. Its sibling declarations introduce Observable as the basic self-adjoint operator, Projector as the idempotent case, and Hamiltonian as the generator of dynamics. The local setting is the quantum bridge that later links to classical and gravitational structures.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the observable types required by the downstream CommutationStructure module (whose doc states projector algebra is idempotent) and by Relativity.ILG.Substrate (whose doc states it connects the ILG framework to the Quantum Bridge). It therefore occupies the entry point for any Recognition Science treatment of measurement or dynamics.
scope and limits
- Does not prove any commutation relations or spectra.
- Does not reference the forcing chain, RCL, or phi-ladder.
- Does not define time evolution or measurement postulates.
- Does not connect observables to mass formulas or constants.