Economic Autonomy of Computational Agents under Resource Constraints

A Proof-Forward Framework with Trust Geometry, Phase Thresholds, and Computability Limits

Author

Cheng Zhang Independent Researcher Email: zhangcheng@alu.uestc.edu.cn ORCID: 0009-0004-1970-1963

Abstract

We develop a rigorous mathematical theory for the economic behavior of computational agents, achieving unification across three levels: the geometric layer (trust-delay metric), the dynamical layer (mean-field games), and the topological layer (resource manifold).

Main Contributions

1. Dual-Scale Graph Limit Theory (Graphon-BS): A unified framework for both dense and sparse networks using Graphon limits and Benjamini-Schramm local weak convergence.

2. Phase Transition Theorem: Rigorous proof of critical phase transitions between geometric parameters and Nash equilibrium organizational forms, with physically calibrated estimates (r* ≈ 100 AU).

3. Chaitin Incomputable Risk Theory: Mapping contract default probabilities to the Chaitin Ω number, proving certain risk metrics are ontologically incomputable.

4. Complexity-Ambiguity Correspondence: A conjectured correspondence between logical undecidability and Knightian uncertainty.

Repository Structure

├── Economic_Autonomy_Computational_Agents.pdf      # Main paper
├── Economic_Autonomy_Computational_Agents.tex      # LaTeX source
├── Economic_Autonomy_Computational_Agents.pdf.ots  # OpenTimestamps proof
├── Economic_Autonomy_Computational_Agents.pdf.asc  # GPG signature
├── pubkey.asc                                      # Author's GPG public key
├── CHECKSUMS.txt                                   # SHA-256 checksums
├── README.md                                       # This file
└── simulations/                                    # Figures and simulation code
    ├── graphical_abstract.pdf
    ├── fig1_trajectories.pdf
    ├── fig2_theory_vs_simulation.pdf
    ├── fig3_phase_transition.pdf
    └── *.py                                        # Simulation scripts

Verification

SHA-256 Checksum

sha256sum -c CHECKSUMS.txt

Expected hash for PDF:

db851f487c77c2f1a3564e3f49fdbe29c7f92265afdcab1406b3a864d2847773

GPG Signature Verification

# Import author's public key (from keyserver)
gpg --keyserver keyserver.ubuntu.com --recv-keys 0B2FE1297A20766FEA88C1CBB9C243DFE3C3BEF5

# Or import from local file
gpg --import pubkey.asc

# Verify signature
gpg --verify Economic_Autonomy_Computational_Agents.pdf.asc Economic_Autonomy_Computational_Agents.pdf

OpenTimestamps Verification

# Install OpenTimestamps client
pip install opentimestamps-client

# Verify timestamp
ots verify Economic_Autonomy_Computational_Agents.pdf.ots

The timestamp proves this document existed on the Bitcoin blockchain at a specific time.

Citation

@misc{zhang2026economic,
  author       = {Zhang, Cheng},
  title        = {Economic Autonomy of Computational Agents under Resource
                  Constraints: A Proof-Forward Framework with Trust Geometry,
                  Phase Thresholds, and Computability Limits},
  year         = {2026},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.18447188},
  url          = {https://doi.org/10.5281/zenodo.18447188}
}

Keywords

Mean-field games, Graphon limits, Benjamini-Schramm convergence, Phase transitions, Chaitin Ω number, Computability theory, Trust geometry, Nash equilibrium, Stochastic control, Autonomous agents, Agentic economy

License

This work is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).

AI Assistance Statement

Large language models (Claude, Anthropic) were used as research assistants for: (i) LaTeX formatting and typesetting; (ii) literature search and cross-referencing; (iii) simulation code generation and debugging; (iv) error detection; (v) graphical abstract prompt design. All mathematical content, theoretical contributions, proofs, and final editorial decisions are solely the author's responsibility.

---

© 2026 Cheng Zhang. All rights reserved.