The Shadow Psychophysical Constitution

17.1 Awareness and explicit laws of manifestation

The constitution is defined relative to the certified realization $R^\ast$ of Chapter 15. Its physical inventory and its declared selection doctrine have been fixed before a subject is assigned. An analyst may investigate only a subset of that inventory, but cannot alter the constitution by performing fewer tests or stopping a calculation earlier.

Constitutive law 17.1 (A0: fundamental awareness)

The unconditioned ground is fundamental. Awareness is the provisional name for a quality attributed to that ground, distinguished from the unsplit $\unsplit$. Fundamental awareness does not mean thought, recognition, knowing or a subject apprehending an object. Physical organization does not manufacture the ground or its quality; it conditions localized experiential manifestation. This adds no independently acting substance or force.

A0 states an ontological commitment rather than an extra numerical input to the construction. Awareness within a localized perspective, including preconceptual presence and developed knowing, must not be projected backward as cognition in the ground. The graph, predictive object and lineage can be computed without settling their experiential interpretation. A0 interprets admitted perspectives as localized manifestation within the same reality; A1–A3 specify their organization. The completion theorem establishes determinacy conditional on these commitments, not a derivation of A0. The ontology gives the construction meaning while leaving its physical probabilities unchanged.

The primitive is not a formally described global episode lacking all contents. The ground has no mathematical symbol here; $\unsplit$ denotes the unsplit, and neither is a state in the working source $S$. Numerical subject counts apply to admitted local perspectives. Fundamental awareness does not posit hidden experience between their episodes or identify reality with a universal experiencer. A physical field requires a specified carrier, degrees of freedom, transformations, dynamics and coupling; A0 does not supply an additional field.

17.2 A1: where perspectives are assigned

Constitutive law 17.2 (A1: native recurrent realization)

A candidate internal SCC carries one localized experiential perspective when it meets Definition 15.5: an executable covering return and at least two distinct native predictive classes in the occurrence's actual native operating/protocol type and resource context. Distinct admitted SCCs carry distinct perspectives. Maximality is an explicit dispositional individuation rule; no additional subjects are assigned to overlapping recurrent subassemblies within one admitted core.

The predicate of Definition 15.5 is physically evaluated before this attribution. The positive motivation is retained differentiation participating in an ongoing organization. The covering schedule prevents a cycle assembled only from incompatible control contexts; maximality provides nonoverlapping support. Neither fact proves experiential unity. A1 makes that further identification openly.

A persistent physical register is not an unchanged annotation in an analyst's description. Genuine self-dependence means an admissible intervention changes a later internal law. It can satisfy the exact return test, including when the process is used as an archive. Thus the law has no general theorem excluding passive memories. A one-time imprint followed by a constant erasing update fails; a physically self-dependent record with an available native return can pass. The labels active and passive cannot replace these tests. The law is deliberately permissive toward minimal organization and imposes no intelligence or biological threshold.

Formal admission and its empirical lower bound.

A1 is the present formal admission law of SPC-2. Accordingly, a certified realization satisfying its conditions receives a localized perspective within the constitution. This is not empirical validation that A1 identifies the actual lower boundary of consciousness in nature. Nor does a toy recurrent controller by itself establish an adequate $R^\ast$: its native records, executable return, boundary isolation, timing, resources and operating contract require physical justification (Sections 15.1 and 15.4). An annotation has no causal return; an externally imposed replay independent of the intervened core state has identical terminal laws. An omitted environmental feedback path cannot certify a return internal to the nominated core. These are failures of the proposed realization, not general proofs of unconsciousness.

Stricter application of the existing certificate does not exclude every simple system. A genuinely realized one-bit self-return process with distinguishable native future laws can meet the certificate, including predictive-fibre congruence and a supplied resource/provenance contract. Its admission is then a consequence of A1, not necessarily an artifact of oversimplification. The concern combines realization adequacy in a particular application with an unresolved empirical and philosophical lower-bound question; it does not, by itself, expose an internal inconsistency. Excluding every such system would change A1 or its constitutive selection doctrine. If independently constrained non-toy realization work shows systematic over-admission, A1 will require refinement.

