Part I
01
Categorical Locality Before Spacetime
Defines contexts, processes, locality, and gluing before any geometric realization.
Paper, source, and review indexedA seven-paper research program
Representation before geometry
Categorical locality and representation provide a shared language. Geometry, quantum theory, and kinetic theory remain separate realization branches with explicit assumptions.
Typed realization trace
A common foundation feeds three separately scoped branches. No arrow here asserts a completed reconstruction theorem.
- ContextI
- CondensedII · optional
- RepresentationIII
- GeometryIV
- QuantumV
- KineticsVI
The sequence
Six stages, then synthesis
The order records dependencies. It does not collapse the physical branches into one theorem.
Part II
02
Condensed Physical Contexts
Studies a condensed ambient setting for generalized spaces and local-to-global data.
Paper, source, and review indexed
Part III
03
Representation-Theoretic Emergence of Measurement, Symmetry, and Observable Structure
Separates symmetry representations, observable interfaces, outcomes, and probability inputs.
Paper, source, and review indexed
Part IV
04
Lorentzian Geometry as a Realization: Coframes, Connections, Curvature, and Einstein Dynamics
Treats Lorentzian geometry and Einstein dynamics as a conditional realization branch.
Paper, source, and review indexed
Part V
05
Quantum Mechanics from Categorical Representations and Compositional Measurement
Compares conditional reconstruction routes to quantum state, effect, and measurement structures.
Paper, source, and review indexed
Part VI
06
Statistical Mechanics and the Boltzmann Equation from Categorical Coarse-Graining
Separates finite coarse-graining checks from imported kinetic-limit theorems.
Paper, source, and review indexed
Part Synthesis
07
Representation Before Geometry
Composes only version-compatible interfaces while keeping the three realization branches separate.
Paper, source, and review indexedStatus discipline
A result means one exact thing
These are repository labels, not decorative confidence badges. The registers are the source of truth for each claim and assumption.
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PROVED
The repository contains proof evidence for the exact scoped statement.
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CONDITIONAL
The statement follows only under the assumptions named with it.
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COMPUTATIONAL
Executable checks support a finite model; they are not a general proof.
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OBSTRUCTED
A registered counterexample blocks the broader statement.
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OPEN
The repository does not currently prove the registered statement.
Provenance