IsSubSaturated
plain-language theorem explainer
A system is sub-saturated when its demanded recognition rate lies strictly below the holographic bandwidth set by area. Workers on unification of recognition cost with holographic bounds cite the definition to separate Newtonian from saturated regimes. The definition is introduced directly as the inequality between demanded rate and bandwidth.
Claim. Let $A$, $m$, and $t$ be real numbers for area, mass, and dynamical time. The system is sub-saturated when the demanded rate for mass $m$ and time $t$ is strictly less than the bandwidth fixed by area $A$.
background
Recognition bandwidth is the maximum ledger throughput inside a holographically bounded region, expressed as $R_max = A/(4 ell_P^2 ln phi * 8 tau_0)$. The module connects five elements: the holographic bound on information, recognition cost per bit $k_R = ln phi$, ILG parameters, the 8-tick cadence, and consciousness boundary cost. demandedRate is the rate required by mass and dynamical time; bandwidth is the area-dependent ceiling.
proof idea
The definition is the direct inequality demandedRate mass dynamicalTime < bandwidth area.
why it matters
The definition supplies the right-hand disjunct for the theorem saturated_or_sub, which asserts every system is saturated or sub-saturated by excluded middle. It operationalizes the Newtonian regime inside the recognition bandwidth module that links the holographic bound to the 8-tick cadence of Recognition Science.
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