A chooser with a history

A decision can be the agent's decision even though the agent has a history. The substantive question is how that history acts now: which commitments remain operative, which can be examined, what evidence is available, and whether an assessment can change the rule used next.

The published paper answers part of this question constructively. Retained commitments are read, candidate rules are assessed, a selected rule is installed and fresh cases reveal the changed disposition. The philosophical development here connects that result to the supplementary mathematics of provenance, capability construction and bounded perspective. Its interpretations extend the discussion; they do not add unproved conclusions to the published theorems.

The chooser as the operating perspective

The agent's perspective is where available evidence, retained commitments and executable possibilities meet. The proposal is to locate choosing in that organized process. A further entity watching the process would need its own means of receiving information and making changes. Adding it would postpone the explanatory work.

This account still has to distinguish an evaluator from a switch. A command changing when an internal bit changes demonstrates dependence. It does not establish that the command agrees with the relevant commitments, that the bit was obtained through a legitimate read, or that a revised disposition was installed. The published inverted-selector example shows why: a faithful selector and a systematically reversed one can have identical causal contrasts.

The physical mechanism, the evaluative relation and the interpretation of a perspective therefore have different jobs. The mechanism supplies causal operations. The declared relation says which amendments accord with the retained commitments. The perspective interpretation concerns the organized agent to which those operations are attributed. None of them can be replaced by simply naming a register "self" or "value."

For a person, the relevant perspective includes an embodied history, learned expectations, attention and practical circumstances. The finite constructions isolate some of those functional relationships. They do not prove the presence of phenomenal awareness in a bit circuit. Under the website's SPC-2 account, experiential assignment requires the separate native constitution and its correspondence laws.

Conditioning can remain as content without ruling every act

An old policy can remain recorded while losing its control over present action. This is a stronger and more useful distinction than treating freedom as the destruction of one's history.

Let $S$ encode an old policy and $L$ a newly installed one. On a ready archive register, the mapping

$$(S,L,0)\longmapsto(L,L,S)$$

is injective and can be extended to a reversible permutation of the full register space. Subsequent actions based on the first register depend on $L$, and, with $L$ fixed, no longer depend on $S$. The old policy survives in the archive. A later authorized audit might consult it, but its mere existence no longer gives it compulsory authority over current deliberation.

This construction does not prove that $L$ was appropriately chosen. For that, attach the published assessment, endorsement and installation tests. It shows that release from an old influence and preservation of its record are physically compatible.

There is an exact information identity behind this separation. Suppose that, conditional on public context $E$, the final controller $C$ and residual system $B$ retain enough information to reconstruct an earlier source variable $S$. Then

$$H(S\mid E)=I(S;C\mid E)+I(S;B\mid C,E).$$

Proof. Reconstruction gives $H(S\mid C,B,E)=0$. Apply the chain rule to $I(S;C,B\mid E)$, which therefore equals $H(S\mid E)$.

If the active controller contains at most $\varepsilon$ bits about $S$, at least $H(S\mid E)-\varepsilon$ bits remain conditionally in the residual system. Historical information can move outside the active decision path without disappearing from the complete physical state. Statistical information, present causal influence and ultimate origination are separate properties.

This is also the right distinction for discussing the constructed self. Personal memories, social roles and practical self-descriptions can remain useful content. The philosophical question is whether they must serve as the unquestioned center from which every interpretation and response is organized. The RCO hypothesis, where RCO means recursively closed observer, addresses a reorganization of that authority. The bounded-agency constructions show particular forms of assessable rule revision; they do not establish the full RCO hypothesis or identify its transition in a human subject.

What the present can reveal about the past

Two different histories may leave the same accessible boundary state while differing in an inaccessible archive. If the boundary gives the observer the same future interaction laws, further questioning cannot extract a difference that those laws do not carry.

Theorem: accessible-boundary provenance bound. Let two histories induce boundary distributions $\mu_0,\mu_1$ and the same subsequent controlled transition kernels. For every fixed adaptive audit policy $\pi$,

$$\operatorname{TV}(P_0^\pi,P_1^\pi) \le\operatorname{TV}(\mu_0,\mu_1).$$

With equal prior probabilities, every binary provenance test has error at least

$$\frac{1-\operatorname{TV}(\mu_0,\mu_1)}2.$$

Proof. Compose the policy and common controlled kernels into a stochastic channel from boundary state to complete transcript. Total variation contracts through a common channel. For equal binary priors, the optimal discrimination error is one half minus one half the transcript total variation. Combining the two statements proves the bound.

Identical accessible laws are thus indistinguishable to every such audit. This is compatible with globally reversible history. Distinct complete pasts need not merge into one complete present state; their differences can remain outside the nominated boundary. Granting access to the archive changes the premise and can reveal provenance.

The published paper states a corresponding limit for identical complete present-state distributions and future boundary laws. It also develops the positive response: record the acquisition of commitments across a declared developmental interval. Observe the proposal, the information inspected, the assessment, the actual installation and its effect on fresh cases. Exclude or identify bypass writes. This provides evidence of audit-mediated acquisition during that interval.

