Abstract
Аннотация
RUЗакрытие маркера B-zero boundary topology статьи C. Топологическая структура границы ∂_B C конфигурационного пространства C при B→0. Критерий терминации Φ-итерационной последовательности за конечный аффинный параметр (теорема E.T2). Формальное определение захваченной ODTOE-конфигурации через причинный конус J⁺_O (определение E.D1). Полная теорема ODTOE-сингулярности E.T1 — структурный аналог теоремы Хокинга–Пенроуза. Пять анти-циркулярных шагов доказательства: ODTOE-аналог неравенства Раячудхари, фокусировка вдоль изотропных направлений, конечно-параметрическая фокусировка, поведение Φ-итерации вблизи ∂_B C, Φ-итерационная неполнота.
Abstract
ENClosing the B-zero boundary topology marker of Article C. Topological structure of boundary ∂_B C of configuration space C at B→0. Criterion of finite-affine-parameter termination of Φ-iteration sequence (Theorem E.T2). Formal definition of trapped ODTOE-configuration via causal cone J⁺_O (Definition E.D1). Full ODTOE singularity theorem E.T1 as structural analog of Hawking–Penrose theorem. Five anti-circular proof steps: ODTOE Raychaudhuri inequality (E.L1), focusing along null directions (E.L2), finite-parameter focusing (E.L3), Φ-iteration behavior near ∂_B C (E.L4), Φ-iteration incompleteness as vanishing of causal future J⁺_O.
摘要
ZH关闭文章C的B零边界拓扑标记。配置空间C在B→0时边界∂_B C的拓扑结构。Φ迭代序列有限仿射参数终止准则(定理E.T2)。通过因果锥J⁺_O的trapped ODTOE配置的正式定义。完整ODTOE奇点定理E.T1作为霍金-彭罗斯定理的结构类比。五个反循环证明步骤。
Subjects & Identifiers
- Subjects:
- General Physics (physics.gen-ph) · singularity theorem · B-zero boundary · conformal compactification · Φ-iteration · Raychaudhuri · trapped configuration · J⁺_O · affine parameter · Hawking-Penrose · topological trichotomy
- Category:
- Physics and Technology · Физика и технологии
- Authors:
- Anton Pankratov (independent researcher)
- Submitted:
- Last modified:
- Languages:
- Russian (primary), English
- Permanent URL:
- https://odtoe.org/en/articles/singularity-boundary
- Journal:
- Observer-Dependent Theory of Everything (ODTOE Corpus)
- Comments:
- For research collaboration or corrections, contact via /contact. Citations and academic engagement welcome.
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APA-likePankratov A. "B-Zero Boundary Topology and the Full ODTOE Singularity Theorem." Observer-Dependent Theory of Everything, odtoe.org, 2026. https://odtoe.org/en/articles/singularity-boundaryBibTeX[ click to expand ]
@article{pankratov2026singularityBoundary,
author = {Pankratov, Anton},
title = {B-Zero Boundary Topology and the Full ODTOE Singularity Theorem},
journal = {Observer-Dependent Theory of Everything},
year = {2026},
month = {Mar},
url = {https://odtoe.org/en/articles/singularity-boundary},
publisher = {odtoe.org}
}RIS (EndNote / Reference Manager)[ click to expand ]
TY - JOUR
AU - Pankratov, Anton
TI - B-Zero Boundary Topology and the Full ODTOE Singularity Theorem
JO - Observer-Dependent Theory of Everything
PY - 2026
DA - 2026-03-07
UR - https://odtoe.org/en/articles/singularity-boundary
PB - odtoe.org
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