Paper 13 of the series Dual Geometry of Wavelength Space and Frequency Space. We answer the series' oldest question — can discrete states be mapped back and forth to position and time? — with exactly zero additions to the axiom inventory. Discrete position is identified as the sign sector of the wave (quarter-period offsets), a change of readout principle only (Theorem 1, with a two-line proof). Position space is the Pontryagin dual of the conserved-quantity (charge-like) lattice, so translation, rotation, and inversion symmetries are theorems of duality (Definition 2, Theorems 2a-2b). The readout hierarchy is exactly three strata: scalar fringes collapse the 21 relation classes to 11, line-position fringes to 13, and branch channels separate all 21 (exhaustive counts). Quarter-lattice displacements are readable with the general component rule m mod 4 (Theorem 4). Time is resolved asymmetrically: the clock targets are exactly all odd integers — proven without range limits via Gauss's triangular-number theorem (Theorem 5) — while t admits no independent inverse map (Theorem 6, with an inventory-audit proof sketch): t is a derived quantity. All claims are machine-verified with labelled methods (true-by-construction / theorem+confirmation / falsifiable checks); reproduction scripts are included in the repository. Reviewed in two rounds under a two-party independent verification protocol (Claude Code and claude.ai). Japanese and English full texts. No physical identification is made.
Noriaki Kihara (Sun,) studied this question.