ODTOE
|
|

Information Geometry of B(O,C): Connection to Perelman's S³ Topology, KL-Identity and Archimedean Isoperimetric Defect (π−3)²

Anton Pankratov(independent)·
information geometryFisher metricKL-divergenceRicci flowPerelman theoremS3 simply-connectednessArchimedean defect(π−3)synthetic RicciLott-VillaniSturm-von Renesse

Abstract

Аннотация

RU

Когерентность ODTOE B(O,C) и observer-correlator метрика рассматриваются на едином статистическом многообразии. Три результата: (i) −logB = D_KL(p_θ||p*) как точное тождество; (ii) метрика Фишера совпадает с формулой F1; (iii) Архимедов изопериметрический дефект (π−3)² как PL-инвариант. Прямое доказательство односвязности страты бутстрэп-замыкания через цепь Банаха.

Abstract

EN

Places ODTOE coherence B(O,C) and observer-correlator metric on a single statistical manifold. Three results: (i) −logB = D_KL(p_θ||p*) as exact identity; (ii) Fisher metric coincides with observer-correlator formula F1; (iii) Archimedean isoperimetric defect (π−3)² as PL-invariant. Direct proof of simply-connectedness of the bootstrap-closure stratum via Banach chain.

摘要

ZH

将ODTOE相干性B(O,C)和观察者-相关器度量置于单一统计流形上。三个结果：(i) −logB = D_KL(p_θ||p*)作为精确恒等式；(ii) Fisher度量与observer-correlator公式F1一致；(iii) 阿基米德等周缺陷(π−3)²作为PL不变量。

Download PDF (RU)Download PDF (EN)

Subjects & Identifiers

Subjects:
Mathematical Physics (math-ph) · information geometry · Fisher metric · KL-divergence · Ricci flow · Perelman theorem · S3 simply-connectedness · Archimedean defect · (π−3) · synthetic Ricci · Lott-Villani · Sturm-von Renesse
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/perelman-information-geometry
Journal:
Observer-Dependent Theory of Everything (ODTOE Corpus)
Comments:
For research collaboration or corrections, contact via /contact. Citations and academic engagement welcome.

Cite this article

Select the text below to copy citations in your preferred format.

Plain text

APA-like
Pankratov A. "Information Geometry of B(O,C): Connection to Perelman's S³ Topology, KL-Identity and Archimedean Isoperimetric Defect (π−3)²." Observer-Dependent Theory of Everything, odtoe.org, 2026. https://odtoe.org/en/articles/perelman-information-geometry
BibTeX[ click to expand ]
@article{pankratov2026perelmanInformationGeometry,
  author    = {Pankratov, Anton},
  title     = {Information Geometry of B(O,C): Connection to Perelman's S³ Topology, KL-Identity and Archimedean Isoperimetric Defect (π−3)²},
  journal   = {Observer-Dependent Theory of Everything},
  year      = {2026},
  month     = {Mar},
  url       = {https://odtoe.org/en/articles/perelman-information-geometry},
  publisher = {odtoe.org}
}
RIS (EndNote / Reference Manager)[ click to expand ]
TY  - JOUR
AU  - Pankratov, Anton
TI  - Information Geometry of B(O,C): Connection to Perelman's S³ Topology, KL-Identity and Archimedean Isoperimetric Defect (π−3)²
JO  - Observer-Dependent Theory of Everything
PY  - 2026
DA  - 2026-03-05
UR  - https://odtoe.org/en/articles/perelman-information-geometry
PB  - odtoe.org
ER  -
Information Geometry of B(O,C): Connection to Perelman's S³ Topology, KL-Identity and Archimedean Isoperimetric Defect (π−3)²

Related Articles

Observer-Dependent Theory of Everything (ODTOE)

Formal metatheory of reality based on the observer principle. One axiom: observer constitutes the observed. Six postulates with mathematical formalization.

ODTOE - Simple Guide

Introduction to the theory for beginners without complex mathematics. Central formula R=O(Psi), three participants, belief as measurable quantity.

Modern Physical Theories as Configurations within ODTOE

Unified map of physics: QM, GR, string theory, LQG, QBism as configurations in field H. Periodic table of theories organized by coherence S and observer dimensionality d.

All articles in “Foundations of Theory”