What self-governance requires

A capacity belongs to an agent only when its installed organization can exercise it. A represented possibility, an experimenter's intervention and a callable operation are different things. The operating contract makes those differences explicit before any claim of self-governance is tested.

2.1 State, information and executive targets

Fix a physical realization and a finite operational envelope. The complete state contains every persistent record, working register, installed program, phase, dispatch state and remaining resource that can affect the permitted future experiment. A native operation $u$ has the joint record and successor kernel

$$K_u(x;r,x'),\qquad \sum_{r,x'}K_u(x;r,x')=1.$$(2.1)

Boundary inputs and persistent source context must be included in $x$ or explicitly conditioned upon. Leaving out information that affects later transitions would change the model being certified.

The controller sees only the observations supplied by its installed interface. Its executive information can be smaller than the catalogue of native physical records used to certify a realization. A diagnostic intervention is an additional physical operation at a named occasion. It is not a free observation available to the ordinary decision procedure.

The deterministic special case is

$$x_{t+1}=F(x_t,o_t),\qquad c_t=\pi(x_t,o_t).$$

Evaluation, competition and installation are physical parts of this update. There is no additional chooser standing outside $F$. A selected command may operate an external actuator or change an internal target such as an attentional gate, retained priority or installed rule. An actuator failure can prevent the outward effect after selection has already occurred. Assessment and installation therefore need their own tests, separate from downstream control efficacy.

The contract names admissible preparations, interventions, native actions, resources and stopping conditions. Resource units are concrete: a one-bit query, an elementary gate, a joint acquisition interval and an individual physical write have different costs. Installing another observation port or permitting an uncharged parallel read changes the theorem's comparison class.

2.2 Executable options and actual decisions

A repertoire contains policies the present architecture can invoke or synthesize within a specified resource envelope. This requires more than physical possibility. It does not require every repertoire member to occur from the same fixed complete deterministic state.

An experimenter might overwrite a register to test its causal role even when the controller cannot perform that overwrite before its deadline. The intervention demonstrates sensitivity to the overwritten value. Endogenous availability requires an installed route by which the controller can reach it.

In the finite constructions, the admitted grammar consists of explicit programs or query trees with charged costs. Active candidates are represented in the present assessment. Accessible candidates can be recruited by an installed procedure before the remaining budget expires. A larger budget may support a different capacity. Duplicating command labels does not add options when the resulting consequences are equivalent.

Definition 2.1: evaluative mediation

An assessment is evaluatively mediated under a declared contract when an installed procedure uses retained evaluative information to assess admitted alternatives, and a specified downstream disposition depends on that assessment through identified physical read and installation pathways. Agreement with an endorsement relation is checked separately from the causal effect of those pathways.

The endorsement relation states which amendments are acceptable given the retained commitments. It need not be a universal scalar utility. A scalar or lexicographic criterion suffices for the finite examples, while its physical presence establishes no moral correctness. The evaluative interpretation is supported by systematic use across candidate comparisons and fresh cases. Arbitrary influence from an internal bit would not establish that role.

Definition 2.2: bounded represented-rule self-revision

A controller has bounded represented-rule self-revision when it can, within its declared budget, assess whether to retain or change a stored rule governing later decisions, install the result, and execute that rule on fresh admitted inputs. Retention after assessment is a legitimate result. The complete physical interpreter and some metarules may remain fixed.

An operative rule has become an object of assessment. This is a minimal reflective capacity. It does not require a model of every physical transition, autobiographical knowledge, general philosophical reflection or the ability to revise every foundational commitment. Each would be an additional capacity to establish.

2.3 The evaluative role

Baseline operational agency is an installed capacity to select among consequence-distinct executable transformations through retained evaluative organization. Learned or innate action tendencies can implement it. Simulating alternative futures is one possible implementation. Reflection adds assessment of the operative rule itself.

Learning from outcomes, planning, changing priorities and modifying a search procedure extend the baseline in different ways. Possessing one does not establish all the others. This restricted-domain account also does not conflict with world-model necessity results: Richens and colleagues recover environment models from competence across a specified goal family in stationary controlled Markov environments 17. The finite evaluator here is not claimed to possess that general competence.

A retained commitment has a comparative role. Across a declared set of situations, it changes which executable outcome or rule is favored. In the editable charter, physical considerations are already represented accurately and both actions are safe. The retained commitments determine how mixed cases should be settled. Revision changes a conditional priority rather than correcting a factual prediction.

This interpretation is fixed before the experiment. Its ranking, actual use and installed consequences receive separate tests. Defining all three after seeing the result would explain nothing. A sensor update can change a prediction; an arbitrary latch can change an output; neither alone establishes the declared ranking.

A simple engineered controller can satisfy the minimal operational criterion. Describing it as a machine does not refute the certificate, just as describing an event as internal does not establish it. A persistent one-bit memory lacks the installed evaluative selection among executive targets. The finite witnesses isolate a component of self-governance without claiming the full reflective life of a person.

Assessment has no need for an infinite sequence of selectors

An assessment can take a represented rule as its object while leaving an interpreter or metarule fixed. Another admitted operation can assess some of those further structures. Requiring an autonomous prior choice of every criterion would change the target to ultimate self-creation.

The present claim is that an organized physical mechanism can assess, retain and change particular operative commitments. The preservation fixed points later in this treatment describe the continuing availability of that capacity. They do not introduce an evaluator outside physical causation.

