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Local Minkowski Kinematics from Cyclic Nearest-Neighbor Event Lattices: Explicit Bounds and Conditional Uniqueness

Year: 2026
Type: preprint
Abstract: We give a self-contained construction of 1+1-dimensional Minkowski kinematics from a time-unwrapped nearest-neighbor event graph with finite cyclic spatial quotients. For even n ≥ 4, lattice spacing a_n → 0, and circumference n a_n → ∞, the spatially lifted parity lattice has exactly the Minkowski causal order. A specified elementary-cell count gives a proper-time function equal to the Minkowski interval on lattice pairs. We prove explicit local approximation bounds for points, causal pairs, and proper time, and a uniform-in-time probabilistic bound for the ballistic limit of a biased classical walk. Rational reciprocal null rescalings preserve the interval on finite-index sublattices. For every fixed finite family of affine Lorentz transformations and fixed maximum composition length, we construct common refining domains on which all corresponding discrete compositions are defined and converge uniformly on compact sets. Conditional uniqueness statements specify the assumptions that select the kernel, square-root interval, and boost form. The construction is a quantitative synthesis of familiar discrete kinematic ingredients; priority and mathematical novelty are not established. In particular, the interval prescription is an assumption, the Markov probabilities do not determine the geometry, and the result does not supply quantum dynamics or an experimental account of spacetime. Status: Mathematical preprint for scrutiny; not peer reviewed or independently validated. JCEE-RTL-SR-C1-R8, version 0.1, 18 October 2026. Revised successor to the author's internal C1-R6 v1.0 and C1-R7 v1.1 review manuscripts of 12 October 2026. The revision repairs a small-cycle definition and replaces an informal action-convergence assertion with an explicit finite-composition theorem. Companion material: LaTeX manuscript source, a Python standard-library verification script, recorded finite-check results, and SHA-256 checksums. The finite checks exercise examples and known failure cases; they are not independent mathematical review, a proof of asymptotic convergence, or evidence of priority. Preparation: OpenAI Codex assisted with mathematical drafting, literature lookup, and executable arithmetic checks. AI assistance is not independent mathematical validation. The author is responsible for the submitted claims. Licensing — per-file scope CC BY 4.0 applies to C1-R8_Preprint_v0.1_2026-10-18.pdf and, inside C1-R8_Source_and_Checks_v0.1_2026-10-18.zip, manuscript.tex, README.md prose, LICENSING.md, verification-results.json, and SHA256SUMS.txt, to the extent copyright or applicable similar rights exist. MIT applies to verify_c1.py and the reproduction-command block in README.md. LICENSE-MIT.txt, included alongside the script, contains the complete MIT license text and copyright notice. LICENSING.md contains the exact file-to-license mapping. The ZIP contains differently licensed materials; listing both licenses does not offer a choice of either license for every file. These grants cover only the identified released C1-R8 materials and rights held by the licensor in them. They do not license or release other JCEE Labs software, repositories, products, infrastructure, confidential material, or unpublished work. This scope statement adds no restriction to rights granted by the standard licenses in the identified materials. Cited third-party works are not relicensed. Licensing-only packaging revision, 18 October 2026: the preprint PDF, manuscript.tex, verify_c1.py, and verification-results.json are unchanged. License documentation and package checksums have been updated. This update makes no new scientific claim.
DOI: 10.5281/zenodo.23444914
Language: English
Open Access status: green
OpenAlex ID: W7222891209
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