What changes when joint replenishment moves from two items to three? This unrefereed candidate gives a precise answer for one rational, common-origin, fixed-interval model. The standard max-frequency relaxation has an exact lower value, while the best coordinated calendar uses primitive period multipliers three, three, and two. Their exact ratio is approximately 1.1487291465—above the producer-certified two-item endpoint. A candidate monotonicity argument propagates this lower bound to every fixed item count of at least three. The computation is finite and exact. It examines 49,981 primitive coordination patterns, checks all boundary regimes, and closes every omitted pattern with a strict tail inequality. Ordinary, optimized, and fresh-extraction replays each pass twenty-one tests. Two exhaustive portfolio documents freeze the five near-tied calendars only as synthetic regression fixtures, while sixteen vertex certificates establish two conservative inner holding-cost boxes. These figures are not operational savings. The 14.8729 percent headline difference measures optimism in one relaxation on a synthetic normalized instance. The strongest witness is exceptionally sensitive to its coefficients. No real orders, service levels, stockouts, labour, or implementation costs were measured. The logistics handoff is therefore staged. Use the oracle to stress-test three products that genuinely share an order, shipment, receiving session, or setup. Then validate event ownership and units, regenerate a verifier-checked instance-specific candidate set across primitive and boundary regimes, model joint uncertainty and omitted constraints, simulate service outcomes, and run shadow planning before any design-adequate field comparison with stop rules. The scholarly creator is Anonymous. Research direction, maintenance and publication roles are recorded in the machine-readable provenance. AI systems assisted within that workflow. Producer-side replay and internal journal-like review are not independent verification, formal proof, field validation, or journal peer review.