Formal A1 admission and a rich biological realization of scene-forming coupling must therefore be distinguished. The mammalian findings in Section 21.4 concern the latter and do not modify A1. A proposed core cannot both satisfy A1 and be declared genuinely without experience by an additional cortical veto: that would be a conflict in the application requiring resolution. Loss of a familiar mammalian scene alone does not decide the status of every remaining subsystem.

For a mature biological vessel, this mathematical admission rule can be approached through the idea of a world-for-the-organism. Internal states have significance relative to bodily regulation, viability, action and learned relationships; conditions can go better or worse for that organism. Calling such organization a minimal center of concern gives the biological interpretation a humanly intelligible focus. It does not mean reflective worry, a narrative ego, or a separately present observer.

SPC-2 does not yet contain a formal general criterion equating such concern with subject admission. Recurrence and the exact return tests remain the computable A1 machinery. Candidate refinements involving integrated endogenous organization, a world-for-the-vessel, minimal concern or stronger native predictive unity remain biologically and philosophically motivated possibilities rather than hypotheses of the current completion theorem. No stronger admission criterion follows here from those descriptions alone. The current law retains its permissive minimal cases without an autopoiesis requirement or arbitrary complexity threshold.

SPC-2 does not imply that all matter is conscious. A rock is not admitted merely because it exists; tissue activity and simple interaction alone do not establish a perspective. A1 concerns a certified organization. Source-aspect ontology consequently need not assign localized experience to every physical object. Equally, the statement does not covertly exclude a minimal physical memory that actually satisfies A1. Any stronger exclusion would be another constitutive commitment.

17.3 A2: phenomenal organization

Constitutive law 17.3 (A2: endogenous predictive structuralism)

The phenomenal relational organization of each qualifying core is a structural copy of its complete endogenous predictive object over all physically admitted finite continuations. The actual phenomenal point is the image of the predictive class of its realized intrinsic state. The copy preserves native operation and outcome labels, every finite test law, the compatible horizon restrictions, and the well-defined class transition instruments. Apart from primitive presence, no further manifested qualitative fact is postulated within this constitution.

Work on mathematical structures of experience motivates specifying the transported relations explicitly [23]; it does not select this particular identification. A2 is the structural law of the lived scene within the constitution. It identifies an organization with phenomenal character; it does not generate awareness, prove its existence, or derive that identification from a sufficient statistic. Its motivation is that an internal distinction acquires a role through the continuations it supports. The complete profile retains which operations distinguish, the distributions of their internal outcomes, and their continuing organization. A supremum distance alone loses these relations and can become discrete even in very different processes.

The future laws characterize current dispositions. They are not future events acting backwards, and they need not be calculated or represented by the vessel. Physical recurrence, a mathematical predictive description, and an internally implemented self-model are distinct. Neither language nor autobiographical reflection is required by this law.

Within SPC-2, the complete endogenous predictive structure exhausts phenomenal organization; the theory does not claim to have proved that no conceivable richer theory could add further qualitative facts. Hidden qualitative differences that leave that complete structure unchanged are excluded within this candidate law. This is a strong internal commitment, not a universal metaphysical no-go theorem.

A structural copy proves mathematical consistency of the assignment. It does not prove that every retained endogenous distinction is experienced. A critic can argue that unconscious processing makes the proposed profile too rich, or that a further intrinsic qualitative remainder survives after every structural relation is fixed. A2 makes an explicit choice on both questions. Its application must face independently elicited phenomenal relations; those relations cannot be redefined after a mismatch merely to preserve an isomorphism.

The gauge is a whole-model change of presentation preserving the specified structure and its calibration. It does not identify different points inside a fixed calibrated model. If an outcome label is renamed, its physical interface, probability laws, and report interpretation must be transported with it. Nor may one change the metric of an independently nominated phenomenal target simply to make it match.

The all-finite family removes dependence on an investigator's chosen forecast cutoff. It does not make the constitutional grammar optional. A new internal operation, a changed physical boundary contract, or a changed endogenous readout may change the organization. Attaching an external report apparatus that preserves these data does not. The distinction is formalized in Section 16.5 rather than left to intuition about what counts as internal.

