Saddle Invariants, and "Accuracy without Catastrophe": From Planck Tables to Genomic, Ecological, and Epidemiological Regimes
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| Format: | Recurso digital |
| Language: | English |
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2025
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| _version_ | 1866901755335278592 |
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| author | Samsonov |
| author_facet | Samsonov |
| contents | <p>Abstract<br>Reliable prediction under hard feasibility constraints is usually associated with microscopic quantum laws and laboratory metrology. Here, a different route is proposed: “accuracy without catastrophe” is treated as a constrained optimization problem whose natural stationary object is a saddle rather than a simple minimum, leading to a unified geometric construction of dimensionless regime steps and loop invariants on concrete measurement scenes. A Möbius‑invariant cross‑ratio of four reference points defines a scene‑dependent step that is stable under admissible rescalings, while a homothety‑limit construction turns self‑similar refinements around a saddle into loop constants with explicit error bounds. This framework is applied to physical tables (Planck spectrum, Josephson effect), to genomic and ecological scenes (ANI gaps and niche clumps and gaps), and to hospital‑based COVID‑19 monitoring, where log‑invariants of load and severity act as early regime indicators. Across these domains, the same structural logic suggests that “quantum‑like” reliability can emerge wherever constraints generate hyperbolic structure and transferable, scene‑specific invariants that can be experimentally tested and, if necessary, refuted.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17846716 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Saddle Invariants, and "Accuracy without Catastrophe": From Planck Tables to Genomic, Ecological, and Epidemiological Regimes Samsonov invariants <p>Abstract<br>Reliable prediction under hard feasibility constraints is usually associated with microscopic quantum laws and laboratory metrology. Here, a different route is proposed: “accuracy without catastrophe” is treated as a constrained optimization problem whose natural stationary object is a saddle rather than a simple minimum, leading to a unified geometric construction of dimensionless regime steps and loop invariants on concrete measurement scenes. A Möbius‑invariant cross‑ratio of four reference points defines a scene‑dependent step that is stable under admissible rescalings, while a homothety‑limit construction turns self‑similar refinements around a saddle into loop constants with explicit error bounds. This framework is applied to physical tables (Planck spectrum, Josephson effect), to genomic and ecological scenes (ANI gaps and niche clumps and gaps), and to hospital‑based COVID‑19 monitoring, where log‑invariants of load and severity act as early regime indicators. Across these domains, the same structural logic suggests that “quantum‑like” reliability can emerge wherever constraints generate hyperbolic structure and transferable, scene‑specific invariants that can be experimentally tested and, if necessary, refuted.</p> |
| title | Saddle Invariants, and "Accuracy without Catastrophe": From Planck Tables to Genomic, Ecological, and Epidemiological Regimes |
| topic | invariants |
| url | https://doi.org/10.5281/zenodo.17846716 |