PUH Theorem 369 — A Lattice Phase Transition 10–12 Billion Years Ago Can Supply the Late Push: In a First Test It Beats a Constant Push, May Spread Region by Region, and Must Leave the Sky Dark

Photonic Universe Hypothesis (PUH) — Proposal and First Test. THE IDEA (the author, 25 September 2026). When the tension of the E8 lattice reaches a critical level, the lattice changes phase suddenly — like air reaching its dew point: the rebound was hot and expansion cools. And because branched flow makes the expansion lumpy — swirls and eddies of high and low tension, the trunk of the tree a large region of low tension — the change need not happen everywhere at once. It answers two questions T368 left open: the late push must be made throughout space, not by the Planck cores, and matter cannot pay for it. THE TEST. The same simplified test used throughout T368: the CMB acoustic angle fixes H₀, and each version is scored against the thirteen DESI DR2 baryon-acoustic numbers (χ², lower is better; a constant push scores 31.0, DESI's own two-parameter shape 10.2). The simplification (matter density fixed at Planck's value) tends to exaggerate improvements over a constant push, so every improvement needs a full CMB analysis before it counts as evidence. RESULT 369.1 (when). A push switched on everywhere at once scores 14.5 to 16.9 if the switch came 10.5 to 11.2 billion years ago, when the universe was 2.6 to 3.3 billion years old; later than about 9 billion years ago is excluded. Sharp and gradual switches score the same: an immediate transition is allowed. RESULT 369.2 (a sign flip). T366 found the lattice field cannot make a push, and that its one route to a vacuum energy gives a NEGATIVE value. If a transition flips that sign — negative before, equal and positive after — a flip 11.4 billion years ago scores 11.0, as good as DESI's own shape (H₀ = 68.8). It does not resolve the Hubble tension: the flip that would give H₀ = 73 scores 202. The size is not derived. RESULT 369.3 (region by region). If each region changes phase when its own tension crosses the threshold, a switch-on spread from 12.6 to 8.3 billion years ago (10% to 90% of space) scores 11.9 — BETTER THAN ALL AT ONCE (14.5). 99.9 per cent of space has changed by today. RESULT 369.4 (not one front). A single front spreading at light speed, started 11 billion years ago, would by now have reached only 7.5 per cent of the observable universe. The change must begin in many places; starting points no farther apart than the homogeneity scale finish within 30 to 60 million years. A spread over billions of years must come from regions reaching the threshold at different times — as the eddies of branched flow would make them. RESULT 369.5 (lumps). While the transition was under way the push was 3 to 8 per cent of the energy budget, so regions differed in expansion rate by at most 4 per cent — harmless. Today the push is 44 per cent of the expansion rate and neighbouring 60-Mpc cells can differ by at most 17–34 per cent, so the transition must be essentially complete now. RESULT 369.6 (more than one). A second transition improves the score by about one for two extra numbers: allowed, not needed. The archive already predicts more ahead (T315): in T368's fitted tension law the threshold ratio passes 9, 3 and the tearing point 0.8, 3.0 and 6.2 billion years from now (fitted, not derived). RESULT 369.7 (energy). The lattice can pay — the push is 1.3 × 10⁻¹²³ of the Planck density (T358) — but the transition must change the lattice's pressure, not release heat or light: heat or light equal to the push's energy would make today's sky 49 to 2,500 times brighter than the microwave background. THE TRIGGER. Not among the archive's named tension levels, all of which lie ahead (T315): a new threshold above today's X ≈ 14 is needed. COMPARISON. The sign flip is the published "sign-switching cosmological constant" shape: Akarsu et al. 2023 (Planck + BAO + supernovae) z ≈ 1.8–2; a 2026 late-universe-only test z ≈ 3.5 ± 1.0 with no preference. This note (DESI DR2 + CMB angle) prefers z ≈ 2.4–3.0 and excludes z ≈ 1.6–2. PUH supplies a reason for the shape and for the sign before it. KILL-CONDITIONS: a full CMB analysis removing the improvement; a transition that must radiate its energy; direction- or region-dependence of today's expansion at the push's level; later data demanding a push strong before 12 billion years ago or fading strongly today; a tension law with every threshold in the future. NOT CLAIMED: that the transition occurred; that its trigger, size or prior negative vacuum energy is derived; that the Hubble tension is resolved; that the region-by-region fit is significant; that more than one transition is detected.