Exponential Coherence Boundaries in Multi-Planet Systems: Mapping 1/e and 1–1/e Shells in Cumulative Log-Period Architecture
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2025
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| _version_ | 1866901747916603392 |
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <p>We present the first systematic map of <em>multi-planet system architectures</em> in <span><strong>C-Space</strong></span>, a cumulative log-period coordinate defined by</p> <p><span>C_k = \frac{\log P_k - \log P_1}{\log P_N - \log P_1}.</span></p> <p>Using a database of 334 confirmed multi-planet systems from Kepler, TESS, and RV catalogs, we show that the distribution of planets is strongly structured, revealing two statistically significant coherence boundaries at</p> <p><span>C_{\mathrm{inner}} \approx \frac{1}{e} \quad\text{and}\quad C_{\mathrm{outer}} \approx 1 - \frac{1}{e}.</span></p> <p>These boundaries partition systems into four Coherence-Island classes: <span><strong>Interior-Island</strong></span>, <span><strong>Inner-Shell</strong></span>, <span><strong>Outer-Shell</strong></span>, and <span><strong>Exterior</strong></span>.</p> <p> </p> <p>Comparison to a log-uniform null model demonstrates <span><strong>excess clustering at the 1/e boundary (+3.9σ)</strong></span>, establishing it as a robust architectural attractor. We also introduce the <span><strong>RTLI Coherence Index</strong></span>, showing that the highest-coherence systems (e.g., TRAPPIST-1, KOI-351, HD 110067) predominantly occupy the <span><strong>Exterior zone</strong></span>, while the most habitability-relevant systems (Kepler-80, K2-138, HD 191939) lie within the <span><strong>Interior-Island</strong></span>, consistent with long-term orbital stability.</p> <p> </p> <p>Together, RTLI and C-Space form a unified framework for identifying structural anomalies, mapping planetary architectures, and prioritizing systems for technosignature and biosignature searches.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18027325 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Exponential Coherence Boundaries in Multi-Planet Systems: Mapping 1/e and 1–1/e Shells in Cumulative Log-Period Architecture De Jesus, Elias • Exoplanets • Orbital Architecture • Resonant Chains • RTLI (Relational Threshold & Latent Interaction) • Cumulative Log-Period Coordinate (C-Space) • Coherence Islands • Planetary System Stability • Multi-planet Systems • Kepler Mission • TESS Mission Technical/Method Keywords • Log-Period Ratios • Orbital Coherence • Dynamical Packing • Resonant Migration • Statistical Architecture Mapping • Period-Ratio Distribution • Data-Driven Exoplanet Classification • 1/e Boundary • Resonant Chains (e.g., TRAPPIST-1, HD 110067) <p>We present the first systematic map of <em>multi-planet system architectures</em> in <span><strong>C-Space</strong></span>, a cumulative log-period coordinate defined by</p> <p><span>C_k = \frac{\log P_k - \log P_1}{\log P_N - \log P_1}.</span></p> <p>Using a database of 334 confirmed multi-planet systems from Kepler, TESS, and RV catalogs, we show that the distribution of planets is strongly structured, revealing two statistically significant coherence boundaries at</p> <p><span>C_{\mathrm{inner}} \approx \frac{1}{e} \quad\text{and}\quad C_{\mathrm{outer}} \approx 1 - \frac{1}{e}.</span></p> <p>These boundaries partition systems into four Coherence-Island classes: <span><strong>Interior-Island</strong></span>, <span><strong>Inner-Shell</strong></span>, <span><strong>Outer-Shell</strong></span>, and <span><strong>Exterior</strong></span>.</p> <p> </p> <p>Comparison to a log-uniform null model demonstrates <span><strong>excess clustering at the 1/e boundary (+3.9σ)</strong></span>, establishing it as a robust architectural attractor. We also introduce the <span><strong>RTLI Coherence Index</strong></span>, showing that the highest-coherence systems (e.g., TRAPPIST-1, KOI-351, HD 110067) predominantly occupy the <span><strong>Exterior zone</strong></span>, while the most habitability-relevant systems (Kepler-80, K2-138, HD 191939) lie within the <span><strong>Interior-Island</strong></span>, consistent with long-term orbital stability.</p> <p> </p> <p>Together, RTLI and C-Space form a unified framework for identifying structural anomalies, mapping planetary architectures, and prioritizing systems for technosignature and biosignature searches.</p> |
| title | Exponential Coherence Boundaries in Multi-Planet Systems: Mapping 1/e and 1–1/e Shells in Cumulative Log-Period Architecture |
| topic | • Exoplanets • Orbital Architecture • Resonant Chains • RTLI (Relational Threshold & Latent Interaction) • Cumulative Log-Period Coordinate (C-Space) • Coherence Islands • Planetary System Stability • Multi-planet Systems • Kepler Mission • TESS Mission Technical/Method Keywords • Log-Period Ratios • Orbital Coherence • Dynamical Packing • Resonant Migration • Statistical Architecture Mapping • Period-Ratio Distribution • Data-Driven Exoplanet Classification • 1/e Boundary • Resonant Chains (e.g., TRAPPIST-1, HD 110067) |
| url | https://doi.org/10.5281/zenodo.18027325 |