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Zenodo
2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.18149797 |
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- <p>Scope and disclaimer (read first). This document is a hypothetical conceptual addendum (“Layer D”) to a broader R^8-bank framework. It proposes an EFT-style mechanism for interpreting wave–particle duality using a bank–leaf discrete phase structure Z48→Z24 and topologically protected localized excitations. No new observational data are claimed here, and nothing in this note should be read as experimental confirmation. All statements are conditional on explicitly stated assumptions. The purpose is to make the hypothesis mathematically precise enough to be falsifiable, and to cleanly separate Hopf bifurcation (dynamical clock generation) from Hopf-type topological invariants (defect protection).</p> <p>Hypothesis in one sentence. We hypothesize that (a) the deep “bank” supports a finer discrete phase structure Z48 while (b) the observable “leaf” inherits only a coarser visibility Z24 via projection, and (c) localized excitations correspond to topologically protected defects in an effective phase-interference field whose natural pinning minima lie on the Z48 grid, whereas delocalized excitations correspond to small-amplitude linear oscillations in the same medium.</p> <p>Field content via interference. Starting from multiple underlying phase angles {Θa(x)}, we define two complex phasor sums ΨA(x)=Σa∈A wa e^{iΘa(x)} and ΨB(x)=Σb∈B vb e^{iΘb(x)} and assemble a normalized CP^1 doublet z(x)=(ΨA,ΨB)^T / sqrt(|ΨA|^2+|ΨB|^2). This yields an effective map n(x)=z†σ z ∈ S^2 and an emergent U(1) connection A=−i z†dz with curvature F=dA, supporting a Hopf charge QH=(4π^2)^{−1}∫ A∧F on domains where the normalization does not vanish. We include an explicit UV-core regularization: where |ΨA|^2+|ΨB|^2 falls below a cutoff εUV, the CP^1 description is declared UV-incomplete and the bank lattice provides the physical cutoff scale.</p> <p>Two complementary mechanisms. Mechanism 1 (pinning/mass) suppresses infrared phase wandering via a bank-dominant periodic potential Vbank(Φ)=u[1−cos(48Φ)] and a leaf term Vleaf(Φ)=v[1−cos(24Φ)] with u≫v. Mechanism 2 (defect network) manages non-perturbative topological sectors: defect cores minimize energy by pinning to Z48 minima. An observer restricted to Z24 generically sees a parity mismatch: states pinned at odd Z48 minima lie at a fixed half-step offset relative to the Z24 grid, ΔΦ=π/24. This motivates a “double-comb” residual structure (even-parity cluster at 0 and odd-parity cluster at Δ) that, in principle, can be searched for in laboratory phase-plateau time series, beyond generic telegraph noise.</p> <p>Stabilization by heavy-mode integration. To address Derrick scaling, we propose an EFT-consistent stabilizer: integrating out heavy stiffness modes (present in the bank scaffold as large eigenvalues ~3κ) can generate higher-derivative quartic-gradient terms of Skyrme type (n·∂i n×∂j n)^2/e^2, providing the short-distance repulsion needed to stabilize knotted textures. We include a derivative-expansion sketch linking 1/e^2 to g^2/mχ^2.</p> <p>Interpretation as duality and status. Within this hypothesis, “wave” behavior corresponds to delocalized linear modes, while “particle” behavior corresponds to localized topologically protected defects pinned to the finer Z48 structure but observed through Z24 projection. This note is a hypothesis generator with explicit failure modes: absence of the parity/projection fingerprint in appropriate datasets would count against the mechanism, and control-quantization artifacts must be excluded by design.</p>