Quantization of Physical Interaction Strengths via Singular Moduli
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Quantum Physics arXiv:2512.23741 (quant-ph) [Submitted on 25 Dec 2025] Title:Quantization of Physical Interaction Strengths via Singular Moduli Authors:Prasoon Saurabh View a PDF of the paper titled Quantization of Physical Interaction Strengths via Singular Moduli, by Prasoon Saurabh View PDF HTML (experimental) Abstract:Since the 2019 redefinition of the SI units, precision metrology has sought to anchor all physical quantities to fundamental constants and integer invariants. While the optical frequency comb revolutionized timekeeping by discretizing the continuum of light into countable teeth, and the Quantum Hall Effect standardized resistance via topological invariants, a comparable standard for interaction strength remains elusive. Currently, measuring the coupling constant ($g$) between quantum systems is an estimation problem, inherently subject to drift, noise, and fabrication variance. Here, we introduce Interaction Metrology, a protocol that transforms the measurement of coupling strengths from an analog estimation into a topological counting problem. By engineering a specific class of algebraic catastrophe -- the Unimodal $X_9$ singularity -- in a driven-dissipative lattice, we prove that the system's interaction moduli are topologically forced to take discrete, quantized values, forming a "Geometric $k$-Comb." We derive the universality class of this quantization, showing that it arises from the discrepancy between the Milnor ($\mu$) and Tjurina ($\tau$) numbers of the effective potential, a strictly non-Hermitian effect forbidden in standard quantum mechanics. Finally, we provide an ab-initio blueprint for a silicon nitride implementation, demonstrating that this quantization is robust against disorder levels exceeding current foundry tolerances. This discovery establishes a universal standard for force sensing and quantum logic gates, enabling the calibration of interaction strengths with topological certainty. Comments: Subjects: Quantum Physics (quant-ph); Optics (physics.optics) MSC classes: 32S40, 58K40, 81Q70 ACM classes: J.2; G.4 Cite as: arXiv:2512.23741 [quant-ph] (or arXiv:2512.23741v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.23741 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Prasoon Saurabh [view email] [v1] Thu, 25 Dec 2025 15:54:48 UTC (3,623 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantization of Physical Interaction Strengths via Singular Moduli, by Prasoon SaurabhView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: physics physics.optics References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)