IndisputableMonolith.ProjectManagement.CriticalPathFromJCost
This module defines J-cost metrics for project scheduling, centering on schedule variance and optimal buffer fractions computed from the actual-to-plan duration ratio. Operations researchers and Recognition Science practitioners would cite it when mapping the J-function to critical-path certification. The module supplies a collection of definitions and elementary lemmas establishing positivity and bounds.
claimLet $r$ denote the actual-to-plan duration ratio. Define scheduleVarianceCost$(r) := J(r)$ with $J(x) = (x + x^{-1})/2 - 1$. The module also introduces optimalBufferFraction as the value minimizing total J-cost and CriticalPathCert as a certificate that a given path realizes the minimal J-cost schedule.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants and the core J-cost machinery from the Cost module. It works in the setting where durations are measured in ticks and the Recognition Composition Law governs additive costs on ratios. The sibling definitions scheduleVarianceCost, optimalBufferFraction, and CriticalPathCert are the primary objects; each is accompanied by elementary properties such as non-negativity and strict positivity for r ≠ 1.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the J-cost interface required for any downstream application of Recognition Science to project management. It sits between the core forcing-chain results (T5 J-uniqueness) and any concrete scheduling theorems that would invoke CriticalPathCert.
scope and limits
- Does not encode resource leveling or multi-project constraints.
- Does not compute explicit numerical schedules or Gantt charts.
- Does not claim equivalence to classical CPM/PERT algorithms.
- Does not address stochastic duration distributions.