PUH Theorem 386 — Planck-Frequency Gamma Holds Planck Cores Open by Count at Any Size Until the Snap Fires the Rebound, the Final Planck Star Included; at the Shell, Light Supplies Half the Support

Abstract

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. Planck cores are permanent, of one design differing only in size (T243), and made at the Rebound. The author proposes that gamma at the Planck frequency, pressing on the inside of the Shell, keeps the cores — and the final Planck star, near 156 billion light-years across — open until the final rebound, as a polariton field acting as one unit (T214), with the core's inside a perfect reflector (T307). The archive already holds the answer. T355's Result 355.4 makes one Planck-frequency quantum per Planck cell both Planck density and Casimir saturation, so the core 'cannot collapse further because there is no configuration with more light in less space'. RESULT 386.1 — HELD BY COUNT, AT ANY SIZE. E_P/l_P^3 = rho_P c^2 (ratio 1.000000). The count contains neither mass nor radius. At Planck density a solar mass fills a ball of 4.5162e-23 m (T348), and the universe's 1.5e53 kg (T140, restated) one of 1.9081e-15 m, about the size of a proton, held by the same count. Nothing in it decays (T206, T361), and the hold ends only at the snap, 9 E_P per cell (T173), where T242 fires the rebound. The author's premise is the archive's own result. RESULT 386.2 — WHAT PLANCK-FREQUENCY GAMMA PUSHES ON PUH'S OWN LATTICE. On T320's lattice the push per unit energy (group over phase speed) is 0.94762 at E_P, 0.75090 at 2 E_P and nothing above the band top at 2.9212 E_P (4.8686 E_P at T372's 0.6 l_P). The 9 E_P quanta of T166, T173 and T214 lie above it, in T214's 'static configuration', and push nothing. T355.4's one E_P per cell and the snap's 9 E_P per site are two states; near the snap the core is held by the count, not by pressure. RESULT 386.3 — AT THE SHELL, LIGHT SUPPLIES AT MOST HALF. T342's tension pulls 2Mc^2/R in all (T259: Delta P = 2 sigma/R). Light of total energy E_L pushes E_L/R, in any arrangement: 20,000 photons on random chords give exactly 1.000000000000, and in coherent fields the stresses add up to the energy density to 4.4e-16, so one coherent unit pushes no harder. T344's flux counts the light's energy too, so push over pull is at most 0.500000, at every size (2,000 random cores), and 0.4738 for gamma at E_P on the lattice. A reflecting core obeys R F_Shell - R_core F_core = E_L: it moves load rather than adding push. The rest of the support must come from the lattice (the membrane paper's stiffening, T166's sites, T231's inflow), not yet computed. RESULT 386.4 — THREE LOOSE ENDS IN THE ARCHIVE. T357's support check withdrawn in the archive's own terms: a full Planck layer on a solar-mass Shell would carry 5.327e39 solar masses, and held by tension its pressure would need 1.094e37 snap caps; the Shell actually asks 8.8387e35 Pa. The count at the Shell under T342's sigma is 1.877e-40 quanta per cell, so T355's kill-condition (iv) applies there: the count lives where the mass sits at Planck density. And where the mass sits is disputed: T348 (a Planck-density ball, 25.8 orders inside the Shell — its text's 'thirty-eight' corrected) against T357's light bulb. THE FINAL PLANCK STAR. On T348's reading it sits at Planck density in a ball the size of a proton, held by the count of Planck-frequency gamma until the snap fires the rebound outward (T242). The author's proposal stands in the archive's own form: by count rather than by pressure. NOT CLAIMED: that the count is derived (T355 calls its identity a consistency check); the Shell's radius (T298); what supplies the rest of the Shell's support; how a core passes from one quantum per cell to the snap; the final Planck star's size; anything in Einstein's equations. KILL-CONDITIONS: T342's sigma not being the Shell's mechanical tension; the lattice holding more than one quantum per Planck cell below the snap; a Planck core losing mass other than at the rebound; a travelling lattice wave above T320's band top. OPEN: the lattice's share of the Shell's support; the factor of nine between T355.4 and the snap; where the mass sits; the Shell's radius.