IndisputableMonolith.ProjectManagement.CriticalPathFromJCost
The module equips project scheduling with J-cost applied to actual-to-plan duration ratios. Recognition Science practitioners modeling operations would cite these definitions when constructing critical path certificates. The structure consists of basic definitions followed by elementary lemmas on non-negativity and bounds derived from the properties of J.
claimLet $r = t_{actual}/t_{plan}$ be the duration ratio. Schedule variance cost is $J(r)$ with $J(x) = (x + x^{-1})/2 - 1$. Optimal buffer fraction $f$ satisfies $0 < f < 1/2$ and equals $J(phi)$ in the self-similar case, with CriticalPathCert witnessing the resulting schedule.
background
Recognition Science derives the J-function in the Cost module from the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y), with the fundamental time quantum tau_0 = 1 tick supplied by Constants. The module specializes these objects to project management by measuring deviation via the ratio of realized to planned duration and applying J directly to that ratio. Sibling declarations introduce scheduleVarianceCost, optimalBufferFraction, and CriticalPathCert as the core objects.
proof idea
This is a definition module, no proofs. The supporting lemmas follow directly from the algebraic properties of J and the fixed point phi established in upstream modules.
why it matters in Recognition Science
The module supplies the J-cost foundation for critical path analysis in the ProjectManagement domain. It realizes the self-similar fixed point phi from the forcing chain (T5-T6) in a scheduling setting and prepares ground for applications of the eight-tick octave, though no downstream uses are recorded yet. The doc-comment identifies the direct mapping from duration ratios to J-cost as the central step.
scope and limits
- Does not model stochastic task durations.
- Does not incorporate resource constraints beyond time.
- Does not compute numerical values for specific projects.
- Does not extend to multi-project portfolios.