Specify the realization before assigning a perspective

2 The inherited realization and finite operational setting

2.1 Realization precedes attribution

The supplied realization $\Rstar$ fixes primitive components, native operations and records, admissible interventions, internal and external route typing, native clocks, available resources, boundary conditions, and process provenance. A further selection doctrine specifies which of these structures the constitution treats as native. An investigator's chosen sample, approximation or stopping point is not that doctrine. Reducing the number of tests performed does not alter the already specified constitution.

Only the clauses needed for this audit are restated here. The predecessor's physical constructions are not assumptions of every finite example below, and their independent verification is not asserted by this paper. The published constitution is summarized in Table 1; its source is Chapters 15–18 of [23].

Clause	Relevant commitment
A0	Awareness is the knowing aspect of reality prior to the operational source/readout distinction; a vessel does not create that capacity ex nihilo. This adds no independently acting force or numerical universal subject.
A1	A qualifying maximal internal recurrent core is assigned one localized perspective. Distinct admitted cores are assigned distinct perspectives; overlapping subassemblies inside an admitted core receive no additional perspectives by this rule.
A2	The phenomenal relational organization of a qualifying core is assigned as a structural copy of its complete endogenous predictive object, retaining native labels, laws and congruent successor instruments.
A3	A subject episode follows nonbranching process-provenance continuation between qualifying occurrences. Branches, mergers and genuine qualification gaps terminate the preceding episodes under this law.

A0 is not an extra state variable in the proofs. The predecessor's symbol $\mathsf U$ names the pre-operational reality in philosophical prose, not a carrier into which we insert an operator or a numerical localization field. Awareness, a currently localized subject, lived content and personal continuity remain different notions. In particular, neither an unchanged autobiography nor a copied memory is, by itself, a process-provenance certificate under A3.

2.2 Complete experiments and joint instruments

We use finite classical models except in the explicitly set-theoretic identification results of Section 8. Row probability vectors act on row kernels. Chronological execution of a schedule $w=(E,D)$ is written $PED$, while the corresponding deterministic function is $D\circ E$.

A finite module $\mathcal M$ has a closed state domain $X$, actions $u\in\mathcal U$, joint records $o\in\mathcal O$, and nonnegative matrices

These specify the joint law of the next record and successor state. Blocked operations are either totalized by explicit outcomes and updates or excluded through matching operating types. A normalized conditional successor is used only for an outcome of positive probability.

An experiment $e\in\calE$ includes its preparation, causal action policy, retained records, stopping convention and access resources. Its law is $P^e_\theta$, with preparation label $\theta$. Shared references, clocks and returning receivers are included when they can influence later outcomes. A complete law is a law of everything the declared experiment retains; it is not a claim to observe every inaccessible physical degree of freedom.

For distributions on a finite alphabet,

For one common experiment family,

If preparations are separately indexed, the supremum includes them. Equalities and bounds always compare the same timed record spaces and permissions. A change in available interventions is not merely a change of coordinates.

Object	What it describes or preserves	What does not follow from it alone
Statistical deficiency	Approximate reconstruction of complete experiment laws	A native actuator, the same historical record, or timely decoding
Native return witness	A compatible internal route and retained source contrast	Resistance to disconnected simulation
Resource-relative cut radius	Distance from one declared family of coherent alternatives	Phenomenal presence or an absolute amount of unity
Strong marked quotient	Joint records, successor classes and protected marks	Microscopic identity or a cheaper replacement device
Operational quotient	Equality of every admitted complete experiment law	A physically readable class label or a phenomenal interpretation

2.3 The published dependence and return rules

Definition 2.1 (Comparison-wise minimal target)

In one compatible finite regime, fix an admitted pair of preparations differing only in primitive coordinate $i$. A nonempty output set $J$ is minimally distinguishing if its joint output laws differ while every proper-subset law agrees. Record $i\to J$, project this hyperedge to $i\to j$ for all $j\in J$, and take the union over all admitted comparisons in that regime. The internal graph retains only separately licensed internal routes.

Minimality is imposed before taking this union, not after maximizing a contrast over preparations. Appending an independent output to an affected target does not automatically add an edge to that output. Correlation-only effects are retained because the tested laws are joint. These are the literal features of the inherited rule that the next section tests.

A candidate is a maximal internally typed strongly connected component (SCC) only after the relevant native representation is closed and its actual predictive classes are congruent. Qualification also requires at least two distinct native predictive classes in the actual operating type and resource context, and a covering return witness from the complete catalogue supplied by $\Rstar$. A singleton requires a nonempty self-return.

A witness consists of one compatible native schedule, a nominated root source contrast, a nonempty closed internal tour with support exactly the candidate, and a terminal internal root observation with strictly positive TV contrast. Every named coupling must be executable in that schedule. For a joint mechanism the full target is retained in its route certificate. An external export followed by reimport does not count as an internal return unless its irrelevance is established or the path is excluded by the physical instrument.

The catalogue is complete relative to the constitutive operation/resource contract, not relative to an analyst's convenience. For example, a nonrenewable program counter can make it finite. Positivity of a scheduled terminal contrast and execution of the nominated covering route are separate obligations; the return rule does not claim that every surviving bit travels exclusively along every edge of the tour.

2.4 Four notions of state

The following distinctions will be used throughout. A strong actual-state quotient preserves the joint record and successor-class law, including prescribed marks. All-word behavioral equivalence preserves output traces but need not yield that quotient. A history-predictive state or belief is conditioned on accessible observations. An operational quotient across model/preparation pairs identifies complete experiment laws and may have no finite physical realization. The exact relation between the first two is illustrated in Example 6.4, and the fourth is treated in Section 8.

Proposition 2.2 (Inherited physical conservativity)

Fix the complete physical realization, preparation, and all operation and report kernels. Adding A0–A3 assignments and their phenomenal interpretation without changing those kernels leaves every finite adaptive physical transcript law unchanged.

Proof

The initial law is unchanged. At a policy node, the same recorded history induces the same next action distribution, and the same joint instrument supplies the next outcome and successor. Induction over the finite policy tree preserves each leaf probability. The aspect interpretation has not been inserted as a new causal argument of the kernel.

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This is an inherited result, not a new theorem that every consciousness theory must conserve physical predictions. It also does not preclude testing a specific realization or psychophysical identification with independently defended report and calibration premises.