The Statistical Bridge

Abstract

A business asks for average revenue per active customer this quarter, with a standard error. The analyst has login events, transaction events, customer identifiers, and a familiar formula. Every arithmetic step can be correct while the analysis has not established what one customer-quarter point is, which points belong to the target, whether no recorded transaction means zero or incomplete coverage, what supplies probability, what formal statement carries inferential authority, or what the reported result is entitled to mean beyond the completed quarter. The difficulty is not inside the formula. It lies in the governed passage by which operational material becomes statistical evidence, evidence bears on a formal target, formal machinery derives an inferential result, and that result returns as a bounded claim about the world. This passage is the Statistical Bridge. The framework has two scopes. Broadly, the Statistical Bridge is the governed interface among application, empirical evidence, formal target, inference, and interpretation. Narrowly, one recurring structural center is the regime-qualified relation [E^{(r)}\rightleftarrowsS^{(r)},] between realized event-side evidence and independently established spine-side targets. Event and spine are recurring existence forms under Theory of Data Version 6: event points are occurrence-established, while spine points exist independently under a declared or generated existence law. They provide the geometry of a possible crossing, not its evidential warrant. Version 3 makes the bridge's middle and return layers more explicit. A statistical analysis must distinguish bridge constitution, probability source, inference certificate, and claim license. Probability sources may be evidence-side, governing how possible evidence could arise, or target-side, placing probability over target-side unknowns. An inference certificate is the formal statement or guarantee carrying inferential authority under the declared sources. A claim license bounds what that certificate may mean over population, time, regime, transport, and sensitivity. These are logical obligations rather than chronological stages; one declaration may discharge several, and later diagnostics may reopen earlier ones. The framework also separates mathematical role from evidential standing: components can coexist inside one statistical construction while having very different warrant. Where possible, the forward evidence-production account should be executable, strengthening internal reviewability without proving large-world truth. The resulting thesis is compact: Statistical analysis is the governed work of making evidence bear on a target, making the warrant inspectable, and bounding what the resulting claim may mean.