Noematics is a framework for making semantic agreement, disagreement, and drift explicit in systems operating over dynamic interaction topologies.
Noematics is a systems framework for representing, updating, and interpreting meaning as a first-class, stateful structure, so that semantic agreement, disagreement, and drift remain explicit under change. It is designed for multi-agent and distributed systems where what is meant changes over time, across perspectives, and under structural drift.
Unlike conventional graph, agent, or routing frameworks, Noematics treats meaning itself—not just messages, tokens, or policies—as the core object of computation.
As a result, many systems exhibit apparent coordination or alignment while masking deep semantic divergence.
Most multi-agent and graph-based systems implicitly assume that meaning is:
- static,
- globally shared,
- or reducible to labels, embeddings, or messages.
In practice, meaning is:
- stateful (it accumulates history),
- perspectival (different agents interpret differently),
- and structurally constrained (it evolves within topologies that themselves change).
Noematics exists to make these properties explicit, inspectable, and enforceable.
Noematics is not just a graph model, agent framework, or semantic routing trick.
It introduces:
-
Noēmata as first-class entities
Structured, stateful units of meaning—not labels or metadata. -
Explicit separation of topology and interpretation
Communication structure provides constraints; interpretation provides transformation. -
Invariant-constrained evolution with explicit exposure of semantic divergence
Meaning changes over time, but within formally stated system invariants. -
Observer-relative semantics without unconstrained subjectivity
Perspectives are bounded, parameterized, and comparable. -
Dynamic topology as substrate, not controller
Structural change shapes meaning without dictating it.
At the heart of Noematics are four ideas:
-
Noema
A structured semantic unit representing what is meant by an entity or relation. -
Noematic Field
A bounded collection of noēmata evolving under shared invariants. -
Interpretation
A constrained transformation mapping structure + perspective → semantic update. -
Dynamic Topology
A mutable interaction graph that conditions, but does not replace, interpretation.
Agents in Noematics are not autonomous decision-makers; they are bounded sources of perspective used to parameterize interpretation.
Noematics is a general framework.
DyTopo-style semantic routing is provided as a reference instantiation.
Specifically, this repository includes a DyTopo-inspired reference implementation of:
DyTopo: Dynamic Topology Routing for Multi-Agent Reasoning via Semantic Matching
Lu et al., arXiv:2602.06039
In Noematics terms, DyTopo demonstrates how:
- query–key semantic matching can drive topology updates,
- interpretation can guide communication structure,
- and coordination traces can be inspected through evolving graphs.
DyTopo is one possible realization, not the limit of the framework.
Noematics enforces system-level constraints, including:
- Noēmata belong to exactly one noematic field at any instant.
- Interpretation cannot directly mutate topology.
- Structural drift must preserve declared invariants.
- Semantic updates are temporally ordered and causally traceable.
- Perspective divergence is observable, not hidden.
These properties are specified formally in the implementation plan.
The framework defines a Minimal Implementable Core to ensure that Noematics is runnable, testable, and useful without:
- learning,
- large language models,
- autonomous agents,
- or external orchestration systems.
The MIC supports:
- noema creation and mutation,
- invariant checking,
- interpretation execution,
- and topology-conditioned evolution.
Everything else is layered on top.
Built on top of the core framework, this repository includes:
- DyTopo-style semantic routing
- Dynamic topology reconstruction per round
- Multi-agent communication graphs
- Optional LLM-backed interpretation
- Interpretable coordination traces
These are examples, not requirements.
To prevent scope creep and misinterpretation:
- ❌ Not a general intelligence system
- ❌ Not a symbolic logic engine
- ❌ Not an agent policy framework
- ❌ Not an LLM orchestration toolkit
- ❌ Not a theory of consciousness
Noematics is about semantic structure under change, nothing more.
-
First Steps — Guided initial execution path — commit-order plan with phases
FIRST_STEPS.md -
Implementation Plan — Full technical specification, invariants, and MIC
implementation_plan.md -
Developer Guidelines
AGENTS.md -
License
LICENSE
The current focus is:
- specification hardening,
- reference implementation of the MIC,
- and validation of invariant-preserving evolution.
Public APIs should be considered experimental.
MIT License — use it, fork it, break it, improve it.
This repository is licensed under the MIT License.
The DyTopo paper is copyright © its authors. This implementation is independent and not affiliated with or endorsed by them.
Noematics builds on ideas introduced in the DyTopo paper.
If you use DyTopo-style routing, please cite:
@article{lu2026dytopo,
title={DyTopo: Dynamic Topology Routing for Multi-Agent Reasoning via Semantic Matching},
author={Lu, Yuxing and Hu, Yucheng and Zhao, Xukai and Cao, Jiuxin},
journal={arXiv preprint arXiv:2602.06039},
year={2026}
}