Void Network Geometry and Bell Non-Locality: Withdrawal of the c√(3/2) Propagation Speed
Abstract
Version 1.0 of this record claimed that the octahedral-void network of the BCC Planck foam has nearest-neighbour spacing shorter than the bubble spacing, and that voids therefore propagate at c_V = c√(3/2) ≈ 1.22c, supplying a finite-speed mechanism for Bell non-locality. That result is withdrawn. Two errors are identified. First, the void spacing is wrong: BCC has three octahedral holes per lattice site, at the face centres and the edge midpoints of the conventional cube, and the nearest-neighbour spacing of the full void network is a/2, not a/√2. Second, the speed ratio is inverted: with a common hop time a shorter hop is slower, not faster. The propagation front of each network is computed exactly (support function of the hop set, confirmed by breadth-first search). Under a common hop time the void front never exceeds the bubble front in any direction (ratio 1 along ⟨100⟩, 1/2 along ⟨110⟩, 1/3 along ⟨111⟩); under a common hop speed both networks reach exactly c in their fastest direction. No model yields a ratio above 1. Independently, any finite influence speed is excluded: experiment bounds such a speed above roughly 10⁴ c (Salart et al. 2008), and Bancal et al. (2012) prove that every finite-speed influence model permits superluminal signalling, so "the void carries no information" cannot rescue a finite c_V. The surviving content is the lattice geometry of the two networks. The mechanism of Bell correlations in UFFT is the one already published in Paper #45 (DOI: 10.5281/zenodo.19307111): the void channel of H = L + ηV is the antipodal map through the incompressible bulk, with no propagation and no speed, and no-signalling follows from incompressibility. The pair state is derived in Paper #75 (DOI: 10.5281/zenodo.21323993). Changes in this version: title changed to state the withdrawal; abstract rewritten, with the v1.0 abstract reproduced in §1 for the record; §2 geometry corrected (all six octahedral sites per cube, d_V = a/2); §3 replaces the speed ratio with the propagation-front theorem and computed table; §4 added (exclusion of any finite influence speed); §5 withdrawn and replaced by a pointer to Papers #45 and #75; verification script verify_void_network_speed_2026-10-05.py added. Unified Foam Field Theory, Part XXXIII. Framework v9. Verification script in the UFFT GitHub repository.