When two theoretical levels connect — statistical mechanics to thermodynamics, quantum chemistry to molecular structure, molecular genetics to organismal phenotype — the connection requires a construct that neither theory provides. Statistical mechanics needs the Stosszahlansatz (molecular chaos hypothesis) to derive thermodynamic entropy from particle dynamics. Quantum chemistry needs bonding analysis to connect wavefunctions to molecular architecture. Molecular genetics needs a gene concept to bridge DNA sequence to organism.
Sticker identifies a pattern: these bridge constructs occupy a third theoretical role, distinct from both the lower-level dynamical theory and the higher-level observational theory. The bridge theory maps between them through a many-to-one relation — many dynamical microstates correspond to each observational macrostate, creating a contingent space of dynamical configurations compatible with observations but not selected by them.
Three conditions complete the bridge in sequence. A Partition defines which dynamical states count as observationally equivalent. A Magnitude characterizes the geometry of the contingent space — how large it is, how its elements relate. A Closure selects or weights elements within that space. The Stosszahlansatz is a Closure condition — it selects the molecular-chaos distribution from the space of all distributions consistent with macroscopic variables.
The framework generates a Mirror Test: any proposed closure should be identifiable as either closing the contingent space (legitimate) or introducing new structure (overreach). This distinguishes productive bridge constructs from smuggled assumptions.
The structural point: inter-level scientific disputes persist not because one side is wrong but because the bridge construct connecting the levels is incomplete or contested. The bridge is not a derived consequence of either theory — it is an independent theoretical contribution, as load-bearing as the theories it connects.