horizonDemand_universal
plain-language theorem explainer
Horizon demand for a Schwarzschild black hole is independent of mass, so any two positive masses yield identical demand values. Unification researchers cite the result to establish uniform holographic saturation across all black hole sizes. The proof is a one-line term wrapper that rewrites each side via the explicit equality for horizon demand.
Claim. For all positive real numbers $M_1, M_2 > 0$, the horizon demand computed from mass $M_1$ equals the horizon demand computed from mass $M_2$.
background
The Black Hole Bandwidth module treats a Schwarzschild black hole as the limiting case of full recognition saturation, where the horizon area $A = 16πM^2$ sets the total ledger bits via Bekenstein-Hawking entropy $S_{BH} = 4πM^2$. Horizon demand is the recognition cost of processing those bits, scaled by the RS Boltzmann analog $k_R = ln φ$ and the eight-tick cadence $8τ_0$. The module imports the definition of $k_R$ from Constants.BoltzmannConstant and the explicit form of horizon demand from the same file.
proof idea
The term proof applies the equality horizonDemand_eq to each positive-mass hypothesis, reducing both sides to the identical mass-independent expression built from horizon area and processing interval.
why it matters
The result supplies the mass-independence step required for the module's central saturation claim (demand equals bandwidth at the horizon for any M). It feeds the no-hair and information-conservation arguments listed in the module doc and aligns with the eight-tick octave (T7) and D = 3 of the forcing chain. No open questions are closed here, but the universality part of maximal saturation is now discharged.
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