Variational Backbone and Regime Closures I: The Effective State Space and the Core Summary Interface A Constitutional Entry Point

Part I formulates the constitutional layer of the VBRC framework. The frameworkbegins with an admissible state space C and a real-valued comparison language E : C → R.A protocol P induces retained and unread coordinates, but the unread coordinate is notidentified with a uniquely specified hidden physical sector; it functions as a virtual boundaryof the retained description.The Internal Invisibility Principle states that unread content cannot enter retained lawsas raw data. It may enter only through a licensed summaryF = ΣH,P (II ).This virtual-boundary status is structural, not merely interpretive: it prevents the frameworkfrom being tied to a specified physical instance of the unread side, thereby preservingbidirectional interface use, scale-neutrality, and observation as protocol-licensed partialreadout. In the first-order representative used here, the licensed summary is realized asF = DI II . The retained-effective state spaceC(H,P)eff = C(P)R × Ran ΣH,Pis the arena on which retained laws are written.Part I declares the minimal core densityecore =β2|DRIR|2 +α2|F|2 + η ⟨IR, F⟩,performs the first variation directly on (IR, F), and only afterwards pulls the result back tothe representative F = DI II . The retained Euler–Lagrange law contains the unread side onlythrough F; the summary-side condition is a constrained-variation condition on admissibleeffective directions, with no raw access to II . The same density is then read through R1(stationarity), R2 (gradient descent), and R3 (minimal retained-time completion). The nonuniqueness of unread interiors is treated as a structural boundary condition: VBRC studiesthe invariant summary-to-law relations that remain readable despite that underdetermination.Part I therefore installs a law-generation interface, not a specific physical regime or a hiddensector ontology.