PUH Theorem 392 — Porphyrion as a Planck Core's Light: If the Largest Known Jets Are a Gamma-Ray Beam of the Full 3 × 10⁶¹ erg, Their Core Needs at Least 3 × 10⁹ Suns at the Top of T389's Window

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. Porphyrion, the largest pair of black-hole jets known (Oei et al. 2024), spans 6.43 Mpc on the sky at z = 0.896; read as plasma jets it carried 1.3e39 W for 1.9 billion years, 7.795e62 erg. Neronov, Vazza, Brandenburg and Caprini (2024) propose instead that it is the trace of a narrow beam of gamma rays above 10 TeV, sent along the black hole's spin axis and turned into radio-bright pairs over megaparsecs, carrying at most 3e61 erg (about 26 times less), injected over at least about 10 million years within the last 10 to 15. In this archive a core's poles let out stored light along its spin axis (T388-T390), and averaged over its life no more than its Shell unfolds, at one rate per square metre of Shell that T389 places between 1.8611e7 and 1.3513e10 W/m². Read as a beam, can Porphyrion be a Planck core's light within that window, and what does it ask of the core? RESULT 392.1 — A BEAM OF LIGHT IS WHAT THE POLES MAKE. A gamma-ray beam along the spin axis is the archive's polar release in the language of standard astrophysics: it carries no plasma across the 3 Mpc of each side, and its axis need only hold steady while light crosses the trace, 10.49 to 11.42 million years. T370's field-driven release, its magnetic spin-down power, reaches at most 2.06e-24 to 4.63e-24 of the beam's power (T390's bound). The reading fits. RESULT 392.2 — THE BUDGET. When Porphyrion's light left, the universe was 6.287 billion years old (flat LCDM with radiation, Planck 2018). A core of 1e9 solar masses, its Shell at 14/13 of the horizon radius, could have unfolded at most 3.410e60 erg by then at the top of T389's window. If the beam carried the full 3e61 erg, its core needs at least 2.966e9 solar masses at that top (2.195e9 at the cap's highest best-bet value, 2.4687e10 W/m²; 7.993e10 at the floor); today's gamma-ray limit held for 10 million years, 1e60 erg, needs 5.416e8, and the conventional jets 1.512e10. If T287's escape cone holds, every least mass rises by at least 1.0647. Read as a beam, Porphyrion fits with a core of a few billion suns and a rate near the window's top. RESULT 392.3 — STORED LIGHT LET OUT IN A BURST. Injected over 10 to 15 million years, the full beam ran at 9.506e39 to 6.338e39 W, 628.7 to 419.1 times what the least-mass core unfolds each second at the window's top: all the light it unfolded in 6.287 billion years, stored and let out in a burst, as the archive's poles allow; the pace at which they can is open. For scale, the beam's power is 0.25 to 0.17 of that core's Eddington luminosity, 3.73e47 erg/s. RESULT 392.4 — THE MATTER IS UNFOLDED, NOT SWALLOWED. The beam needs 1.678e7 solar masses of waiting matter unfolded at the Shell, at full conversion. The core does not feed (T388), so the conventional bound that the black hole gained more than 2E/c², over 8.5e8 solar masses, does not apply. Oei and colleagues' case for the host galaxy, resting chiefly on the jets and their orientation, stands; were the quasar SDSS J152933.03+601552.5 (2.5 +- 0.3e8 solar masses, z = 0.799) the source instead, with the beam's energy scaled to its distance (2.265e61 erg), its core would need 1.337e12 W/m², 98.95 times the window's top: OPEN. RESULT 392.5 — WHAT A WEIGHING WOULD SHOW. Porphyrion's black hole has not been weighed. If its beam carried the full 3e61 erg, its core should be at least about 3e9 solar masses; a lighter one would need a rate above Sgr A*'s cap, and below 2.19e9 above every best-bet value of it. With the beam's energy known from below, the weighing would set a second floor on the unfolding rate beside M87*'s: for the full beam, above M87*'s for any core below 7.993e10 solar masses, reaching Sgr A*'s cap near 3e9. NOT CLAIMED: that Porphyrion is a gamma-ray beam; the mass of its core; that the unfolding rate lies at the window's top; how the poles focus their light, at what energies, or how fast; which galaxy hosts the source; anything about the magnetic field beyond consistency. KILL-CONDITIONS: Porphyrion's black hole weighed below 2.19e9 solar masses while its beam is shown to have carried the full 3e61 erg; Porphyrion shown to be plasma jets carrying the core's light with QT = 7.795e62 erg from a core below 1.119e10 solar masses; a pole shown unable to let out stored light faster than it is unfolded. OPEN: the mass of Porphyrion's core, and the beam's energy from below; how tightly the poles focus their light and in what band it leaves; the pace at which a pole can let out stored light; whether Porphyrion is a beam or plasma jets, and what drives plasma outside the Shell; the seed of the cosmic web's field; the source, were the weighed quasar shown to be it, which would need a mechanism not yet found or a beam under about 1 per cent of the estimate.