The Wall Ratio Governs Chiral Asymmetry of Fibonacci and Lucas Sequence Residue Sets

For a prime , let denote the rank of apparition of in the Fibonacci sequence (the least with ), the Pisano period, and the Wall ratio (Wall, 1960), which takes values in . Let be the set of distinct residues of the Fibonacci sequence over its full Pisano period, and define the chiral asymmetry as the fraction of elements of whose mirror image is absent from . We prove: and verify computationally that across all 9,590 primes below (zero violations; conjectured). The proof uses the multiplier identity where , together with Cassini's identity, which gives : when , forces a sign flip within the period, making closed under negation and . The previously observed sufficient condition (equivalently ) always forces and is subsumed by this result. The same law holds for the Pell sequence and is expected for all Lucas sequences. The deposited script reproduces all results. Earned and open. Earned: the multiplier identity (an identity; the backward implication (proved); the Pell case (verified exhaustively below 5,000). Open: the forward direction is a conjecture, verified over the stated range and open; the extension to all Lucas sequences is expected and open. What this says about any physical system stays open here. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.