Factor Agent

What It Solves#

Multi-agent system architecture using prime factorization as the decomposition principle. Agents are structured like factors of a number — each has a distinct identity, and compositions are computed through multiplication.

Key Innovation#

Prime Factorization as Architectural Decomposition:

Just as every integer factors uniquely into primes, every agent capability factors into prime-weighted primitives. This guarantees:

Unique identity: No two agents have the same prime factor signature
Composable authority: Agent capabilities combine through multiplication, not addition
Invariant preservation: The Fundamental Theorem of Arithmetic ensures no authority is lost or duplicated

OTP Supervision as Computational Factorization#

The Elixir/OTP supervision tree implements:

Factor decomposition: Processes are organized hierarchically by prime weight
Restart strategies: Failed factors are replaced without disrupting the whole system
Message passing: Inter-agent communication respects factor boundaries

The Repair Mechanism#

When a perturbation arrives, the system computes:

$z' = z + kM, \text{ where } M = \prod_{p \in S} p$

This is identical to the CRT repair in Geometry of Conditional Logic! The same safe-corridor mathematics applies to multi-agent repair.

Architecture#

TransactionalHarness
├── Compositional Invariants
├── Prime Factor Decomposition
└── Region-Based Repair (z' = z + kM)

Agent Primitives
├── p₁: Authentication
├── p₂: Authorization
├── p₃: Computation
└── pₙ: Custom capabilities

For the full distributed runtime architecture, including Elixir/OTP process trees, Horde recovery, ScyllaDB temporal state, lag-aware probes, and FactorAgent governance, see Agentic AI as a Distributed System.

Website#

Live: sethuiyer.github.io/factor-agent

Connection to Core Vision#

Factor Agent extends the Arithmetic Manifold to multi-agent systems. Prime factorization provides:

A principled way to decompose agent capabilities
Guaranteed compositionality (multiplicative, not additive)
The same CRT-based repair mechanism as Geometry of Conditional Logic

The “factorization” of authority mirrors the “factorization” of constraints in the multiplicative PINN framework — both use the Euler product structure to ensure compositional correctness.