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| Автор: | |
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| Формат: | Recurso digital |
| Мова: | Англійська |
| Опубліковано: |
Zenodo
2025
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| Предмети: | |
| Онлайн доступ: | https://doi.org/10.5281/zenodo.17023749 |
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Зміст:
- <p>This record contains two companion papers — <em>The Calculus of Time Modes I: Involutive Algebra, Dynamics, and Boundary Invariance</em> and <em>The Calculus of Time Modes II: Involutive Algebra, J-Unitary, and Lorentz Analogy</em>. Together they extend the Time-Field Framework into a six-dimensional algebra of temporal modes and their complementary negations.</p> <p>In Part I, three involutive operators — negation, entropic orientation, and cosmic flip — generate a Klein four group, reframing quantum collapse, Loschmidt irreversibility, and relativistic singularities as algebraic residues rather than theoretical failures. The Boundary Encoding Law (BEL) is formalized as a quadratic invariant with floor <span><span>Δinfo≥ακ2</span></span>, embedding paradoxes into a universal information bound.</p> <p>In Part II, the calculus is completed with dual unitary structures: ordinary unitarity preserves quantum probabilities, while J-unitarity preserves paradox pairings under the cosmic flip. The pseudo-unitarity group <span><span>U(3,3)</span></span> emerges as a Lorentz-style invariance principle in mode space, preserving paradox intervals in direct analogy to how <span><span>O(1,3)</span></span>preserves spacetime intervals. Non-commuting connections introduce curvature, modeling horizons as finite residues regulated by the BEL floor.</p> <p>Together, these works provide a predictive algebraic scaffold unifying paradoxes across quantum mechanics, thermodynamics, and relativity while embedding consistently into the broader time-field ontology. Falsifiable predictions include:</p> <ul> <li> <p>CMB damping ≤ 0.01% (CMB-S4, 2027),</p> </li> <li> <p>Hubble tension relief 7–9% via void growth (Euclid, 2026),</p> </li> <li> <p>Proton decay lifetimes ~10³⁸–10³⁹ yr (Hyper-Kamiokande, 2035),</p> </li> <li> <p>Laboratory demonstrations of chirality-driven quantum error correction fidelity boosts (12–25%).</p> </li> </ul> <p>By elevating paradoxes to algebraic residues, the Calculus of Time Modes closes the structural loop of the time-first ontology, offering a minimal, falsifiable extension to unification programs.</p>