Repair as Local Optimization in Constraint Geometry
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901885346119680 |
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| author | Kemple, Kurtis |
| author_facet | Kemple, Kurtis |
| contents | <p>Repair is local optimization under irreducible geometric constraint. This paper introduces repair as a first-class process in the constraint geometry framework, proving via a Repair–Geometry Compatibility lemma that any repair operation traversing a non-integrable feasibility map incurs a strictly positive geometric overhead bounded below by the Hodge spectral gap. Two empirically distinct modes emerge — persistent local optimization (aging-like decay) and net-positive structural repair (sharp threshold) — captured by a single gating function whose sharpness classifies system regimes. The repair-augmented RG system couples maintenance load, effective dimension, and repair actuation with explicit parameter dependence. Empirical validation from 7,515 Gaia DR3 white dwarfs reveals a sharp compactness-controlled threshold at R/R_S ≈ 10³ (14.5σ, Wilcoxon p = 4.3 × 10⁻⁸⁴), with a monotonic gradient from +345 Myr median excess in the ultra-massive 500–700 bin (using relativistic ONe-core tracks) through +108 Myr at 700–900 to null above R/R_S ≈ 1300, yielding η_crit = 0.46 and total overhead c = 0.292.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18602871 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Repair as Local Optimization in Constraint Geometry Kemple, Kurtis repair local optimization constraint geometry RG flow dissipation maintenance overhead dimensional flow aging structural recovery curl <p>Repair is local optimization under irreducible geometric constraint. This paper introduces repair as a first-class process in the constraint geometry framework, proving via a Repair–Geometry Compatibility lemma that any repair operation traversing a non-integrable feasibility map incurs a strictly positive geometric overhead bounded below by the Hodge spectral gap. Two empirically distinct modes emerge — persistent local optimization (aging-like decay) and net-positive structural repair (sharp threshold) — captured by a single gating function whose sharpness classifies system regimes. The repair-augmented RG system couples maintenance load, effective dimension, and repair actuation with explicit parameter dependence. Empirical validation from 7,515 Gaia DR3 white dwarfs reveals a sharp compactness-controlled threshold at R/R_S ≈ 10³ (14.5σ, Wilcoxon p = 4.3 × 10⁻⁸⁴), with a monotonic gradient from +345 Myr median excess in the ultra-massive 500–700 bin (using relativistic ONe-core tracks) through +108 Myr at 700–900 to null above R/R_S ≈ 1300, yielding η_crit = 0.46 and total overhead c = 0.292.</p> |
| title | Repair as Local Optimization in Constraint Geometry |
| topic | repair local optimization constraint geometry RG flow dissipation maintenance overhead dimensional flow aging structural recovery curl |
| url | https://doi.org/10.5281/zenodo.18602871 |