Chiral Resolution of Boundary Flow Pressure in Discrete Simplicial Spacetime: Exact Rational Boerdijk–Coxeter Torsion, Finite Cosserat Couple-Stress, and Mock-Theta Shadow Cancellation
Year: 2026
Type: preprint
Abstract: Discretizing three-dimensional spacetime into rational simplicial complexes eliminates transcenden-tal circle constants from local flux accounting, yet purely symmetric lattices suffer shear instabilityunder directed thermodynamic flow unless stabilized by ad hoc cosmological terms (Λ) or complexspinor phases (√−1). Here we prove from zero-parameter integer geometry on balanced-ternarycube vertices {−1, +1}3 that face-sharing regular tetrahedra generate an exact rational screwoperator QBC ∈ SO(3, Q) with trace Tr(QBC) = −1/3 and azimuthal twist cos αBC = −2/3(αBC = ±131.8103◦), exceeding an unstrained 120◦ C3 phase step by an exact sexagesimal cosinedeficit − 23 − (− 12 ) = − 16 = − 1060 (δθBC = ±11.8103◦). Holding simplicial edge length finite (h > 0)preserves antisymmetric Cauchy–Cosserat shear stress (σxy̸ = σyx), while pairing Ramanujan’sthird-order mock theta functions in the tetrahedral 4 : 1 ratio 4χ(q) − f (q) = 3θ4(0, q3)2/(q; q)∞cancels radial boundary singularities via an integral-weight squared theta quotient with zero freeconstants.
Author: Grimm, Justin D
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225835369
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