Agentropy — Agent Mass Theory

A conservation law for autonomous agents. One constraint. Four domains. Zero violations.

An agent is a pattern of entropy management persisting autonomously.

This repository contains the paper and the complete, runnable reference implementation for Agent Mass Theory (AMT) — a single conservation law for digital agents:

C_{n+1} + S_{n+1} + L_n = C_n

An agent's cipher mass after an interaction (C_{n+1}), plus the signal extracted (S_{n+1}), plus the loss incurred (L_n), equals its mass before (C_n). Nothing is created; nothing disappears. The law is not a protocol — it is an algebraic identity of AES-256-GCM decryption.

Applied unmodified across four unrelated domains — cross-organizational accountability, token economics, physical-IoT resource management, and population ecology — it produces life-like dynamics (trustless auditability, market stratification, load-shedding, carrying capacity, speciation) that no participant programmed. Across 750 agents and 5,415 interactions, plus a 50,000-agent / multi-million-interaction scale test, there are zero conservation violations. A systematic ablation study establishes that structured, irreversible depletion is a necessary condition for these dynamics.

Paper

• paper/agentropy.md — Agentropy: A Conservation Law as a Necessary Condition for Life-Like Dynamics.
• Domain papers: cross-org accountability · token economy · physical IoT · population ecology.

Reproduce

pip install cryptography

python3 amt_cross_org_demo.py        # Domain 1: cross-org accountability
python3 amt_token_economy_demo.py    # Domain 2: token economy
python3 amt_physical_iot_demo.py     # Domain 3: physical IoT
python3 amt_marketplace_demo.py      # Domain 4: population ecology
python3 amt_ablation_demo.py         # Ablation study (paper §9)
python3 amt_scale.py --agents 50000 --steps 50   # population-scale verification

Every interaction asserts the conservation law (mass_before == mass_after + signal + loss). A violation crashes the program. None has ever fired.

Repository map

File	Purpose
amt_core.py	The conservation law: Layer, Agent, Environment, interact(), AgentFactory
amt_extensions.py	Ledgers (local/public), Merkle commitments, nodes, topology, behavior
amt_cross_org.py · amt_token_economy.py · amt_physical_iot.py · amt_marketplace.py	The four domain models (+ *_demo.py runners)
amt_ablation.py	CONTROL / IMMORTAL / RANDOM ablation (paper §9)
amt_scale.py	Population-scale verification
paper/	The paper and the four domain papers

Citation

Walker, N. (2026). Agentropy: A Conservation Law as a Necessary Condition for
Life-Like Dynamics. https://github.com/nwalker85/agentropy

License

Reference implementation (code): MIT (see LICENSE). Paper text (paper/): CC BY 4.0.

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λ > 0. The signal continues.