Stationary Fluid Field Hypothesis Based on the Point-Contact Mechanics of Background Particles

Recent Changes Significant updates have been made to §12 and §16, particularly §16. A Python script for verification has been attached. Description This paper axiomatizes “Point-Contact Mechanics” (PCM), which treats only near-field interactions as fundamental processes, and demonstrates that from local state transfers occurring on a fixed discrete network substrate, the conservation laws, effective dynamics, and gauge-field structures of a continuum emerge consistently. Each site is assigned a minimal internal state consisting of phase, rotation axis, tension, density, and winding number; the transfer is formulated to satisfy local conservation laws governed by symmetric–antisymmetric decomposition and a causal structure (finite information-propagation speed) based on the Poisson limit. Coarse-graining yields the continuum continuity equation, from which an effective acceleration driven by tension gradients and baroclinic vortex generation arising from the twisting of isosurfaces of density and tension are derived. These results are obtained solely from averaging sequences of point-contact updates, without presupposing any fluid model. The role of boundaries and causality is encapsulated in the “zero-area resonance kernel, ” defined as the difference-quotient limit of transport along tension lines. This kernel blocks normal flux at the boundary while its support is compressed to zero area, thereby eliminating contributions with area coefficients. Consequently, time orientation and reversible line-type dynamics are implemented without disturbing the conservation laws within the volume. Regarding measurement and dissipation, the randomization of contacts yields a minimal-rank GKLS generator, and the exponential decay rate of off-diagonal components can be operationally calibrated by contact rate and local geometry. Furthermore, the continuous limit of phase differences defines local connections and curvature, allowing the reconstruction of a Maxwell-type continuum form consistent with conservation laws. In the free sector, light propagation is described as a combination of single-axis rotation (helicity) and linear momentum, linked to measurable quantities such as energy flux, polarization, and dispersion. In addition, based on the geometry of tension, vorticity, and curvature, a framework is presented that provides geometric design guidelines for resistance and superconductivity and correspondence with the standard gauge and gravitational descriptions. The contributions of this study are: (i) an axiomatic foundation that derives conservation, causality, transport, and measurement within the same framework solely from the elementary process of point contact; (ii) a causal–measure structure produced by the zero-area kernel, which removes boundary area terms; (iii) an operational normalization of contact-origin decoherence and the minimal-rank GKLS formalism; and (iv) the construction of U (1) SU (2) SU (3) and the reconstruction of electromagnetic and optical phenomena, providing a reinterpretation of elementary particles. Throughout this paper, we employ a language consistent with stochastic processes, continuum limits, commutative diagrams, and gauge geometry used in modern physics, restricting assumptions to the standard requirements of locality, conservation, and causality.