PUH Theorem 386 — No Planck Core Can Collapse: Planck-Frequency Gamma Sets a Floor by Count at Every Size, the Final Planck Star Included, Until the Rebound; Light Gives the Shell Half Its Support

Abstract

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. Planck cores are permanent, of one design differing only in size (T243), and made only at the Rebound event (BigBang analog). 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 a core 'cannot collapse further because there is no configuration with more light in less space'. The author's own picture is used throughout: T357's light bulb, in which the Shell is the mass and a core is as large as its Shell. RESULT 386.1 — A FLOOR UNDER EVERY CORE, AT ANY SIZE. E_P/l_P^3 = rho_P c^2 (ratio 1.000000). The count contains neither mass nor radius, so the same floor lies under every core — a solar-mass core whose Shell is some kilometres across, and the final Planck star at 156 billion light-years — as T140 (restated) reads it: T355 and T357 'supply the Shell's minimum radius'. Today's Shells sit far above the floor: under T342's sigma a solar-mass Shell's light is 1.877e-40 of the count, the final star's 2.631e-64. Nothing in a core decays (T206, T361), so no core can collapse before the snap at 9 E_P per cell (T173) fires the rebound (T242). 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; toward the snap, what keeps a core from collapsing is the count, not 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. Result 355.4 is the floor under a Shell, not its present state, as T355's own kill-condition (iv) anticipated; the floor rests on T173's smallest cell. T348's 'mass radius' (a core's mass squeezed to Planck density, 4.5162e-23 m for a solar mass) is arithmetic, not the size of a core: a core is as large as its Shell (T357); T348's 'thirty-eight orders' should read 25.8. THE FINAL PLANCK STAR. Near 156 billion light-years across, it is a core like any other: its Shell holds the universe's mass, its light supplies at most half of the Shell's support, the same floor lies beneath it, and nothing in it decays until its energy density reaches the snap and the rebound fires outward (T242). The proposal stands in the archive's own form: Planck-frequency gamma guarantees that the final Planck star cannot collapse before the rebound — by its count rather than by its pressure. NOT CLAIMED: that the count is derived (T355 calls its identity a consistency check); the size of any core, which is set by its Shell (T298: not derived); what supplies the rest of the Shell's support; how a core passes from one quantum per cell to the snap; 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; how T348's mass radius and T260/T344's volumetric mass fit T357's light bulb; the Shell's radius.