The Sailing as a Scheduled Value Coverage: Dimensionless Purchase Evaluation for Multi-Port Itineraries

This is the authors' abstract. We don't add key points for this paper.

A price rate is not a measure of what a purchase delivers. The Guarino Manufacturing Effectiveness Metric derives overall equipment effectiveness as a complete dimensionless basis over a dimension set that excludes money (Guarino 2026a); a companion construction admits economic value V as a conventional base dimension anchored to a dated unit, and bounds the error of mixing vintages of that unit at the product of its decay rate and the vintage gap (Guarino 2026b); and the bridge between them forces an ideal value ratio, a material share, an exact factorization and a closed-form breakeven (Guarino 2026c). This paper carries that construction to the consumer side of a purchase, the multi-port cruise itinerary, where the unit of delivery is not a quantity of goods but a scheduled port call the buyer can afterwards audit. Over the dimension set {T, L, M, V, U} the governing set forces twelve independent groups in four families, two of itinerary, two of passage, four of loading and four of economics, and realized value coverage factorizes exactly as ΠVC = ΠVC* × Δ × ΨS with breakeven Ψmin = 1 / (ΠVC* × Δ × (1 − Πa/QS)). Three commitments are kept separate from the derivation. The exclusion of safety is re-proved on this matrix as a theorem of its own rank structure: destination incident rate and hours ashore populate the T row alone, cannot carry V, and reach trip cost only through the travel insurance premium, whose published destination schedule is exhibited as the measured transducer. The anchoring of the reference shore-value rate is a convention rather than a theorem output, and it is measured against the nearest observable rather than defended, at 4.81 times what a packaged shore hour costs. And dimensional analysis supplies the form of a relation and never its function, so the paper states which choice closes it. The construction is then tested on 83 sailings across 16 lines assembled from published sources, and it does not close. Scheduled value coverage is not a monotone restatement of cost per night, at Spearman ρ = 0.650, but an ablation ladder shows that scheduled shore hours per all-in dollar already recovers that ordering at 0.845, so the marginal contribution of the construction to a ranking is the traveler-weighted price level alone. The itinerary groups do not improve out-of-sample prediction of market fare, median ΔR² = −0.056, while two ship variables do, at +0.165, an ordering that holds under random, ship-grouped and line-grouped splitting. A completeness coefficient of 0.455 fails the parent framework's own closure threshold, and the realization factor ΨS cannot be measured per sailing on public data for structural rather than clerical reasons. The result is a diagnostic ordering rather than a validated consumer ranking: the paper analyses the ordering its groups induce and does not offer it as a decision instrument. The negative results are the load-bearing ones. The deposit holds the manuscript (37 pages) and its complete LaTeX source; the rebuilt Cozumel delivery-panel data packet behind Section IX (January 2024 to September 2026, from the Quintana Roo port administration's public arrival calendar), with a script that reproduces every Section IX figure; a consistency pass that checks every symbol, dimension, Π group and stated figure against the manuscript's own Nomenclature, by executed code, with its report; two companion documents written for this edition, one collecting what the manuscript says about its preregistered plan and one giving the delivery-panel and shore-spend protocols; and the scripts and exact edit records that rebuilt this edition from the 10 August 2026 PDF. The August 83-sailing dataset, plan and analysis scripts were not available and are not deposited; a preregistered replication is deposited separately.