Poincarè Symmetries, Gravitoelectromagnetic Coupling, and Emergent Conservation Laws from Worldline Non-Injectivity

This paper derives two sets of results from the principle of worldline non-injectivity within the TPST–DGQ framework. A timelike worldline X^ () with Lorentz factor > ₂ₑ₈ₓ intersects a constant-time hypersurface ₜ in N > 1 distinct spatial points, generating a multi-sheet structure of spacetime with topological phase offsets ₙ = ² v (ₙ - ₁). The first result concerns the Poincaré symmetries of classical physics. We prove that all four conservation laws — energy, momentum, angular momentum, and Lorentz boost invariance — emerge from the invariance of the topological average W = N^-1ₙ L^ (n), dt under the corresponding transformations. The inter-sheet corrections to each conservation law involve ₙ = 0 or ₙ = 0 and vanish exactly by the symmetry of the fold distribution. The conservation laws are therefore derived consequences of the multi-sheet geometry, not postulated symmetries of a background spacetime. The second result concerns the coupling between gravitation and electromagnetism. A gravitational field breaks the time-translation symmetry of the topological average by producing a non-zero inter-sheet phase gradient: ₜₙ| ₆ₑ₀ₕ = GM₀/ (c² r²). In the presence of an external magnetic field Bᵦ, this phase gradient induces a fluctuation of the local electric field: (Eᵧ) = GM Bᵦ/ (c² r²). This gravitoelectromagnetic effect is of first order in Newton's constant G, in contrast to standard general-relativistic couplings between gravity and electromagnetism which arise at higher order. For terrestrial experiments the signal is below current sensitivity. For neutron stars with surface magnetic fields B 10^12 T, the induced electric field reaches 21 MV/m, a scale potentially relevant for pulsar magnetosphere electrodynamics. Both results follow from the universal cancellation identity N () ^d-2 = O (1), which now operates at nine levels spanning holography, classical electromagnetism, quantum mechanics, thermodynamics, electromagnetic fields, gravity, quantum statistics, noncommutative spacetime geometry, and Poincaré symmetries. The paper is fully self-contained. This manuscript is current in Official Peer Review. Not final version. Copyright©2026 Alex De Giuseppe. All rights reserved. This work is protected by copyright. Any form of plagiarism, unauthorized reproduction, or misappropriation of ideas, mathematically results, or text without proper citation constitutes a violation of academic and intellectual property standards and common laws. No commercial use, adaptation, or derivative works are permitted without explicit written permission from the author. For correspondence, citations, collaboration inquiries, or feedback please contact: degiuseppealex@gmail. com The hash files that determine ownership have been created