From Microscopic Complementary Closure to Macroscopic Binary Coarse-Graining: A Quantum–Binary Multilevel Observation and Dual-Projection Hypothesis

王有福

Published Aug 28, 2026• 0 citations

Abstract

This work proposes a conceptual framework for connecting quantum closure structures, local observation, fine-grained binary records, and conventional binary coarse-graining. At the binary level, the framework introduces a structural representation distinct from ordinary ordered binary notation. The states 00, 11, and \{01,10\} are first grouped into three basic relational classes. Adding a positive/reverse distinction produces six states. Assigning one of four source labels, A, B, C, or D, to each of the two binary positions further generates 3\times2\times4\times4=96 labeled structural states. These 96 states are interpreted as a fine-grained record space rather than as 96 new conventional binary values. A separate quantum-level hypothesis is then introduced. In this candidate model, externally observed quantum values 0 and 1 are associated with complementary internal closure structures represented as 01 and 10. The labels A,B,C,D refer to four correlated positions or orientations within a single closed structure rather than to independent binary labels. Local observation of such a structure may yield source-labeled outcomes such as 0^A or 1^B. Repeated local observations generate source-labeled binary sequences, while conventional binary representation is obtained after discarding source, orientation, and positive/reverse information. The framework distinguishes microscopic structural complementarity from macroscopic statistical balance. A closed microscopic structure may be exactly complementary, while short binary observation sequences may still contain arbitrary local concentrations such as 0000 or 1111. Under symmetric and unbiased sampling conditions, long-run binary statistics may approach balance without requiring local balance at every observation step. The work also introduces a dual-projection viewpoint. The same underlying binary object can be represented through different observational rules. Conventional ordered observation yields the familiar four states 00,01,10,11, whereas relational observation yields the three classes 00, 11, and \{01,10\}, which may then be refined into the 3\rightarrow6\rightarrow96 hierarchy. These descriptions are treated as different coarse-grainings or projections of the same underlying object rather than as mutually exclusive binary systems. The 3\rightarrow6\rightarrow96 construction is presented here as a formally defined representational structure. By contrast, the proposed quantum 01/10 internal closure, the physical meaning of the A,B,C,D orientations, and any claimed quantum-to-binary correspondence remain hypotheses requiring mathematical formalization and experimental testing. Future work will focus on formal mathematical modeling, exhaustive state analysis, numerical simulation, comparison with standard quantum-mechanical predictions, falsifiable experimental protocols, and possible applications in quantum readout, feedback control, error diagnosis, and information processing. Version v0.1 is intended to establish a time-stamped record of the original hypothesis, definitions, conceptual boundaries, and research roadmap. It does not claim experimental confirmation of the proposed internal quantum structure.

DOI: 10.5281/zenodo.22142162

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