| _version_ | 1866901490841419776 |
|---|---|
| author | Panagis, Christoforos |
| author_facet | Panagis, Christoforos |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18140827 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | On the Impossibility of Primitive Space, Time, and Force in Physical Description Panagis, Christoforos <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> |
| title | On the Impossibility of Primitive Space, Time, and Force in Physical Description |
| url | https://doi.org/10.5281/zenodo.18140827 |