IndisputableMonolith.Quantum.ComplexHilbertStructure
ComplexHilbertStructure supplies the complex Hilbert space definitions that bridge Recognition Science ledger states to standard QM formalism. Researchers formalizing the quantum sector of RS cite it for constructing normalized complex spaces from ledger data. The module contains only definitions and structure declarations with no proof content.
claimProvides $ ext{complex_hilbert_from_ledger} : ext{Ledger} o ext{ComplexHilbertSpace}$, the map $ ext{normalized_state_unit_norm}$ enforcing unit norm on states, and the overall $ ext{complex_hilbert_structure}$ over $\mathbb{C}$.
background
The module resides in the Quantum domain and imports Mathlib together with IndisputableMonolith.Quantum.HilbertSpace. The upstream HilbertSpace module supplies the base Hilbert space for the Recognition Science QM bridge. Sibling declarations inside the module introduce ledger-derived complex spaces, state normalization, and the composite structure object.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the complex Hilbert space layer required by the Recognition Science quantum mechanics bridge. It directly supports the ledger-to-Hilbert construction used by sibling declarations and feeds the broader quantum formalization.
scope and limits
- Does not contain any theorems or proofs.
- Does not address dynamics, measurement, or time evolution.
- Does not reference the J-cost, phi-ladder, or forcing chain.
- Does not connect to classical RS constants or mass formulas.