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May 26, 20260 citationsOpen Access

Discrete Holonomy Phase Spectrum (Intrinsic Sector)

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CHCraig Edwin Holdway

Key Points

  • This research aims to differentiate between intrinsic holonomy and observable phase structures within a quantum transport framework.
  • Developed a discrete holonomy-layer interpretation within reduced Q5 transport architecture.
  • Identified an internal holonomy sector with specific rotational residues.
  • Modeled observable phase structure using a first-order decomposition including intrinsic and symmetric contributions.
  • Establishes a distinct internal holonomy phase structure with \\Delta\Omega_{hol} in \\{0,\\frac{\pi}{2},\pi,\\frac{3\pi}{2}\\}.
  • Demonstrates that observable effective phase structure is not solely defined by intrinsic holonomy contributions.
  • Proposes a hidden discrete phase layer that is embedded within a continuous effective observable geometry.

Abstract

T66 develops a discrete holonomy-layer interpretation within the reduced Q5 transport architecture while explicitly separating intrinsic transport structure from observable effective phase structure. The theorem identifies an internal holonomy sector with quarter-turn rotational residue, \₇₎₋\0, {2, , 32\}, an intrinsic \ (Z₄\) -type phase structure associated with the mediated rotational generator algebra. However, the theorem further shows that the observable effective phase operator is not identical to the intrinsic holonomy contribution alone. Instead, observable phase structure is modelled through a first-order decomposition of the form\₎₁ₒ₇₎₋+ₒₘ₌, the symmetric contribution smooths the observable phase geometry into an effectively continuous structure. T66 is structurally important because it resolves a potentially fatal overprediction problem in the earlier framework. Without the distinction between intrinsic and observable phase sectors, the architecture would incorrectly predict directly observable discrete quantum phase quantization. The theorem instead establishes that discrete holonomy survives as an internal transport-layer structure while observable interference behaviour remains effectively continuous after mediated reduction and symmetric-sector averaging. The theorem, therefore, introduces the concept of a hidden discrete phase layer embedded within a continuous effective observable geometry. Status: solid for the intrinsic holonomy-sector decomposition and the distinction between internal and observable phase structure under the stated operator assumptions; conditional on the first-order decomposition framework and mediated observable reduction model; speculative for any physical claim regarding hidden discrete phase layers in actual quantum systems.

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Cite This Study

Craig Edwin Holdway (2026) studied this question.

synapsesocial.com/papers/6a153a88b5d9c58d83e8d15bhttps://doi.org/10.5281/zenodo.20369036
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