محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Preprint |
| منشور في: |
2026
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://arxiv.org/abs/2605.03350 |
| الوسوم: |
إضافة وسم
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جدول المحتويات:
- This paper develops a form of finite knot theory as a diagrammatic sequel to the ideal-stratum and deformation-persistence framework for knot types. Thick representatives in bounded ropelength sublevel spaces are studied through the finite Reidemeister data visible in generic projections. For each projection direction $u$, we introduce the ropelength-filtered lifted Reidemeister graphs $\mathcal{G}^{\mathrm{lift}}_{Λ,u}(K)$, for $Λ\ge \mathrm{Rop}(K)$, recording diagram data and Reidemeister moves that lift to admissible thick deformations below the ropelength level $Λ$. Using the finite-local reconstruction theorem of Barbensi--Celoria, we define characteristic Reidemeister patterns and the finite recognition length $L_{\mathrm{char},u}(K)$, the first ropelength scale at which a finite pattern recognizing $K$, up to mirroring, appears in the lifted graph. The finite-local graph-theoretic part is unconditional; finite-dimensional and polygonal models provide controlled settings; the corresponding statements for the full $C^{1,1}$ ropelength-sublevel space are conditional on explicitly isolated projection--Cerf tameness and coherent finite-pattern thick-movie liftability hypotheses.