hawking_contains_eight_tick
plain-language theorem explainer
The theorem establishes that the Hawking temperature of a Schwarzschild black hole with positive mass M equals 1 divided by the product of the eight-tick cadence, pi, and M. Researchers in quantum gravity and holographic models would cite it to identify the factor of 8 in the standard Hawking formula with the recognition octave. The proof is a direct algebraic reduction obtained by unfolding the definitions of hawkingTemp and eightTickCadence then simplifying via the ring tactic.
Claim. $T_H(M) = 1/((8τ_0) π M)$ for all real $M > 0$, where $τ_0$ is the fundamental time quantum and $8τ_0$ is the eight-tick cadence of one octave.
background
In the Black Hole Bandwidth module a black hole is the limiting case of full recognition saturation: every holographic bit on the horizon is consumed by gravitational dynamics, leaving zero excess bandwidth. The Hawking temperature is expressed through the horizon scale πM together with the recognition cadence. Upstream, the tick definition supplies the fundamental RS time quantum τ₀ = 1, while the octave is defined as exactly eight ticks; eightTickCadence is therefore the product 8τ₀. The result also rests on ledger factorization and phi-forcing structures that calibrate the J-cost and defect measures used throughout the unification layer.
proof idea
The proof is a one-line wrapper that unfolds hawkingTemp, eightTickCadence, τ₀ and tick, then applies the ring tactic to obtain the algebraic identity.
why it matters
The declaration supplies the explicit identification of the 8 in the Hawking temperature with the eight-tick octave (T7) of the forcing chain. It directly supports the bandwidth account of the no-hair theorem stated in the module, where full saturation (demand equals bandwidth) leaves no capacity for additional structure. The result feeds the downstream claims no_hair_from_saturation and entropy_is_bandwidth, confirming that horizon entropy equals total recognition bandwidth times processing time. It touches the open question of how the recognition operator enforces information conservation during evaporation.
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