Stable Canonical Indexing for Sparse Vision Domains, with Standard Algebraic Reductions under a Functor-Model Validation Discipline

We separate three claims that are often conflated in discussions of efficient vision operators, and state each at the strength it can bear. (1) A Cantor-style pairing gives a width-independent, insertion-stable canonical index for sparse, dynamically expanding domains (event-camera streams, LiDAR clouds, adaptive feature maps); this is its genuine contribution and it is architectural, not complexity-theoretic—it does not reduce arithmetic. (2) The reductions that do lower cost—FFT diagonalization of circulant/convolutional operators, and restriction to the effective subspace when an operator is rank-deficient—are standard tools; we present them as such, and we correct the kernel claim to its honest form, since trained operators generically have trivial exact kernel, making the relevant statement one about approximate low rank with an explicit truncation-error bound. (3) The Functor Model framework contributes a validation discipline: a reduced implementation may replace a canonical specification only when certified equivalent (exactly, or within a stated tolerance). The novel and defensible content is (1) and (3); (2) is organized, not invented. We make no asymptotic claim for the indexing and attach no fixed energy figure to any step.