The System of Streams: A Strict Mathematical Representation, Operator-Soundness, and Applicability Theorem for Dynamic Systems
- Posted
- Server
- Zenodo
- DOI
- 10.5281/zenodo.20693113
This paper formulates a strict representation-and-applicability theorem for the System of Streams.
The central thesis is retained in its absolute form: The System of Streams is applicable to any dynamic system. The proof is not based on a definitional identification of dynamics with a Stream structure. Instead, it defines a generalized dynamic system, constructs a Stream-representation, proves preservation of minimal dynamic structure, introduces a typed operator layer, proves non-vacuity, representation invariance, operator soundness, compositionality, boundary-case coverage, and minimality, and separates formal applicability from domain-level explanatory adequacy.
The result is an operator-theoretic theorem: every specified dynamic system admits a Stream-representation preserving its minimal dynamic content, and the System-of-Streams operators are well-defined and sound on that representation. The absolute thesis therefore concerns formal applicability.
It does not assert that every domain-specific explanatory problem is solved automatically; explanatory adequacy depends on domain predicates, kernels, measurements, thresholds, and validation criteria.