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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18140827 |
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Table of Contents:
- <p>A physical theory is a closed system of distinctions. Distinctions require relations;</p> <p>relations require composition; composition must remain meaningful under finite observational discrimination and refinement. A descriptive language is formalized as a family of quotient-level assignments Φϵ : Oϵ → Iϵ into composable descriptors, modulo gauge. Three requirements are forced by description itself:</p> <p>(A) composability without external reference, </p> <p>(B) refinement coherence, and</p> <p>(C) non-circular definability.</p> <p>Requirement B is made explicit in two tiers: (B1) naturality under refinement (semantic coherence without invertibility), and</p> <p>(B2) gauge coherence (invertible coherence). Under A, C, and B2, any language employing primitive space, primitive time, or primitive force violates admissibility. Stable identity factors through finite-resolution partitions and is therefore discrete at each ϵ; continuous carriers cannot be fundamental identity carriers under refinement coherence. For ratio-like relational observables (scale factors) whose operational concatenation is multiplicative by definition, quotient-level observability forces measurability with respect to the quotient σ-algebra; under this forced regularity, additive homomorphic coordinates are logarithmic uniquely up to affine gauge. An admissibility projector on gauge-classes of languages is defined; its fixed points are characterized and shown unique up to gauge equivalence. The resulting fixed-point vocabulary—logarithmic relational representation for ratio-regimes, discrete spectral identity, ordering only as an observable, and interaction only as refinement-stable constraints—is named the Unified Substrate Theory (UST) admissibility protocol. This is conditional descriptive necessity, not ontology.</p>