saturationAccel_well_defined
plain-language theorem explainer
Saturation acceleration is proven strictly positive and nonzero. Researchers modeling the transition between Newtonian gravity and information-limited regimes would cite this to anchor the critical scale before classifying dynamical regimes. The proof is a one-line term construction that pairs the positivity result with the implication that any positive real is nonzero.
Claim. Let $a_{sat}$ denote the saturation acceleration at which demanded recognition rate equals holographic bandwidth. Then $0 < a_{sat}$ and $a_{sat} ≠ 0$.
background
The Bandwidth Saturation module derives ILG gravity from recognition throughput limits. Saturation acceleration $a_{sat}$ is the critical value where Newtonian dynamics demand more recognition events per unit time than the holographic bound $A / (4ℓ_P² · k_R · 8τ₀)$ permits, with batching in 8-tick cycles producing the ILG time kernel $w_t > 1$. The module states that this scale is defined implicitly from φ and the holographic bound via the equality $M / T_{dyn} = A / (4ℓ_P² · k_R · 8τ₀)$ using gravitational area and dynamical time.
proof idea
The proof is a one-line term that constructs the conjunction by pairing the positivity theorem for saturation acceleration with the lemma that any strictly positive real number is nonzero.
why it matters
This result confirms the critical acceleration scale is well-defined and positive, serving as the foundation for the module's regime classification theorems such as below_saturation_is_newtonian and above_saturation_needs_ilg. It directly supports the derivation of ILG parameters from bandwidth constraints and ties into the eight-tick octave structure of the recognition framework. The claim is fully proved with no open scaffolding.
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