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The Apple-like Manifold: A Unified Phase-Space Framework Resolving Singularities, Decoherence, Parity Non-Conservation, and Heisenberg Uncertainty via Entropic Topological Dimension

Marlin Z. Cyber, Yi Chiang Wang

Published Jul 6, 2026• 0 citations
Publisher
DOI
10.5281/zenodo.21223935

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This paper establishes a background-independent geometric determinism for quantum measurement and cosmic genesis by treating the micro-spacetime domain as a Porous Spacetime Manifold with a Planck-scale cutoff. Born's probability amplitude (|ψ|²) is redefined as a deterministic initial distribution ratio of the spacetime fluid membrane across microscopic void boundaries.Critically, this model resolves the long-standing logical breakdowns in quantum foundations: temporary energy non-conservation in time-energy uncertainty and the superluminal collapse of wave packets are geometrically explained via the manifold's non-local straddling and its subsequent surface-tension-like pull-in mechanism, without violating special relativity.Furthermore, we formulate the "initial cosmic fluctuations" as a direct 100% causal transcription of the preceding universe's cumulative entropy, transferred via quantum entanglement threads (ER bridges) across generations. This model comprehensively unifies particle localization, non-resettable causal histories, and the cosmic reincarnation cycle under a single background-independent topological framework.
This work presents a topological phase framework in which time is treated as a generated quantity arising from phase collapse rather than as a fundamental background dimension. In this model, space corresponds to a completed manifold of resolved states, while time emerges as an index of unresolved phase transitions between spatial configurations. Quantum measurement, consciousness, and computation are described as different projections of the same underlying phase-selection process. The framework introduces formal definitions for phase collapse, dual-sphere manifolds, and projection operators linking physical, computational, and cognitive domains. These structures provide a unifying basis for phase-based physics, large-scale computation, and emergent intelligence architectures. This work was developed independently and does not rely on operator-theoretic or quantum-information formalisms, instead adopting a phase-theoretic and topological perspective.
We propose a unified framework, dubbed topological word, for the complete non-Abelian bulk-boundary correspondence in multigap non-Abelian topological insulators. Composed by an ordered sequence of letters, each a non-Abelian charge depicting the gap-resolved topology, the topological word captures both the global non-Abelian topology corresponding to the homotopy classification, and the band-adjacency information. The latter, though crucial for the edge-state pattern across multiple gaps, is often overlooked in previous studies. We confirm our framework using both static models and periodically driven Floquet systems, and discuss its connection and distinction with existing descriptions, such as the phase-band singularities and braiding representations. Intriguingly, topological word continues to provide insight regarding topology and edge states, even as the global non-Abelian topology becomes ill-defined under broken parity-time symmetry.