A research series in structural mathematics
A representation is recorded as a five-part tuple of state space, observables, dynamics, symmetries, and composition rules. The series fixes a morphism vocabulary with explicit preservation laws, classifies restricted classes in full, and states the structural classification conjecture with its five proof obligations. Twelve volumes, one synthesis.
Part 1 of The Classification of Mathematical Representations of Physical Systems
The classification of mathematical representations of physical systems is a structural problem before it is a physical one, and this paper establishes…
Part 2 of The Classification of Mathematical Representations of Physical Systems
This paper develops the family-level taxonomy that a classification of mathematical representations of physical systems requires. Ten structural famil…
Part 3 of The Classification of Mathematical Representations of Physical Systems
Structural classification of physical systems requires a precise account of irreducibility: the objects counted as basic, the constructions that assem…
Part 4 of The Classification of Mathematical Representations of Physical Systems
The Yoneda embedding sends each object of a category to the functor it represents through its relationships with all other objects. This paper develop…
Part 5 of The Classification of Mathematical Representations of Physical Systems
This paper classifies restricted classes of classical physical systems: symplectic and Poisson systems and classical statistical systems. The central …
Part VI of The Classification of Mathematical Representations of Physical Systems
Quantum physical systems admit a complete structural classification only in restricted regimes, and this paper records where those regimes begin and e…
Part 7 of The Classification of Mathematical Representations of Physical Systems
We develop the classification of gauge structures and quantum field theories within the CMRPS program. The subject divides into two territories of une…
Part 8 of The Classification of Mathematical Representations of Physical Systems
This paper classifies and reconstructs spacetime and separates what is proved from what is proposed. Four results are complete within their stated hyp…
Part 9 of The Classification of Mathematical Representations of Physical Systems
This paper examines the relationship between information geometry and gravity from the viewpoint of classification: which geometric structures on stat…
Part 10 of The Classification of Mathematical Representations of Physical Systems
The classification problem of mathematical representations of physical systems is a quotient: classify objects of a category of systems up to an equiv…
Part 11 of The Classification of Mathematical Representations of Physical Systems
This paper determines what can be established about the completeness of a classification of mathematical representations of physical systems. Seven pr…
Volume 12 of The Classification of Mathematical Representations of Physical Systems
This paper assembles the registered results of the Classification of Mathematical Representations of Physical Systems into the three-layer architectur…
Synthesis of The Classification of Mathematical Representations of Physical Systems
This paper states the structural picture formed by the twelve parts of the Classification of Mathematical Representations of Physical Systems, a progr…
The classification chart of the program: ten candidate structural families with their defining invariants, exceptional structures, proven reconstruction relationships, and the claim status of every row.
The structural picture formed by the twelve parts: the registered results, the dependency structure among the volumes, and the obligations the classification conjecture still carries.
The definitional root of the series: the system record schema, five morphism kinds with preservation laws, admissibility conditions, and three restricted classifications proved in full.