IndisputableMonolith.ProjectManagement.CriticalPathFromJCost
This module defines J-cost applied to the actual-to-plan duration ratio along with derived schedule variance and buffer quantities. Project schedulers or operations researchers extending Recognition Science to variance analysis would cite these objects. The module consists of definitions and elementary properties with no complex proofs.
claimThe central object is the J-cost of the actual-to-plan duration ratio, written $J(t_{act}/t_{plan})$, together with scheduleVarianceCost, optimalBufferFraction, and CriticalPathCert.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants and the J-cost machinery from the Cost module. It works in the setting where J satisfies the Recognition Composition Law and J-uniqueness from the forcing chain. Sibling definitions introduce schedule variance cost as a direct application of J to duration ratios and optimal buffer fraction as the value that extremizes J-ph.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the J-cost objects that feed CriticalPathCert and the associated certificates in the ProjectManagement domain. It applies the core J function to scheduling without invoking the phi-ladder or spatial dimension results.
scope and limits
- Does not derive the J function itself.
- Does not connect duration ratios to the eight-tick octave or D=3.
- Does not prove optimality for arbitrary project graphs.
- Does not address multi-resource constraints.