The Remnant Mass Implied by the Aldred Limit: Where the Horizon Meets the Density Cap

The remnant mass is 8.659e+10 kilograms, or 8.659e+13 grams, which is 3.979e+18 times the Planck mass. Its horizon radius at the meeting point is 1.286e-16 metres, and the radius check returns 1.000e+00, unity to the precision shown, confirming the algebra. The remnant is therefore far heavier than a Planck-scale object: the density bound, not the Planck density, sets the endpoint, and because the bound lies well below the Planck density the remnant sits correspondingly above the Planck mass. A Planck-mass remnant is the endpoint often assumed when quantum gravity is invoked without a specific mechanism. Computed from stated assumptions, not measured.