GACTP and the Enantiomeric Branch Pair in Canonical Deparameterization: Canonical Chirality

The canonical deparameterization of time yields the familiar discrete branch label σ = ±1, but its physical meaning has long been recognized as too thin to capture temporal orientation 4, 7, 9, 10, 13, 14, 11. This manuscript makes σ’s geometric content explicit: it is the sign of a constructed three-dimensional enantiomeric structure in canonical phase space. The σ = +1 and σ = −1 branches are related by the composition of three independent flips—chiral, vertically inverted, and horizontally mirrored—exactly the relation that makes optical isomers nonsuperimposable in three dimensions. Under chirally complete admissibility, the branch-oriented temporal ledger cancels in the same way that a racemic mixture shows no net optical rotation. This is the Global Asymmetry Condition for Temporal Persistence (GACTP): determinate temporal evolution requires a global selector that excludes one chirality class from admissibility rather than treating it on equal footing with its enantiomer. The band-anchored DWTT model is presented as a clean, canonical control case in which the deparameterized clock structure is explicit, and the branch pair is unambiguous. The paper establishes the need for a selector but does not build one; identifying the physical principle that selects one chirality class over its enantiomer is left for future work. The paper does three things. First, it identifies the geometric content of the canonical branch label σ = ±1 as the sign of a three-dimensional enantiomeric structure in the deparameterized phase space, rather than as a one-dimensional gauge label. Second, it proves that under chirally complete admissibility, the branch-oriented temporal ledger cancels (the GACTP theorem). Third, it presents the band-anchored DWTT model as a clean canonical control case that makes both points concrete. The paper does not construct the global selector whose existence GACTP requires; that question is the open frontier and is left for subsequent work.