17.4 Enacted constitution and the full predictive commitment

The enacted account and SPC-2 address compatible questions without yet being proved equivalent. Complete-enactment identity identifies the qualifying actual occurrence; current incorporation specifies its presently interpreted contributions. A1 supplies the formal core and individuation rule of SPC-2, A2 specifies complete phenomenal organization, and A3 specifies episode continuation. A joint application must justify the correspondence between the nominated interpretive unit, its complete physical enactment and the realized core assignment. A container around the act or a successful content readout supplies no such correspondence.

This requirement reaches beyond current foreground content. For an exact intrinsic carrier $X$ under its fixed full native contract, let $q_\infty:X\to Z_\infty$ be the complete native predictive quotient of Chapter 16. If a fixed property $f:X\to Y$ is asserted to be phenomenal under both A2 and the enacted correspondence, compatibility requires

Equivalently, $f=\bar f\circ q_\infty$ for a well-defined $\bar f$ on the attained predictive classes. Equal classes receive the same assigned phenomenal organization, so every fixed property of it agrees on the fibre. Conversely, fibre constancy makes $\bar f(q_\infty(x))=f(x)$ well-defined. This factorization criterion is proved in the whole-field companion's Appendix B [62].

Factorization of a current-incorporation projection is a compatibility condition, not a proof that the complete accounts coincide. If two nominations under full A2 identify the same complete phenomenal organization and the same actual phenomenal point, their complete labelled pointed predictive objects must be isomorphic. A claimed bridge must preserve native operation and record labels, all admitted finite continuations, horizon restrictions, successor instruments and the realized point. A projection that retains only current contents can leave distinct complete organizations unresolved. Nor does the omission of an arbitrary contextual variable refute A2: one needs a distinction in a property actually claimed as phenomenal on a single predictive fibre.

The positive gain is a more explicit constitutive organization for a field, including linked realization, occasion roles and actual incorporation. The remaining obligation is an independently justified complete correspondence, together with resolution of any disagreement in unit qualification or formative-history requirements. Both accounts can be used at their stated scope without discarding either or silently replacing full A2 with a foreground summary.

Here primitive presence in A2 means the localized experiential presence assigned under A1. It is distinct from the fundamental quality provisionally named in A0. A2's structural completeness concerns manifestation in the qualifying perspective, not a complete description of the ground.

17.4.1 Compatibility at different explanatory levels

The joint account separates admission, complete predictive organization, currently incorporated content and episode provenance. Whole-field constitution is applied within a warranted qualifying unit; it does not automatically supply a rival universal selector. Consequently equal current foreground with different complete A2 points is not a contradiction. A conflict arises when a property claimed as phenomenal differs on one complete predictive fibre under the same realization and calibration. The following cases locate that test without treating absence of rich adult uptake as a veto on A1.

These are conditional cases, not classifications of actual devices. A replay may fail to enact the represented person's context-responsive organization while its executor contains a different qualifying minimal process. Represented person, actual executor and any assigned perspective must therefore be nominated separately. Likewise, distress, fragmented interpretation or impaired autobiographical coherence does not by itself negate presence: constitutive unity is not a scale of psychological health or achievement. A3 follows qualifying process provenance, not improvement, successful reporting or the investigator's confidence.

17.5 Process provenance and temporal identity

The identity of an experiential episode, the persistence of a person, and the ontological status of awareness answer different questions:

The end of a localized subject is the end of that subject under the stated identity law. Persistence of $\unsplit$ is not its survival or migration elsewhere. Memory copying and uploading do not, by themselves, transport a subject; a fresh qualifying receiver has a new admission, with any genuine branch handled by A3.

A physical state is not a permanent material label. Cells turn over, hardware is repaired, components enter and leave an active organization, and its operating mode changes. A temporal law must describe those events without equating memory equality with identity or requiring every atom to remain in place.

The realization supplies native physical time cells indexed by $t$, component sets $\mathcal B_t$, and a directed process-provenance relation

An edge records continued implementation of a component process or an explicitly realized local transfer of its operative role. This relation is supplied with the physical event history: retained carriers, births, retirements, and renewal operations have declared antecedents. A mere statistical match or information-copy edge is not a provenance edge. An information-copy edge belongs to a separate information-transfer relation. Both may exist in one event, but neither is inferred from the other.

