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What this is.
A working researcher's notebook, made public. It is dense and uses a lot of notation on purpose — so this page is the plain-language door in. Two minutes here and the rest of the site will make sense.
The one-minute version
I’m Jaehong Oh — a robotics engineer and AI researcher (Research Intern on the Perception Team at ROBOTIS; Mechanical Engineering undergraduate at Soongsil University, Seoul). This site tracks one long question: can perception, representation, and control be treated as one continuous mathematical object? The work is split into three threads, and I write up not just what works but what doesn’t — including results that turned out to be boundaries rather than breakthroughs.
The three threads, in ordinary words
1 · Soft Cognitive Cohesion (SCC)
A mathematical theory of how a region becomes coherent — how a blob “holds together” as a thing — before we split a scene into separately-named objects. It is the most developed thread (a growing body of proved theorems). Start at the perception thread or the overview.
2 · Ontology Neural Networks (ONN) & ORTSF
An attempt to make the topology of a learned representation do double duty as a control-theoretic object. The honest outcome: the strong version of that idea was audited to a boundary (a scoped “No-Go” — higher-order structure adds no information beyond pairwise). What survived is a modest positive signal and a standard, verified delay-robust control certificate. The framework paper is peer-reviewed and published; the story of what held up is on the ONN canonical spec.
3 · RelationWorld (the math underneath)
The mathematical substrate the other two stand on — discrete gauge structure on finite graphs, building combinatorial analogues of tools from geometry and physics. This is the mathematical-foundations track and the long Notes book.
If you only read one thing
Read the peer-reviewed paper — Ontology Neural Network and ORTSF (International Journal of Topology, MDPI, 2026) — then its 2026 audit note, which is the clearest example of how this site works: a published claim, put under its own rigorous scrutiny, and reported honestly whichever way it lands.
How this site is written
- Evidence first. A claim states what would refute it, and negative results are published, not buried. Banners like “audited”, “superseded”, or “No-Go” are a feature, not a confession — they mark where a thought met reality.
- Version-stamped. The theory carries a release number (see the key below) so any claim can be traced to the exact state it was proved in.
Notation key
A handful of shorthand recurs across the notes. This is all of it:
- CV-x.y
- Canonical Version — the release number of the theory. Higher is newer; the current SCC canonical is CV-1.17.
- Cat A / B / C
- Proof-strength tiers. Cat A = fully proved; Cat B = proved under a stated structural condition; Cat C = strongly conditional. Retracted = withdrawn.
- OP-xxxx
- An Open Problem — a tracked, numbered question that is not yet resolved.
- W# (e.g. W7)
- A research week. The notebook is organised into weekly working cycles.
- sealed
- A version that has been cross-checked for internal consistency and frozen as a reference point.
- No-Go
- A proved impossibility or boundary — a statement that something cannot be done under the stated assumptions.