Möbius–Lorentz Quotients and Null Pin Holonomy: Affine Normal Forms, Null-Displacement Loci, Mapping-Torus Topology, Pin Lifts, and Mirror-Residue Pairing
Year: 2026
Type: article
Abstract: We present a geometric research programme that re-examines two foundational questions in quantum physics from a topological perspective. Foundational Hypothesis H0 (stated as an independent, unproven assumption): the electron possesses an intrinsic internal geometry with characteristic scale ℓe. All conjectures in this programme are conditional on H0. The first question concerns the carrier of the electron’s rotational phase: while the experimentally confirmed π phase shift under 360° rotation is not in dispute, we ask whether this phase is an intrinsic property of the abstract SU(2) spinor representation or whether it may alternatively be attributed to a specific internal geometric structure of the physical electron. We conjecture (Conjecture 2.1) that a 360° rotation may constitute a complete topological event for this internal geometry, with the conventional 720° periodicity reflecting the global topology of the spinor representation rather than uniquely determining the electron’s local internal structure. The second question concerns the geometric origin of Cooper pair formation. We propose that the internal geometry of the electron provides a natural geometric descriptor of the pairing topology, complementing — without replacing — the established BCS microscopic mechanism. V2 additions: (i) H0 is explicitly stated as an independent foundational assumption, breaking the circular reasoning of V1; (ii) the characteristic scale is estimated as ℓe ≈ λC ≈ 2.4×10−12 m based on Zitterbewegung, making Falsifiability Criterion FC-1 genuinely testable; (iii) a detailed comparison with Hestenes’ geometric algebra is provided; (iv) compatibility with the ACME electron EDM bound is demonstrated; (v) compatibility with the Spin–Statistics theorem is explicitly stated; (vi) the folding map Φ is given a concrete form on the Bloch sphere; (vii) a dimensional analysis for Candidate C is provided; (viii) a logical dependency graph of all conjectures is included. The programme is designed to be falsifiable and invites mathematical verification or refutation.
Authors: Sun, Scott, Chen, Solomon
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169673367
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