8 papers
A Structural Criterion for the Applicability of Algebraic Phase Theory
Joe Gildea
Algebraic Phase Theory (APT) exhibits a marked structural selectivity. In certain mathematical and physical settings it gives rise to rigidity phenomena, constrained representation…
Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory
Joe Gildea
We study finite-depth reconstruction frameworks based on representation theory and show that non-rigid reconstruction behaviour is naturally accompanied by intrinsic structural bou…
Boundary Calculus, Rigidity Islands, and Deformation Theory in Algebraic Phase Structures
Joe Gildea
We develop a general boundary calculus for algebraic phases and use it to formulate an intrinsic structural framework for deformation and obstruction phenomena. Structural boundari…
Why the Bethe Ansatz Works: A Structural Explanation via Interaction Propagation
Joe Gildea
The Bethe Ansatz provides exact solutions for certain interacting quantum many-body systems, yet its success is confined to narrow regimes and breaks down abruptly outside them. De…
Algebraic Phase Theory IV: Morphisms, Equivalences, and Categorical Rigidity
Joe Gildea
We complete the foundational architecture of Algebraic Phase Theory by developing a categorical and -categorical framework for algebraic phases. Building on the structural notio…
Algebraic Phase Theory III: Structural Quantum Codes over Frobenius Rings
Joe Gildea
We develop the quantum component of Algebraic Phase Theory by showing that quantum phase, Weyl noncommutativity, and stabiliser codes arise as unavoidable algebraic consequences of…