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May 22, 20260 citationsOpen Access

Heluo Geometry: Meta-Constraints

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CXCheng Xi

Key Points

  • This research aims to explain the foundational reasons behind key physical constants and parameters through meta-constraints and a mathematical framework.
  • Introduces the concept of meta-constraints guided by the axioms of discrete sampling geometry.
  • Analyzes pulsar glitch data to find statistically significant curvature quantization peaks.
  • Proposes a structured approach to derive major physical laws as mathematical necessities rather than free parameters.
  • Establishes that the gauge group SU(3)×SU(2)×U(1) and the fine-structure constant 1/137.03599918 arise from meta-constraints.
  • Finds pulsar glitch data showing significant peaks at {0,2,5}×10⁻⁹ (Bootstrap p < 0.05 to < 0.001), supporting curvature quantization.
  • Demonstrates that if meta-constraints are valid, they eliminate the need for anthropic explanations in physics.

Abstract

This paper is the Physical Philosophy Volume of the Heluo Geometry system. Modern physics faces a fundamental dilemma: it cannot answer the question "Why these isomorphisms rather than others? " Why is the gauge group SU (3) ×SU (2) ×U (1)? Why is the fine-structure constant 1/137. 03599918? Why can curvature take arbitrary real values? This paper introduces the concept of Meta-Constraints — physical laws themselves are constrained by a more fundamental mathematical structure. This structure is Discrete Sampling Geometry: a system based on three axioms that yields 12-partition of the sphere, the measurement function f (k) = cos (5πk/6), and the three-level quantization of Sheng-Ke curvature 0, 2, 5. This paper proves that from this structure, the gauge group, fine-structure constant, and curvature quantization values are not free parameters but mathematical necessities. In particular, pulsar glitch data from the Jodrell Bank catalogue exhibit statistically significant peaks at 0, 2, 5×10⁻⁹ (Bootstrap p < 0. 05 to < 0. 001), providing independent astrophysical evidence for curvature quantization. Meta-constraints are not "a fifth force. " They are the Zeroth Constraint — acting not on matter, but on "what kinds of physical laws matter can generate. " If meta-constraints hold, physics will no longer need the anthropic principle to explain why the universe is this way — because the universe could only be this way. Keywords: Meta-Constraints; curvature quantization 0, 2, 5; Discrete Sampling Geometry; pulsar glitch; fine-structure constant; zeroth constraint Mathematical Foundation: All geometric theorems in this paper are derived from Discrete Sampling Geometry: A Rigorous Axiomatic Reconstruction (DOI: 10. 5281/zenodo. 20301581).

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Cite This Study

Cheng Xi (2026) studied this question.

synapsesocial.com/papers/6a0ff38cd674f7c03778c380https://doi.org/10.5281/zenodo.20302981
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