Visible Return and Lifted Return: The Dirac Belt, Projection, and Lost Path-History

Version 1.2 sharpens the mechanism of the loss established in v1.1.

It introduces the situated identity 1′ — the unit already placed inside the path-bearing scene before rotation — and shows the first loss as the disembodiment of 1′ into the bare 1, before any motion. The loss is presented as a composition of two factorizations, Z → Z/2 → {I}.

An elementary vector scene, AB + BC = AC, serves as the minimal model of route compression and separates three temporal registers: planning time, in which the route stays segmented; projective time, in which only the endpoint is kept; and traversal time, in which the path is performed. The diagnostic mark −1↓ records a path-bearing midpoint read after route compression.

The version states a stronger form of the central claim: projection can render distinct lifted histories inseparable within the register that has erased their distinguishing coordinate — a projected non-separability that belongs to the register rather than to the paths, and that stands apart from quantum entanglement.

The central claim of v1.1 is unchanged: endpoint equality can hide path inequivalence. This version does not propose a new physical theory, a revision of arithmetic, or a new explanation of the cited lattice mechanism.