Mixed-Multiplicity Sharpness in Local Integer Convolution Readouts
Year: 2026
Type: preprint
Abstract: This note studies mixed-multiplicity sharpness in local integer convolution readouts. A previous completion-seam result showed that a local readout can acquire a coarser gcd grain when a binary support geometry completes every kernel footprint sampled by the readout. Here the support model is extended to additive layering. One completed support layer is held fixed while a second layer enters the same local readout window. When the second layer also completes every footprint, all local overlaps are uniformly rescaled: the raw gcd doubles, while the normalized local probabilities and reduced modes are unchanged. When the second layer is partial, the readout enters a mixed-multiplicity regime. In the deterministic examples studied here, the overlap values form a small geometry-generated alphabet, the local gcd collapses to 1, and no robust affine residue lock is observed under the bounded finite-character diagnostics tested. The result separates three local arithmetic regimes: pure completion, uniform multiplicity scaling, and mixed multiplicity. It provides a controlled static precursor for later walker-ensemble and wake-construction studies.
Author: James, John R.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162944478
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