Abstract
Elapsed laboratory time does not uniquely determine how much a system has evolved. This article proposes boundary-relative state-time as a systems-measurement framework for accumulated histories indexed by explicit analytical boundaries. Its primary contribution is a measurement-lineage rule: when a boundary is enlarged at inherited resolution, contained histories and their measurement semantics must remain recoverable and coherent; otherwise the larger model is a replacement rather than an extension. The framework separates direct full-boundary accumulation, component-preserving ledgers, and optional scalarization, and distinguishes analytical boundary expansion from coarse-graining or physical modification. Geometric and event-count examples show nonempty admissible constructions and pre-outcome rejection criteria, while an LED thermal-coupling case illustrates boundary reclassification without claiming predictive validation. Empirical usefulness is reserved for prospective tests of pre-specified implementations against established domain metrics.
In plain language
A model always draws a line around what counts as the system. Move that line, and something that used to appear as an external input or boundary flow can become an internal part of the larger system. The paper asks what must remain unchanged if the enlarged description is supposed to be an extension of the original one rather than a different model using the same words.
The central answer is measurement lineage. If a subsystem was assigned an accumulated history under a declared measurement rule, then enlarging the boundary at the same resolution should preserve both that history and what the measurement meant. New components and interactions can be added, but the inherited accounting should remain recoverable.
Why it matters
Many scientific and engineering descriptions are nested. A component can be analyzed by itself, then as part of an assembly, and later as part of a larger coupled environment. Without an explicit lineage rule, a change in the reported quantity can come from three very different sources: the physics changed, the resolution changed, or the measurement definition changed. Those possibilities should not be conflated.
The framework provides a way to keep that distinction visible. It allows a larger model to add histories, interactions, and boundary-crossing processes while preserving the calibrated meaning of measurements inherited from the smaller model. When that preservation fails, the paper argues that the honest description is not “the same measure at a larger boundary,” but a new model lineage.
The proposal is deliberately not a universal replacement for clock time, energy, entropy, damage, or other domain-specific measures. Its significance is methodological: it provides a discipline for deciding when measurements remain comparable as the object being modeled changes.
Publication record
Submitted to Systems Research and Behavioral Science. A public preprint or repository record has not yet been posted. When available, the canonical scholarly link will appear near the top of this page.