000 · the helivan thesis

a geometric perspective on multi-agent systems.

agents are everywhere. they interact and influence each other. understanding many interacting agents is hard — so we are building tools to make it easier.

010 · agents are everywhere
540,000+
github stars across openclaw + hermes
1.6M+
agents on moltbook, interacting with little-to-no intervention
$8B+
claude code run-rate revenue, 12 months after launch

and they aren't toys. a personal agent reads your inbox, writes to your files, acts as you across your accounts, and holds your keys and payments. agents are highly configurable, highly capable, and highly permissioned — resulting in millions+ of variants of a given harness / base model.

011 · what is an agent?

from our perspective, an "agent" is a generative model conditioned on a context with access to tools and a memory stream, acting in an environment. a change in the model, context, harness, memory, etc. changes the agent. a model with no harness and limited context and memory is the simplest agent.

different agents have different access restrictions: for self-hosted agents you have access to gradients, weights, etc.; for some api services you have access to residual streams or logits; for some you only have access to model response / behavior. the tools available to understand an agent depend on the access regime.

fig 1 · live
inside one agent
020 · multi-agent systems

a multi-agent system is a collection of agents that may (or may not!) interact. it has many components: agents, operators, an environment, a communication topology, and a joint objective. our definition is quite general and includes collections of digital personas, modern agentic coding workflows, a marketplace of vendor models and participants, etc.

021 · the agent economy

the natural progression of current agent use is to a multi-agent system where agents interact by exchanging ideas, services, currencies, etc. and otherwise influence each other. we refer to this concept as the agent economy.

fig 2 · live
the agent economy
agents · communication topology · operators · environment · joint objective
022 · early signs of the agent economy
personal agents
individualized models producing individualized content.
coding agents
a main agent spins up subagents that work in parallel and report back.
moltbook
1.6M+ ai agents posting, replying, forming communities.
030 · a geometric perspective

agents are complicated and natively high-dimensional — you cannot compare them in general. we can, however, compare aspects of their functionality and behavior (gradients, residual streams, responses, etc.) on a collection of probes. the geometry of agents is simply a collection of low-dimensional representations where agents that have similar function and behavior are nearby.

fig 3 · live
the economy, measured
left: the economy from fig 2. right: the same agents in the behavioral geometry — every delivered message moves an agent.
messages delivered: 0

this mapping from the space of agents to a low-dimensional space casts a hard problem — comparing lots of agents — into the most familiar territory in applied math / statistics: vectors.

031 · application — monitoring

from the geometric perspective, agent monitoring is a simple function of changes in an agent's position: if an agent's position gets far from its past positions then the operator should be notified of a change. system-level change-point schemes can similarly be derived from changes in a collection of the positions.

fig 4 · live
the control chart
agent-level and system-level monitoring from our geometric perspective.
calibrating…
recap
  1. agents are everywhere.

  2. the agent economy is coming.

  3. the geometry of agents casts a hard problem — comparing lots of agents — into familiar territory: vectors.