Paper 60S: Microscopic Derivation of Harmonic Selection in Admissibility-Gated Transport
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2026
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| author | Sarnowski, Michael |
| author_facet | Sarnowski, Michael |
| contents | <p>This paper asks whether a preferred BAO-like scale can emerge from transport rules rather than from a built-in geometric ruler. We study a minimal admissibility-gated transport model in which propagation proceeds through discrete steps, each limited by a local mismatch threshold and a finite cumulative mismatch budget. These constraints define a survivor fraction of admissible trajectories as transport depth increases. The observable contribution of a harmonic is then determined by the product of geometric engagement and admissibility-limited survival. This produces a preferred harmonic scale that follows the transport scaling relation <span><span>n⋆∼δbudget/ϵstepn_\star \sim \delta_{\text{budget}}/\epsilon_{\text{step}}</span><span><span><span><span>n</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>∼</span></span><span><span><span>δ</span><span><span><span><span><span><span><span>budget</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>ϵ</span><span><span><span><span><span><span><span>step</span></span></span></span><span></span></span></span></span></span></span></span></span>, where <span><span>δbudget\delta_{\text{budget}}</span><span><span><span><span>δ</span><span><span><span><span><span><span><span>budget</span></span></span></span><span></span></span></span></span></span></span></span></span> is the cumulative mismatch budget and <span><span>ϵstep\epsilon_{\text{step}}</span><span><span><span><span>ϵ</span><span><span><span><span><span><span><span>step</span></span></span></span><span></span></span></span></span></span></span></span></span> is the local admissible step scale. Numerical sweeps show that a finite transport regime exists in which the dominant surviving harmonic is <span><span>n⋆=3n_\star = 3</span><span><span><span><span>n</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>3</span></span></span></span>. In this framework, the BAO-like feature is not the dominant intrinsic mode of a geometric spectrum, but the dominant surviving mode of an admissibility-gated transport process. The result provides a minimal, falsifiable transport-based mechanism for the emergence of a preferred harmonic scale without assuming a pre-existing BAO ruler.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19420958 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Paper 60S: Microscopic Derivation of Harmonic Selection in Admissibility-Gated Transport Sarnowski, Michael BAO, admissibility-gated transport, harmonic selection, survivor measure, transport scaling, finite transport depth, cumulative mismatch budget, discrete transport model, Holosphere Theory, large-scale structure <p>This paper asks whether a preferred BAO-like scale can emerge from transport rules rather than from a built-in geometric ruler. We study a minimal admissibility-gated transport model in which propagation proceeds through discrete steps, each limited by a local mismatch threshold and a finite cumulative mismatch budget. These constraints define a survivor fraction of admissible trajectories as transport depth increases. The observable contribution of a harmonic is then determined by the product of geometric engagement and admissibility-limited survival. This produces a preferred harmonic scale that follows the transport scaling relation <span><span>n⋆∼δbudget/ϵstepn_\star \sim \delta_{\text{budget}}/\epsilon_{\text{step}}</span><span><span><span><span>n</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>∼</span></span><span><span><span>δ</span><span><span><span><span><span><span><span>budget</span></span></span></span><span></span></span></span></span></span><span>/</span><span><span>ϵ</span><span><span><span><span><span><span><span>step</span></span></span></span><span></span></span></span></span></span></span></span></span>, where <span><span>δbudget\delta_{\text{budget}}</span><span><span><span><span>δ</span><span><span><span><span><span><span><span>budget</span></span></span></span><span></span></span></span></span></span></span></span></span> is the cumulative mismatch budget and <span><span>ϵstep\epsilon_{\text{step}}</span><span><span><span><span>ϵ</span><span><span><span><span><span><span><span>step</span></span></span></span><span></span></span></span></span></span></span></span></span> is the local admissible step scale. Numerical sweeps show that a finite transport regime exists in which the dominant surviving harmonic is <span><span>n⋆=3n_\star = 3</span><span><span><span><span>n</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>3</span></span></span></span>. In this framework, the BAO-like feature is not the dominant intrinsic mode of a geometric spectrum, but the dominant surviving mode of an admissibility-gated transport process. The result provides a minimal, falsifiable transport-based mechanism for the emergence of a preferred harmonic scale without assuming a pre-existing BAO ruler.</p> |
| title | Paper 60S: Microscopic Derivation of Harmonic Selection in Admissibility-Gated Transport |
| topic | BAO, admissibility-gated transport, harmonic selection, survivor measure, transport scaling, finite transport depth, cumulative mismatch budget, discrete transport model, Holosphere Theory, large-scale structure |
| url | https://doi.org/10.5281/zenodo.19420958 |