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April 7, 20260 citationsOpen Access

Structural Correspondence between a 48-Element Planar Geometric Symbol System and an SM-Inspired Particle Taxonomy: A Reproducible Coordinate-Based Classification Study

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TKTakada KenEEnumiaze

Key Points

  • The study aims to explore the correspondence between a geometric symbol system and a particle taxonomy inspired by the Standard Model.
  • Conduct a geometric analysis using a 48-element symbol system.
  • Apply an automated feature-extraction pipeline based on coordinate data.
  • Utilize classifiers to match symbols with particle classification across multiple sectors.
  • A four-way arc-span classifier successfully matches 46 out of 48 symbols with 95.8% accuracy.
  • A line-type classifier accurately identifies all 19 half-arc fermionic symbols.
  • Arc orientation divides half-arc symbols into four distinct families.

Abstract

We report a reproducible geometric analysis of a 48-element planar symbol system (System-48), defined by exact coordinate data and constructed from a minimal set of primitives (circles, arcs, line segments, and dots). Using an automated feature-extraction pipeline that operates solely on coordinate data, we test whether deterministic geometric rules can recover a fixed 48-slot particle taxonomy inspired by the Standard Model (SM), spanning gauge, fermionic, scalar/neutral, and flavour-mixing sectors. The analysis reveals a highly structured and statistically significant correspondence: A four-way arc-span classifier matches the macro-sector assignment for 46/48 symbols (95.8%). A line-type classifier perfectly recovers the L/R (doublet/singlet) labels for all 19 half-arc fermionic symbols (19/19). Arc orientation completely partitions the half-arc symbols into four disjoint species-level families. An archaic subset of three symbols uniquely maps to symmetry-breaking-related slots (Higgs/neutral, CKM mixing, and CP-phase). Furthermore, the two residual exceptions (labelled 'e' and 'tsu') are shown to admit constrained, logically consistent identifications within the reference scheme (a right-handed up-type slot and a diagonal SU(3) generator, respectively). This paper does not claim a derivation of the Standard Model from first principles, nor does it assert historical origins. Rather, it establishes a rigorously defined, fully reproducible structural correspondence that warrants further mathematical and physical investigation.

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Cite This Study

Ken et al. (2026) studied this question.

synapsesocial.com/papers/69d49fe5b33cc4c35a22857bhttps://doi.org/10.5281/zenodo.19425770
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