Cosmic voids are where vector dark energy breaks: an exact closure law, a present-day date, and a two-sided bound on the Proca amplitude

In generalized Proca gravity with the cubic interaction G3 = γX2, dark energy is a massive vector field whose expansion history is fixed by the present density fractions, leaving one free amplitude φ0. We show that the scalar part of this field has a wave cone that can shut at the centre of a cosmic void, and that whether it shuts is decided by one number: the normalized electric divergence S = dE/(m2T) the void builds at its centre. We derive the exact threshold S* in closed form from the model's constraints, with no expansion in the density contrast, reduce it on the cosmological background to a function of ΩA(a), Ωm(a), the central contrast and U = φ2/M2, and obtain its late-time limit S* → −1 + √(1 − 1/UdS). The law reproduces four previously computed special cases to all displayed digits and predicted an unreported simulation to a tenth of a percent. A naturally grown 85%-underdense void at the benchmark amplitude φ0 = 3 closes its cone at a = 1.011 — the present epoch to within 150 Myr — confirmed by four independent numerical routes to Δa ≤ 1.5×10−3; 57% of the closing rate is the background's transition to vector domination, and closure is impossible in the matter era for any amplitude. The new upper bound UdS < 1, below which no void can ever close the centre cone, combined with the model's causal lower bound UdS ≥ (3 − √3)/6, leaves 0.438 ≤ φ0 < 0.954 as the only amplitude range in which deep voids keep a Lorentzian scalar cone for all time; the benchmark sits a factor ten outside it. The state just before closure is certified by interval arithmetic. Either the vector amplitude lies in a narrow window, or deep voids close the scalar cone in the vector-dominated era — at the benchmark amplitude, now. Files. void_closure_prd.pdf — the Physical Review D manuscript (REVTeX, 12 pp., 57 references); void_closure_prl.pdf and void_closure_prl_SM.pdf — the Letter version and its Supplemental Material; void_closure_source.zip — the LaTeX sources and the three figures; void_closure_reproduction.zip — the scripts (extract.py, analyze.py, report.py, tests.py, verify_closure_law.py, fig_window.py, fig_prl.py) and tables (closure_series.csv, key_numbers.json, tests_known_outcomes.json) that regenerate every number and figure; IRGD_Rev4_calculation_archive.zip — the 310 MB calculation archive of the companion manuscript (4,139 files; 3,481 constraint-projected SBP4 evolution snapshots at 192/384/768/1536 points, run records, the interval-arithmetic certificate, the manuscript sources), which the scripts read directly. The companion manuscript itself is the linked record doi:10.5281/zenodo.22731216.