complexDemand
plain-language theorem explainer
complexDemand extends the base maintenance demand by a linear factor in complexity Z, yielding demand(L, Z) = maintenanceDemand(L) * (1 + |Z| * ln φ). Researchers modeling holographic bounds on conscious extent would cite this when quantifying how conserved information increases recognition cost per barrier cycle. The definition is a direct algebraic scaling of the prior maintenanceDemand term using the recognition Boltzmann constant.
Claim. For a boundary of extent $L$ with complexity integer $Z$, the demand is $d(L,Z) := d_0(L) (1 + |Z| k_R)$ where $d_0(L)$ is the base maintenance demand over the barrier period and $k_R = ln φ$ is the cost per recognition bit.
background
The ConsciousnessBandwidth module derives a holographic limit on conscious extent from the information budget of a boundary of size $L$. Maintenance cost is proportional to the J-cost integrated over the 360-tick barrier period, while holographic capacity is $L^2 / (4 ℓ_P^2)$. Each recognition event costs $k_R = ln φ$ bits (C-006), so total events are bounded by that capacity divided by $k_R$ (MODULE_DOC). The integer $Z$ is the conserved complexity drawn from anchor relations in Masses.Anchor and Physics.AnchorPolicyCertified. maintenanceDemand L already folds in the barrierPeriod and J(L) factors; complexDemand simply multiplies by the extra cost of higher $Z$. Upstream k_R definitions from Constants.BoltzmannConstant and Gravity.UltramassiveBH supply the same $ln φ$ value.
proof idea
One-line definition that multiplies the already-defined maintenanceDemand L by the factor (1 + |Z| * k_R). No tactics or lemmas are invoked beyond the algebraic expression itself.
why it matters
This definition supplies the Z-dependent term required by the two immediate downstream theorems complexDemand_ge and higher_Z_more_demand. Those results in turn support the module claim that higher Z-complexity reduces the critical coherent extent (z_complexity_reduces_extent in MODULE_DOC). It directly implements the scaling “Higher Z requires more recognition events per barrier cycle” stated in the declaration’s own doc-comment and sits inside the Recognition Science forcing chain at the point where information cost meets holographic bounds.
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