Origin of the Observer in ODTOE: Existence Theorems for the Self-Observation Fixed Point
Anton Pankratov(independent)·
fixed pointself-observation operatorSchauder theoremBanach theoremcontractionanti-circularityKAMgolden ratio
Abstract
Аннотация
RUЗакрытие «открытой задачи первого приоритета» базовой статьи ODTOE: достаточные условия существования (и единственности при сжатии) неподвижной точки Ψ*=Φ(Ψ*). Теорема Шаудера (существование без единственности) и теорема Банаха (единственность при сжатии). Явная константа сжатия q_contract(B,S). Аудит антициркулярности подтверждает, что определение Φ не предполагает Ψ*.
Abstract
ENCloses the «open task of first priority» from the base ODTOE article: sufficient conditions for existence (and uniqueness under contraction) of the fixed point Ψ*=Φ(Ψ*). Schauder theorem (existence without uniqueness) and Banach theorem (uniqueness under contraction). Explicit contraction constant q_contract(B,S). Anti-circularity audit confirms Φ definition does not presuppose Ψ*.
摘要
ZH关闭ODTOE基础文章的「首要开放任务」：不动点Ψ*=Φ(Ψ*)存在（和收缩下唯一性）的充分条件。Schauder定理和Banach定理。显式收缩常数q_contract(B,S)。
Subjects & Identifiers
- Subjects:
- Mathematical Physics (math-ph) · fixed point · self-observation operator · Schauder theorem · Banach theorem · contraction · anti-circularity · KAM · golden ratio
- Category:
- Foundations of Theory · Основы теории
- Authors:
- Anton Pankratov (independent researcher)
- Submitted:
- Last modified:
- Languages:
- Russian (primary), English
- Permanent URL:
- https://odtoe.org/en/articles/origin-of-observer
- 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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Plain text
APA-likePankratov A. "Origin of the Observer in ODTOE: Existence Theorems for the Self-Observation Fixed Point." Observer-Dependent Theory of Everything, odtoe.org, 2026. https://odtoe.org/en/articles/origin-of-observerBibTeX[ click to expand ]
@article{pankratov2026originOfObserver,
author = {Pankratov, Anton},
title = {Origin of the Observer in ODTOE: Existence Theorems for the Self-Observation Fixed Point},
journal = {Observer-Dependent Theory of Everything},
year = {2026},
month = {Feb},
url = {https://odtoe.org/en/articles/origin-of-observer},
publisher = {odtoe.org}
}RIS (EndNote / Reference Manager)[ click to expand ]
TY - JOUR
AU - Pankratov, Anton
TI - Origin of the Observer in ODTOE: Existence Theorems for the Self-Observation Fixed Point
JO - Observer-Dependent Theory of Everything
PY - 2026
DA - 2026-02-21
UR - https://odtoe.org/en/articles/origin-of-observer
PB - odtoe.org
ER - Origin of the Observer in ODTOE: Existence Theorems for the Self-Observation Fixed Point
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