Chiral Asymmetry of Integer Sequences at Primorial Moduli: A General Framework

For a set of integers and modulus , define the chiral asymmetry as the fraction of residue classes in whose mirror image is absent from . We prove two main theorems. Theorem 1 (Divisor monotonicity): implies for every divisor ; equivalently, if for some then . The numerical value of need not be monotone and can increase or decrease freely; only the zero/positive dichotomy is constrained. Theorem 2 (Multiplicative sequences): For and odd prime , the cyclic sequence satisfies if and only if is even, equivalently . All asymmetry values in Table 1 are computed from full-period residue sets; sequences without a well-defined period (Catalan, Bell, partitions) are excluded from quantitative comparison as their asymmetry does not converge with sample size. A notable consequence of Theorem 1 is that chiral asymmetry can arise purely from composite structure: and yet (since ), showing that does not require any prime factor of to exhibit positive asymmetry. Earned and open. Earned: Theorem 1, Theorem 2, Theorem 2 and Corollary 1 are proved outright; the composite example is a computed fact. Open: the necessary condition on inherits the conjectured half of the Paper 52 result and is therefore conditional, as stated at that point; the characterisation of which pairs with give is unsolved. 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.