To Throw a Stone with Six Birds: On Agents and Agenthood

To Throw a Stone with Six Birds: On Agents and Agenthood is a reproducible, audit-backed research artifact that defines and demonstrates agenthood and agency within the Six Birds Theory (SBT) framework. In SBT terms, a theory is an induced layer/closure; this paper argues that an agent is not the layer itself, but a theory object: a maintained, packaged subsystem inside the layer with a ledger-gated interface whose interventions make stable counterfactual differences in the outside world. This deposit contains the complete paper source, the full experimental code used to generate all figures/tables, and audited result artifacts. The implementation is intentionally minimal and exact (finite-state kernels) to keep the claims checkable and robust under refactoring. What’s included Paper source (LaTeX) and build scripts for the PDF. Finite-state kernel / channel / empowerment utilities, including exact channel capacity via Blahut–Arimoto. Viability kernel computation (controlled-invariance, robust successor-support semantics). A toy “ring-world” substrate with primitive toggles corresponding to SBT mechanisms (maintenance/repair, constraints, protocol holonomy, staged identity, operator rewrite/learning). Evidence suite + guardrails: Packaging/objecthood: an empirical packaging endomap and idempotence defect (shows repair collapses defect under a coarse lens). Difference-making: feasible empowerment as an operational proxy for within-layer causal leverage. Null regimes: single-action empowerment ≈ 0 and an exogenous-schedule trap (wrong model → spurious empowerment; correct model → ≈ 0). Protocol holonomy: empowerment diverges for horizons (H \ge 2) when protocol is enabled (with a concrete noncommutativity witness). Operator rewriting: a discrete skill variable (\theta) rewrites effective dynamics, increasing empowerment. Phase diagram: noise vs maintenance affordability shows collapse of viability and empowerment. Audited artifacts (hash-traceable configurations, manifests, and regression invariants). Optional Lean 4 formal anchor: a lightweight theorem that the finite descending iteration computes a greatest fixed point for a contracting monotone operator (used to justify the viability kernel algorithm). How to read the resultsThe paper is structured as a small set of operational definitions (kernel, feasibility/ledger, viability, packaging endomap, empowerment) followed by exhibits that isolate each mechanism with matched controls and explicit null baselines. The goal is not to “prove” intelligence or goals, but to make agenthood vs agency a typed, testable claim inside SBT’s emergence calculus. KeywordsSix Birds Theory; emergence calculus; agency; agenthood; closure; viability kernel; empowerment; channel capacity; holonomy; reproducibility; audit; finite-state kernels; maintenance and repair.