The TS5D Programme: Physical Foundations and Predictive-Closure Audit

This deposit contains two companion documents of the TS5D programme, a classical, deterministic, five-dimensional geometric framework in which elementary particles are modelled as stable topological solitons of a single field, and in which the compact fifth dimension is physically interpreted as the geometrization of energy (spacetime–energy). Document 1 — Physical Foundations of the 5D Solitonic Programme (TS5D): From Deterministic Skepticism to Spacetime–Energy Geometry. This paper states the physical postulates of the programme, which constitute its original content, deliberately separated from the mathematical apparatus used to develop them (standard differential geometry and classical field theory). It formulates six postulates — determinism, field ontology, energy as a compact spacelike dimension, four-dimensional projection, scale-dependent wavelike geometry, and a trace criterion binding every five-dimensional structure to measurable four-dimensional consequences — states the motivating problems (the unprincipled boundary between probabilistic microphysics and deterministic macrophysics; the accommodating character of the cosmological dark sector), summarizes what the existing Zenodo corpus constructs from the postulates, and assigns each claim its epistemic status. Document 2 — A Predictive-Closure Audit in Five-Dimensional Geometry: Geometric Mechanism and Predictive Underdetermination in the TS5D Framework. This monograph subjects the cosmological application of the framework — a depth-dependent inferred Hubble rate — to a systematic predictive-closure audit. Within the declared diagonal metric class it derives exactly: the local propagation of the visible projected null mode at c₀; the redshift integral ln (1+z) = ∫H dτ; a no-go theorem for static factorized radial profiles; the mixed Einstein constraint −2H′−K′+ (H−K) c′/c = κ₅qᵣ, identifying the only three channels capable of producing a radial gradient of the visible expansion rate in this metric class; and the exact 4+1 compact identity □₄c/c = κ₅ (T₄−2pₑ) /3. It then proves that the mechanism, while exact, is not predictively closed: the verdict is controlled underdetermination — the mechanism is neither excluded nor predicted — and the audit examines the observational viability of any realized compact variation (varying-constant, fifth-force, and post-Newtonian bounds; stabilization tension). The central tensor results have been independently verified by a complete symbolic computation. This closure analysis supersedes the stronger predictive-completeness claims of the earlier deposit "Complete Dynamic Derivation of the Hubble Tension Resolution" (doi: 10. 5281/zenodo. 17466050), while retaining its proposed geometric channel as a conditional mechanism. The two documents are complementary: the first states what the programme postulates and why; the second establishes exactly what the current corpus derives, what it allows, and what it does not yet predict. Together they define the epistemic baseline for all future TS5D work. A condensed journal article derived from the audit is in preparation.