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A Deformed Non-Commutative Framework for Variable-Order (p(t),q(t))-Spacetime Manifolds and the Resolution of the Modified Noether Identity |
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PP: 1-5 |
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doi:10.18576/qpl/150101
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Author(s) |
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Akwaboah Vincent,
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Abstract |
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| This work introduces a new mathematical framework based on variable-order post-quantum calculus defined over an arbitrary non-commutative time-scale manifold. Standard quantum calculus, q-calculus, and its two-parameter extension (p,q)-calculus inherently break the classical Leibniz rule, rendering standard conservation laws invalid.
This paper resolves the resulting conservation crisis by constructing a Generalized Non-Commutative Covariant Differential Geometry governed by dynamically shifting parameters p(t) and q(t). We prove the existence and uniqueness of these variable- order dynamic maps using fixed-point topology, and derive a closed-form expression for the manifold flux tensor, offering a novel alternative to dark energy cosmic dynamics. |
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