Theorems and Results

The theorem cards provide rapid lookup without duplicating full derivations. Each mature card gives an exact statement, a hypothesis ledger, the most important limitation, and a direct link to its reviewed canonical owner.

Selected theorem cards

Formalism Theorems currently contains five cards:

• Spectral Theorem
• Stone’s Theorem
• Stone–von Neumann Theorem
• Wigner’s Theorem
• Gleason’s Theorem

Information and Foundations contains four no-go and inequality cards:

• CHSH Inequality
• Bell Theorem
• Kochen–Specker Theorem
• No-Broadcasting Theorem

Many-Body Results currently contains one locality card:

• Lieb–Robinson Bound

The sidebar includes further result families and cards. A route name alone does not establish that its statement, prerequisites, or canonical owner has been reviewed; check the content and editorial status of the page.

Reading rule

A theorem name is never enough. Before applying a card, check the operator domain, topology, continuity, dimension, locality norm, interaction decay, irreducibility, regularity, central character, or additivity assumptions named there. Use the owner link whenever a proof boundary or failure case matters.

Card-owner contract

• The card owns compact lookup and no derivation.
• The linked owner owns the full statement, examples, proof architecture, exercises, and canonical references.
• Compare the card with its canonical owner before applying it.
• If their statements disagree, the discrepancy must be resolved before the card can support a calculation.

References

• B. C. Hall, Quantum Theory for Mathematicians, Springer, 2013.
• N. P. Landsman, Foundations of Quantum Theory: From Classical Concepts to Operator Algebras, Springer, 2017.
• M. Reed and B. Simon, Methods of Modern Mathematical Physics, Volume I: Functional Analysis, revised and enlarged ed., Academic Press, 1980.