{
  "id": "oai:papers.qnfo.org:functorial-framework-for-morphological-computing",
  "slug": "functorial-framework-for-morphological-computing",
  "title": "Functorial Framework for Morphological Computing",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "This work introduces a formal framework for morphological computing that resolves the longstanding reconstruction paradox in Residue Number System (RNS) arithmetic by leveraging the physics of topological quantum matter. Conventional RNS-based accelerators are bottlenecked by the serial, computationally expensive conversion of a parallel residue vector into a scalar integer via the Chinese Remainder Theorem. We dissolve this bottleneck by proposing a vectorial topological encoding scheme where the computational result is the residue vector itself, physically embodied as a vector of Chern numbers in a moiré superlattice. We address the critical challenge of formal verification in physical computing by constructing a structure-preserving functor from the algebraic category of RNS computations to the physical category of adiabatic evolutions in topological phases. This functor provides a formal guarantee of computational correctness. The final result is read out directly via a multi-terminal quantum Hall conductance measurement, which yields the Chern vector without any algorithmic post-processing. [...]",
  "abstract_markdown": "This work introduces a formal framework for morphological computing that resolves the longstanding reconstruction paradox in Residue Number System (RNS) arithmetic by leveraging the physics of topological quantum matter. Conventional RNS-based accelerators are bottlenecked by the serial, computationally expensive conversion of a parallel residue vector into a scalar integer via the Chinese Remainder Theorem. We dissolve this bottleneck by proposing a vectorial topological encoding scheme where the computational result is the residue vector itself, physically embodied as a vector of Chern numbers in a moiré superlattice. We address the critical challenge of formal verification in physical computing by constructing a structure-preserving functor from the algebraic category of RNS computations to the physical category of adiabatic evolutions in topological phases. This functor provides a formal guarantee of computational correctness. The final result is read out directly via a multi-terminal quantum Hall conductance measurement, which yields the Chern vector without any algorithmic post-processing. [...]",
  "date": "2025-10-01",
  "first_published": "2025-10-01",
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        "name": "Rowan Brad Quni-Gudzinas",
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        "description": "This work introduces a formal framework for morphological computing that resolves the longstanding reconstruction paradox in Residue Number System (RNS) arithmetic by leveraging the physics of topological quantum matter. Conventional RNS-based accelerators are bottlenecked by the serial, computationally expensive conversion of a parallel residue vector into a scalar integer via the Chinese Remainder Theorem. We dissolve this bottleneck by proposing a vectorial topological encoding scheme where the computational result is the residue vector itself, physically embodied as a vector of Chern numbers in a moiré superlattice. We address the critical challenge of formal verification in physical computing by constructing a structure-preserving functor from the algebraic category of RNS computations to the physical category of adiabatic evolutions in topological phases. This functor provides a formal guarantee of computational correctness. The final result is read out directly via a multi-terminal quantum Hall conductance measurement, which yields the Chern vector without any algorithmic post-processing. [...]",
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