scheduleVarianceCost
plain-language theorem explainer
Defines schedule variance cost as the J-cost of the ratio of actual to planned duration. Critical chain project management researchers cite it to quantify plan deviations via the Recognition Science J function. The definition is a direct one-line application of Jcost to the duration ratio, enabling the nonnegativity and zero-on-plan theorems.
Claim. Let $J$ be the J-cost function. For actual duration $a$ and planned duration $p$, the schedule variance cost is $J(a/p)$.
background
The module Critical Path and Project Buffer from J-Cost links Critical Chain Project Management (Goldratt 1997) to Recognition Science, predicting an optimal buffer of $J(φ) ≈ 0.118$ of critical path duration, consistent with empirical 10-20% buffers. J-cost is imported from IndisputableMonolith.Cost and satisfies the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. This definition translates duration variance into the J-cost framework for project certification.
proof idea
It is a one-line definition that applies Jcost directly to the ratio actual_duration / planned_duration.
why it matters
This definition supplies the cost measure for the CriticalPathCert structure, which asserts zero cost on plan, nonnegativity, and that optimalBufferFraction is positive yet less than 1/2. It realizes the module's RS prediction tying J(φ) to project buffers within the T5 J-uniqueness and phi fixed-point chain. The three downstream theorems (scheduleVarianceCost_on_plan, scheduleVarianceCost_nonneg, and CriticalPathCert) all unfold this definition.
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