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Jaehong Oh

χPublished · 2026· International Journal of Topology (MDPI), 3(2), 9

Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control

Jaehong Oh

383 words1 min read

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Abstract

The advancement of autonomous robotic systems has led to significant capabilities in perception, localization, mapping, and control, yet a critical challenge remains in representing and preserving relational semantics, contextual reasoning, and cognitive transparency essential for collaboration in dynamic, human-centric environments. This paper introduces a unified architecture comprising the Ontology Neural Network (ONN) and the Ontological Real-Time Semantic Fabric (ORTSF) to address this challenge. The ONN formalizes relational semantic reasoning as a dynamic topological process by embedding Forman–Ricci curvature, persistent homology, and semantic tensor structures within a unified loss formulation, aiming to maintain relational integrity as scenes evolve. Building upon ONN, the ORTSF transforms reasoning traces into actionable control commands while compensating for system delays through predictive operators designed to preserve phase margins. Theoretical analysis and extensive simulations demonstrate that ORTSF maintains designed phase margins, offering advantages over classical delay compensation methods. Empirical studies indicate the framework's effectiveness in unifying semantic cognition and robust control, providing a mathematically principled solution for cognitive robotics.

Update (2026-07-10). This is the paper of record for the original ONN + ORTSF framing. Its central higher-order thesis was subsequently audited to a scoped No-Go / identifiability boundary — measured higher-order / cohomological structure adds no information beyond pairwise — and the strong control claims reduce to a standard delay-margin certificate (the microsecond bounds and cohomological-Lyapunov language are not regenerable from the research code). See the current ONN status and canonical spec. The publication facts below are unchanged.

Publication

Published in the International Journal of Topology (MDPI, ISSN 2813-9542), 3(2), 9 — open access under CC BY. Received 20 December 2025; revised 9 February 2026; accepted 3 April 2026; published 12 May 2026. Academic editors: Michel Planat and Edward A. Rietman.

At a glance

The paper's original central claim was that the topology of the representation space is itself a control-theoretic object — that delay-robustness could be stated in terms of cohomological invariants of the learned ontology, with the ORTSF operators exploiting that structure. Subsequent audit did not sustain this in its strong form (see the update above): the delay margin is a standard plant-pole phase-margin result, decoupled from the ontology's cohomology.

Contributions

  • ONN architecture. A neural model whose latent state inherits the type structure of a target ontology rather than being a flat vector. Forman–Ricci curvature, persistent homology, and semantic tensor structures are folded into a unified loss so that relational integrity is preserved as scenes evolve (Theorems 1, 2, 5, 7).
  • ORTSF operators. A composition of predictive and compensating operators that transform the ONN's reasoning trace into delay-robust control commands, preserving closed-loop phase margin (Theorems 3, 4, 6).
  • Unified seven-theorem framework. Convergence, uniqueness, tracking, delay stability, constraint handling, and contextual adaptation guarantees, tied together by Theorem 8.
  • Empirical validation. Theoretical analysis plus extensive simulations confirming that ORTSF maintains designed phase margins and outperforms classical delay-compensation baselines on topologically-conditioned tasks.

Keywords

ontology neural network · semantic fabric · topological reasoning · delay-robust control · cognitive robotics

Where this sits in the broader programme

This paper is the first formal statement of the ONN + ORTSF framework. It sits downstream of the RelationWorld mathematical foundations (see the notes) and upstream of the cognitive-robotics work on collaborative manipulation. Related recent manuscripts include Constructive Lyapunov Functions via Topology-Preserving Neural Networks and Advanced Topology-Preserving Neural Networks, both listed in the papers index.

BibTeX

@article{oh2026ontology,
  author    = {Oh, Jaehong},
  title     = {Ontology Neural Network and {ORTSF}: A Framework for Topological Reasoning and Delay-Robust Control},
  journal   = {International Journal of Topology},
  volume    = {3},
  number    = {2},
  pages     = {9},
  year      = {2026},
  publisher = {MDPI},
  doi       = {10.3390/ijt3020009},
  url       = {https://www.mdpi.com/2813-9542/3/2/9}
}