Mass Without Mass, Held by Itself: Wheeler's Geon, Priced

In 1955 John Archibald Wheeler proposed the geon: a ball of electromagnetic radiation held together by its own gravitational attraction — mass without mass, a particle built from nothing but light and geometry. I credit the proposal at full strength: it is one of the most beautiful constructions in classical relativity, it founded the study of self-gravitating field configurations that runs through boson stars and oscillatons to this day, and Wheeler himself printed its central difficulty in the open — the classical geon is unstable, leaking its radiation away. Nothing in this paper falsifies the geon programme, and nothing here is news to its author, who evaluated its instability before anyone. What I evaluate is the construction's arithmetic: where the numbers run, and where they run out. On declared inputs only — a radius grid, printed as declared — my bench places each geon at its self-gravitating condition, mass M = Rc^2/(2G), and returns the population the condition forces. At R = 1.000000e+02 m the geon masses 6.732955e+28 kg (3.385998e-02 solar masses), carries 6.051278e+45 J, and is made of 1.914037e+73 photons each of wavelength 6.283185e+02 m, at a mean field of 1.806425e+25 V/m — while its leakage time is R/c = 3.335641e-07 s, one light-crossing, by construction. The scaling is the finding: across the grid the photon count grows as R^2 (1.914037e+65 at a centimetre to 1.914037e+77 at ten kilometres), the field falls only as 1/R, and at every radius the confinement is exactly as strong as the escape — the construction sits at its own Schwarzschild condition, which is both its definition and its instability, in one equation. Counted plainly: stable geon solutions returned by the arithmetic = 0; confinement mechanism supplied by the construction beyond its own gravity = 0 — because self-gravity is the postulate, not a derived container. Grade for this census entry, printed at full size: REASON FOUND / STILL TURNING — explicitly not a kill and not a falsification. The program headline stands unmoved: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.