PUH Theorem 389 — One Unfolding Rate per Square Metre of Shell: Sgr A*'s Waiting Matter Caps It at 1.4 × 10¹⁰ W/m², M87*'s Jet, If Steady, Floors It at 2 × 10⁷, and Earth's Core Supplies at Most 11 W

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. A Planck core's Shell unfolds what reaches it at a rate per unit of its area (R_sub; T213), and the archive has no derived value for it: T262 calls it 'the one irreducible unknown', and the Throughput Law paper shows dimensional analysis cannot reach it. The author's picture: one unfolding rate per unit of Shell area, the same for every core — per square inch every unfolding rate is equal, so a core's total rate is proportional to its Shell's area, with nothing to do with spin and nothing to do with mass (as T243 has it) — and its value set by Sgr A*, whose matter waits at its Shell to be unfolded (T388), so the rate is slow. Only the unfolded photons enter the core; some leave at its poles, by a mechanism not yet known (T388). RESULT 389.1 — THE ARCHIVE'S 3.2 mW/m² WAS PER SQUARE METRE OF PLUTO. T197's figure is 'the heat flux at the surface of the rocky body': over Pluto's surface (radius 1,188.3 km) it is 5.6782e10 W. T330 applied it per square metre of Shell (P = q·4πr_s²), which gives Pluto's core 1.5048e-11 W, 2.650e-22 of the heat T197 credits to it (3.074e-22 with the Shell where T311 places it). Read with the complete relation the archive already had (Internal-Consistency Note; T267: F = R_sub (r_shell/R_body)²), Pluto's heat needs 1.0412e19 to 1.4862e25 W per square metre of Shell, and a core supplying Earth's 13 to 23 TW non-radiogenic remainder (Earth's core 4.96e21 kg, T346, its Shell 15.9 micrometres across) 1.6437e22 to 2.9080e22 W/m². The figure is not a measurement of the rate. RESULT 389.2 — SGR A*'S WAITING MATTER CAPS THE RATE. With the EHT's 4.14e6 solar masses and the Shell at 1.07692 times the horizon radius (X = 14; T298, T300, T311), Sgr A*'s Shell has an area of 2.1797e21 m². For its matter to wait at every intake the EHT's best-bet models allow, (5.2–9.5)e-9 solar masses a year, the Shell must unfold less than reaches it: the rate is below 1.3513e10 W/m² — 8.7181 MW, or 97.0 nanograms of matter a second, per square inch (2.4687e10 at the highest best-bet intake; 5.1973e9 to 5.1973e11 over the range Faraday rotation allows). One rate per square metre makes this a cap on every core. RESULT 389.3 — M87*'S JET, IF STEADY, FLOORS THE RATE. A core never releases its own content (T206), so averaged over its life its poles release no more than its Shell unfolds (T388). If M87*'s jet (6.5e9 solar masses; Shell area 5.3732e27 m²) is light its poles release and has run at its present power over the core's life, the rate is at least 1.8611e7 W/m² at the EHT's conservative 1e42 erg/s (1.8611e9 at 1e44). The window then runs from 1.8611e7 to 1.3513e10 W/m², 12.0 kW to 8.72 MW per square inch, 726 times wide, and a steady jet above 7.2608e44 erg/s would close it; if M87*'s matter waits too (T213: infall exceeds processing in active nuclei), its top falls to 3.1626e8 to 2.1084e9. A younger jet lowers the floor in proportion. Whatever the rate, and the tear-zone light aside, Sgr A*'s poles may let out per unit of light at most 0.25 (against its quiet output of about 1e28 W) to 2.3 (against the best-bet models' own luminosity) times the share M87*'s conservative jet needs, and 0.25 to 2.3 per cent of the share a jet of 1e44 needs, if Sgr A*'s output were seen. RESULT 389.4 — EARTH'S AND PLUTO'S CORES SUPPLY ONLY WATTS. At the window's top Earth's core unfolds at most 10.688 W, 2.274e-13 of Earth's 47 TW (Davies and Davies 2010); even a core holding all of Earth's mass would supply 3.297e-7 of it. Pluto's core, even holding all of Pluto's mass, unfolds at most 73.697 W, 1.298e-9 of Pluto's heat; a core able to supply that heat would weigh 2.776e4 times as much as Pluto. The heat of Earth and Pluto is their own. T197's Pluto heat source, its habitable-zone threshold and its reading of Earth's flux are narrowed to nothing measurable, and the Geodynamo note's 'few-terawatt convective power' to at most 11 W. The geoneutrino data, which set only an upper limit on the core's share (Geoneutrino Lead Note), fit. What keeps Pluto's ocean liquid is left to T360's three rivals or a mechanism not yet found. RESULT 389.5 — SGR A* IN THE WINDOW: T388 RE-READ. Sgt A*'s Shell unfolds 7.539e-4 to nearly all of what reaches it, not T388's 1e-13; at the floor 72 to 131 solar masses wait after 13.8 billion years, as T388 found. The core takes in at most 1.7333e-5 of its mass in that time and does not feed. Against its quiet output, its dimness needs its poles to let out at most 0.247 (floor) to 3.395e-4 (top) of the light its Shell unfolds, if that output were seen. The share escaping the tear zone (T287: 11.781 per cent at the Shell's radius) stays below the quiet output only for a rate under 3.8941e7 W/m² (2.6480e8 to 3.5826e8 against the best-bet luminosity): OPEN. RESULT 389.6 — THE ARCHIVE'S OTHER BOUNDS. Rescaled to a square metre of Shell, T309's conditional floor (7.9432e39 W/m²) lies 5.8782e29 above the window's top: a merger of 60 solar masses at the top would take 5.493e19 years over the Shell's area, so mergers are not throughput-limited and merging is topological, as T309 leaned; its fork, left untouched by T371, is decided. T294's ceiling (3.9522e30 W/m²) and T368's (1.2500e123 W/m²) lie far above. The conclusions T330, T341 and T375 drew from T330's rate keep their direction with narrower margins: a solar-mass core falls 8.3 to 11.2 orders short of the Sun where T330 had twenty-one. T370's 'beyond any instrument' no longer holds across most of the window — the seed's own output, if all of it ended as annihilation at or above the Sun's surface, would reach up to 1.763 times the Galaxy's whole 511 keV line — and its Result 370.2, no glow from a core at the centre, now carries the Sun's missing glow. The Throughput Law paper's negative result stands: its ansatz needs a Compton length of 145.0 to 1,303.6 m. NOT CLAIMED: the rate's value within the window, or its derivation; that M87*'s jet is light its poles release, or steady; how the poles release light, how much, or when; that the light escaping Sgr A*'s tear zone would be seen, or in what band; what keeps Pluto's ocean liquid; what powered the geodynamo before the inner core formed; anything about Earth's heat beyond its core's share. KILL-CONDITIONS: the rate per square metre shown to differ from core to core; Sgr A*'s Shell shown to unfold all that reaches it; Earth's core shown to supply more than about 20 W; M87*'s jet shown to be light its poles release, steady above 7.2608e44 erg/s; a merger of cores shown to be throughput-limited. OPEN: the rate within the window and its origin (T213, T262); whether M87*'s jet is light its poles release, and steady; how the poles of different cores let out different shares of their light (T388's OPEN 5); the light escaping Sgr A*'s tear zone, if seen (T287); what keeps Pluto's ocean liquid (T360); M87*'s jet history; what powered Earth's field before the inner core formed (the Geodynamo note's power paradox).