Even a faithfully operating assessor can be misled by a controlled evidential environment. Suppressing contrary observations or fabricating apparently credible evidence can preserve every internal audit pathway. Current responsiveness therefore does not, by itself, distinguish transparent persuasion from deceptive information supply. Provenance has to be investigated at the sources and channels where that difference exists.

A new capability need not break a law

Calibrating an unknown affine sensor gives a concrete example. References at $0,e_1,\ldots,e_d$ identify its offset and columns. A learner can retain those records, compute a decoder and install it. The active controller now has an effective repertoire it previously lacked.

An equally equipped universal controller, given the same observations, storage, time and permission to run that procedure, can also execute it. Expanding the installed repertoire does not exceed a comparator class that already includes its construction. Conversely, a preinstalled correct decoder contains sensor-correlated information; calling it a cost-free baseline would hide the acquisition resource.

Both statements can hold together. Learning changes what this controller can presently do. Fixed laws can govern that change. A person learning a skill need not rewrite physics for the skill to become a new practical possibility.

The distinction has a formal normal form.

Proposition: effective construction on a fixed carrier. If states, instruments and programs have finite descriptions, and transition and installation rules are computable, the whole process can be represented on one fixed countable state space of finite words.

Proof. Choose effective encodings with tags for program, data, apparatus and records. Concatenate the current descriptions into one finite word. A universal interpreter implements each allowed transition, including writing a new program or apparatus description. The set of all finite words is fixed even when the process reaches descriptions absent from its former active repertoire.

The result concerns computably described processes. It does not declare every physical or experiential possibility computable. Within its scope, effective novelty is compatible with a fixed mathematical carrier and fixed transition law.

Lawful does not mean predictably exhaustible

There is a sharp difference between checking a finite budget and deciding every future capability of a universal system.

Take a fixed universal controller with a protected latch. The latch reveals a fair hidden bit only after a supplied program halts. The admitted primitives prevent directly opening it. Before opening, best correct bit control is $1/2$; afterward it is one. Deciding whether any finite amount of internal computation eventually enables an improvement of at least $1/4$ would decide whether the supplied program halts.

Proof of the obstruction. Transform any program into the stated controller instance. A total procedure deciding eventual capability gain would answer its halting question. The diagonal halting argument rules out such a total procedure: a program could use its predicted halting behavior to do the opposite on its own description.

A fixed finite horizon with an explicitly finite action alphabet and finite kernels can instead be exhaustively evaluated. The unbounded theorem does not make every instance difficult, and it does not prevent discovering a particular new skill. It establishes that lawful self-development need not admit one universal complete forecast of every eventual capability.

Ultimate authorship is a further demand

One proposed standard of ultimate authorship requires every qualifying act of self-constitution to be authorized by a strictly earlier qualifying act. Under a well-founded earlier-than relation, that requirement contradicts the existence of any qualifying act.

Proof. A nonempty set of qualifying acts has a minimal element. The requirement gives that element a strictly earlier qualifying authorizing act, contradicting minimality.

The inference is exact; the philosophical premise is disputed. Partial observation does not imply that every act must have this sort of prior authorization. The result cannot be substituted for a physics theorem excluding every account of agency.

The published paper deliberately permits fixed metarules. It asks whether an agent can assess and revise an operative rule, not whether it created every condition by which the assessment has meaning. That is a substantive local capacity with possible limits, rather than an answer obtained by demanding an impossible infinite ancestry of choices.

Randomness does not settle the issue either. Every finite stochastic kernel can be represented as a deterministic function of its input and an independent uniform seed by partitioning the unit interval. Rational probabilities permit finite noise tapes. This operational representation does not supply a local hidden-variable model for every quantum experiment, and it does not show that biological choices are deterministic. It shows why a stochastic transition table alone cannot decide ultimate authorship.

Even complete action-conditioned marginals need not fix individual counterfactuals. The models $(Y_0,Y_1)=(U,U)$ and $(U,1-U)$, for fair $U$, agree on the distribution observed under either action but disagree on whether the unchosen outcome equals the chosen one. Claims about that cross-action relation require an additional coupling assumption.

Freedom across occasions

Freedom in this treatment has an operative profile: the process through which evaluation mediates choice, the consequence-distinct actions recruitable now, and the rules open to assessment and revision under the available budget. Information, integration and reasons responsiveness can guide philosophical evaluation of that profile. The finite mathematics does not supply a canonical moral score for them.

A commitment can protect a valued future and close another route. A self-binding decision can exhibit reflection now while reducing revisability later. Retaining a rule after examination can express responsiveness as clearly as changing it. A conflict can remain real after a decision has been settled. These cases require the time, target and evaluative relation to be specified rather than assuming that more options or more frequent change always means more freedom.

The resulting position gives self-governance something concrete to do. An agent can investigate its situation, assess inherited rules, redirect attention, install a new disposition and act through it. Its history constrains that process without making every historical influence permanently authoritative. Questions of moral responsibility, phenomenal identity and ultimate sourcehood remain additional arguments, with their own evidence and premises.