Inward acts, inhibition and tools

An executive target can be internal. Evaluation can redirect attention, inhibit an available action or install a revised rule. Mere storage of a sensory event is insufficient. The relevant selection or gating process must govern the update.

Inhibition need not be represented as a separate explicit command or assigned a universal additional energy cost. Its causal role is what needs establishing. These are possible executive targets; the finite witnesses specifically implement rule installation and command selection.

A tool's launch and its later operation are distinct causal stages. A one-way launch can express agency without telemetry. A jam can frustrate an attempt without erasing its prior assessment. Continuous feedback supports ongoing regulation but is unnecessary for every individual act. When a tool evaluates subordinate choices, proximal attribution may apply at both levels. Whether the tool belongs within an SPC-2 subject remains a separate physical boundary question.

2.4 Freedom has a profile

This account tracks three context-dependent, time-dependent capacities:

There is no asserted canonical scalar that combines these axes. Restraint can shrink an executive repertoire while leaving assessment intact. A previously adopted commitment can later obstruct revision. More output labels do not imply greater reflection.

Paired interventions, bounded decision trees, error probabilities and preservation sets measure parts of this profile in declared models. They do not rank every possible agent. Continued callability of an audit is required by the preservation theorems, not by every instance of agency. An intentionally irreversible act can still be agentic at the occasion of its selection.

Three distinctions keep the profile operational.

Representation and execution need a realization map. An overlooked exit may be physically available but unrecruited. An imagined escape may be impossible. Before comparing repertoires, connect represented options to policies the architecture can execute at the relevant state and budget. An impossible counterfactual may help thought without adding an executable option.

Stored possibilities require a dispatcher. A memory entry becomes accessible only when an installed procedure can retrieve, parameterize and assess it before the deadline. An analyst's ability to invoke a dormant subroutine is not the agent's ability to do so.

Consequence diversity needs a horizon. Specify the observed variables, time horizon, risks and future continuation opportunities. Otherwise redundant micro-command encodings can inflate the apparent number of choices.

Revision has the same temporal structure. An audit may be underway, callable before the present deadline, or feasible only under a larger future budget. A high-friction review procedure can act as a practical lock now even if it succeeds later. Charging inspection and installation gives this distinction exact content.

Structural reconfiguration can expand a search grammar, but expansion is not the only improvement. Removing a redundant branch may make deliberation more efficient. Precommitment can protect one valued trajectory and foreclose another. Changes must be assessed on the affected axes and occasions. An earlier exercise of self-governance does not automatically increase present freedom. The finite charter changes a stored rule and read order; the validator construction changes audit modes. Neither establishes unrestricted cognitive self-redesign.

For sentient agency, qualifying SPC-2 organization is an additional constitutive requirement. Evaluative control and experiential assignment are different predicates. Their coexistence needs a common realization, which the later native construction provides conditionally.

2.5 Testing the actual causal pathways

Take two admitted preparations with identical present external query, phase and resources, but different retained evaluative states. Let $P_0,P_1$ be the laws of a downstream record that reveals the assessment or installed disposition. Apply a common intervention on the actual read route and, separately, on the actual installation route.

The scored record begins after the intervention and excludes a direct copy of the pre-intervention archive. A surviving historical copy would otherwise look like a bypass of the tested route. A positive intact contrast that falls under an actual cut certifies the tested mediated contribution. It does not establish that all historical influence uses that route.

Proposition 2.3: transport of a finite certificate

Suppose state and record bijections transport the preparation laws, joint kernels, diagnostic interventions, executive observation maps, resource charges and stopping rule of a finite experiment. Every intact and intervened transcript law is then transported exactly. Event scores and total-variation contrasts are invariant.

Proof. The transported joint kernels give the one-step equality. Conditional on corresponding histories, the transported executive chooses corresponding actions. Multiplying by the next joint kernel and summing over corresponding states preserves the joint history/state law. Diagnostic interventions satisfy the same step. Induction reaches the bounded stopping horizon. Bijections preserve event probabilities and total variation. $\square$

This compatibility principle agrees with causal abstraction 1, 22. An equivalent lookup implementation is not disqualified because it looks less deliberative. Ordinary input-output agreement is still insufficient: it can coexist with incorrect intervention behavior or extra information access. Mixing components or changing the physical subject boundary needs its own realization argument. Proposition 2.3 does not assert SPC-2 invariance under those changes.

Finite implementation error

If corresponding joint kernels differ uniformly by at most $\epsilon_t$ in total variation, and the initial laws differ by at most $\epsilon_0$, a stepwise coupling gives

$$\operatorname{TV}(P_{\mathrm{trace}},\widetilde P_{\mathrm{trace}}) \leq \eta:=\min\left\{1,\epsilon_0+\sum_t\epsilon_t\right\}.$$(2.2)

Until the first mismatch, the adaptive actions coincide. A union bound on that first mismatch proves the inequality. With common per-arm error $\eta$, an intact-minus-cut contrast can fall by at most $4\eta$, and a two-arm expected-score advantage can fall by at most $2\eta$.

These are guarantees on a finite experiment's joint record and successor law. Output marginals alone do not control them. Faithful realization preserves the machinery that makes the certificate meaningful, including what the executive can and cannot observe.