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| Format: | Recurso digital |
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Zenodo
2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.19276727 |
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Inhaltsangabe:
- <p><span>Eckmann & Tlusty (2025) proved that random walks in rotation spaces SO(3)</span><span><span> </span>almost never return to their starting point in a single traversal, but return </span><span>with positive probability when the trajectory is doubled and scaled by an</span><span><span> </span>optimal factor λ*. We show that this purely mathematical property has direct</span><span><span> </span>application to ecological regime shifts, agricultural intervention planning,</span><span><span> </span>and sustainability portfolio analysis.</span></p> <p><span>We map ecological system states to elements of the product group G = SO(3) × </span><span>R⁺ⁿ × Tᵐ, where SO(3) encodes microbial community orientation, R⁺ⁿ encodes</span><span><span> </span>nutrient concentrations, and Tᵐ encodes seasonal cycles. Under this mapping, </span><span>the optimal scaling factor λ* acquires a concrete interpretation as</span><span><span> </span>intervention dosage — the intensity of management action required to return a</span><span><span> </span>degraded system to a regenerative trajectory.</span></p> <p><span>We present three contributions: (1) a lambda-as-dosage interpretation yielding</span><span><span> </span>three ecologically distinct regimes (resilient, proportional, catalytic); (2)</span><span><span> </span>a five-pillar verification cascade derived from SE(3) structure and</span><span><span> </span>independently rediscovered from the physics side, providing convergent</span><span><span> </span>validation; and (3) a portfolio lambda-distribution that characterises</span><span><span> </span>multi-site intervention profiles and provides a physics-grounded alternative</span><span><span> </span>to qualitative ESG scoring. We demonstrate the framework using production code </span><span>(6,004 lines of C physics solvers, TypeScript verification layer) deployed</span><span><span> </span>for agricultural soil assessment in Australia's Murray-Darling Basin.</span></p> <p><span>Companion paper: "The Neo-Kardashev Scale" (Nicke 2026, DOI: </span><span>10.5281/zenodo.19270806).</span></p>