Introduction to Rhombic Lattice Dynamics: Intrinsic carrier conflict in SR slice read out; TD as velocity carrier fix.
Abstract
Note: By making the carrier trace explicit in the cone–slice (two–circle) geometry, we expose the hidden slot choice behind the SR read–out. Part I develops the foundation from the two–circle diamond construction to an optical field formalism. Relativistic timing relations are treated as cone–slice read–outs, with midpoint (two–reach) pairing kept distinct from one–way reception geometry. Uniform motion is taken as a kinematic descriptor: γarises from projection ratios in the equal–reach (two–circle) slice geometry, while protocol translations restore admissible embeddings when slice read–outs are compared to intrinsic focus– orbit closure. Beyond local timing, the same reach logic extends to a four–circle symmetry, yielding a geometric scaffold for Kepler–type areal flow and orbital structure without taking gravitational force as a primitive postulate. The discrete viewpoint also motivates an ellipse perimeter law via equal–reach lattice refinement that remains well defined under a Planck–scale cutoff. Finally, the bounded geometry motivates a continuous optical metric g-opt = Ω2h with reach field Ω(x). In stationary settings this field provides a geometric description of light–path observables and endpoint clock comparisons, summarised by ∇·(Ω∇Ω) = S(x), introduced here as the entry point to the dynamical ADYN formalism developed in Part II. NOTE: Earlier drafts showed persistent notation friction around “eccentricity”. This revision identifies the geometric cause: a carrier/parameter swap between the SR cone–slice read– out and the intrinsic equal–reach (focus–orbit) ellipse. What is new: • a strict convention: the classical eccentricity is always focus–defined, ε:= f/a, for the currently active focus pair; • an explicit carrier dictionary that keeps the rhombus carriers visible and prevents silent slot mixing in the speed label; • a three–layer protocol separation (invariant layer / slice layer / event–pairing layer), with TD read as drift–closure and carrier–trace restoration (without changing the slice itself). By making the carrier trace explicit in the cone–slice (two–circle) geometry, we expose the hidden slot choice behind the SR read–out: the scalar γ may be preserved, but SR suppresses which rhombus carrier populated the reported speed parameter. Revision note V2: We introduce a carrier--restoration map(CRM) to denote the protocol step that restores the explicitcarrier trace when a scalar read--out has silently suppressed it.The Minkowski read-out, ellipse perimeter law, and light-clock sections have been revised to align better with the updated carrier/slot bookkeeping.
Fields of Study & Subjects
Relativity and Gravitational Theory
Advanced Differential Geometry Research
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 8 February 2026
- Document type
- Preprint