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

Abstract

Six Birds Theory (SBT) treats macroscopic objects as induced closures rather than primitives. Empirical discussions of agency often conflate persistence (being an object) with control (making a counterfactual difference), which makes agency claims difficult to test and easy to spoof. We give a type-correct account of agency within SBT: a theory induces a layer with an explicit interface and ledgered constraints; an agent is a maintained theory object whose feasible interface policies can steer outside futures while remaining viable. We operationalize this contract in finite controlled systems using four checkable components: ledger-gated feasibility, a robust viability kernel computed as a greatest fixed point under successor-support semantics, feasible empowerment (channel capacity) as a proxy for difference-making, and an empirical packaging map whose idempotence defect quantifies objecthood under coarse observation. In a minimal ring-world with toggles for repair, protocol holonomy, identity staging, and operator rewriting, matched-control ablations yield four separations: calibrated null regimes with single actions show zero empowerment and block model-misspecification false positives; enabling repair collapses the idempotence defect; protocols increase empowerment only at horizons of two or more steps; and learning to rewrite operators monotonically increases median empowerment (0.73 to 1.34 bits). These results provide hash-traceable tests that separate agenthood from agency without making claims about goals, consciousness, or biological organisms, and they are accompanied by reproducible, audited artifacts.

Figures (4)

• Figure 1: Packaging stability requires maintenance. Idempotence defect $\mathrm{Def}(E)$ of the empirical endomap $E$ under the macro lens $\pi(y,u,\phi,r,\dots)=(y,r,\phi)$ that hides the damage bit $u$. Repair disabled (policy cannot reset $u$) yields maximal defect at $\tau=2$; repair enabled and used collapses defect to zero at $\tau=2$.
• Figure 2: Protocol holonomy yields horizon-dependent control. Median feasible empowerment (bits) on the viability kernel $\mathcal{K}$ as a function of horizon $H$ for protocol ON vs OFF, using output lens $f(s)=y$ (outside position). The curves coincide at $H=1$ but diverge for $H\ge 2$, as predicted by P$_3$ noncommutativity: ordered action composition creates additional reachable outside futures that are not present in the phase-independent regime.
• Figure 3: Noise--maintenance sweep (phase diagram). Top: viability kernel size $|\mathcal{K}|$ under the safe predicate $(r\ge 1)\wedge(u=0)$ and robust successor-support semantics. Bottom: median feasible empowerment (bits) on $\mathcal{K}$ at horizon $H=2$ with output lens $f(s)=y$. As noise increases and repair becomes expensive, the feasible set shrinks and the robust kernel collapses; empowerment collapses along the same boundary because difference-making requires an induced layer that can be maintained.
• Figure 4: Operator rewriting (P$_1$) increases difference-making. Median feasible empowerment (bits) at horizon $H=2$ using output lens $f(s)=y$ (outside position), grouped by discrete skill $\theta$ that reduces effective slip/noise in the ring-world kernel. Empowerment increases monotonically with $\theta$, consistent with P$_1$ as an induced law change rather than merely an internal record.