This is an explicit realization premise, not a solution of the philosophical identity problem by renaming it. For a fixed-carrier circuit, $\Lambda_t$ is the ordinary persistence of active registers; newly allocated copies have new lineages. A physically documented in-place renewal can transport an ongoing process to new material. A proposed application with two incompatible process-provenance assignments has not yet supplied one $R^\ast$. The present theory does not choose between them from matching transition tables alone.

Let $\mathcal C_t$ be the qualifying cores already computed at cell $t$. Form the bipartite core-provenance graph with relation

Only qualifying predecessors and successors enter this graph. Addition of a previously nonqualifying support component is not, merely by that addition, a merger of subjects. The relation is evaluated before any numerical identity is assigned.

Constitutive law 17.4 (A3: nonbranching process continuation)

A core $C$ at $t$ continues as $D$ at $t+1$ precisely when $C\mathsf L_tD$, $C$ has exactly one qualifying successor in $\mathsf L_t$, and $D$ has exactly one qualifying predecessor. Subject episodes are maximal chains of these continuation edges. At branching, merging, or a physical loss of qualification the predecessor episodes end; qualifying successors without a continuation edge begin new episodes. An analyst's truncation censors an episode and does not terminate it.

This law deliberately admits change of support. Nonbranching growth, shrinkage, and renewal need not carry every old component into the new core. At least one realized process-provenance connection across each native cell is required. No numerical fraction of retained matter or memory is inserted. The cost is explicit: a very small surviving process connection can sustain identity if all other conditions hold. A stronger requirement that a specified backbone, proportion, or organizational invariant survive would be another constitutive law, not a consequence of numerical identity alone.

Proposition 17.5 (Episodes and gradual replacement)

For any supplied $\Lambda_t$ and qualifying core sets, A3 defines an unambiguous partition of qualifying core occurrences into episodes. If a sequence $C_t,\ldots,C_{t+n}$ has a provenance edge at each adjacent pair, where each adjacent source has exactly one qualifying successor and each adjacent target exactly one qualifying predecessor, all its occurrences lie in the same episode even when $C_t\cap C_{t+n}$ is empty. Restricting an already constructed episode to an observation window preserves identity at common times.

Proof

The retained continuation graph has indegree and outdegree at most one and increases time strictly along every edge. Its connected components are therefore directed paths, not branching trees or cycles. Path membership is an equivalence relation and gives a unique partition. Every adjacent pair in the stated sequence is a retained continuation edge, so transitivity gives the conclusion without any endpoint material-overlap condition. Restricting the paths changes only which part is observed. Branch degrees must be evaluated in the full native provenance graph before restriction; deleting an unseen competitor and then recomputing degrees would be a different operation.

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Physical provenance $\Lambda_t$ can describe a persisting organism or vessel during an interval without experience. The subject graph in A3 contains only qualifying occurrences: a genuine qualification gap contains no currently instantiated localized experiential subject and ends the episode. Return of qualification begins a new episode, even when biological and person-level continuity is preserved. Lineage is not hidden experience. Sleep and anesthesia therefore require separate assessments of vessel continuity, scene occurrence and later memory (Section 2.7).

The treatment of split and merger preserves ordinary numerical identity. If one predecessor were identical to each of two distinct successors, transitivity would identify the successors. Ancestry and informational continuity may branch; episode identity here does not. The law chooses the symmetric termination convention rather than privileging one successor. It concerns experiential episodes, not every legal, biological, or narrative use of the word person.

Native-time refinement needs particular care. Inserting additional cells is harmless when each old continuation edge is subdivided into a nonbranching chain and every old branch or qualification gap remains visible. Under that condition contraction of the inserted vertices recovers the same episode relation. Sampling only before and after an unobserved split, merger, or loss of qualification need not do so. Temporal resolution is therefore part of $R^\ast$, and the observational window is not.

17.6 Reports, phenomenal identification, and access

Reports are produced by physical channels with their own state, resources, timing, noise, and later decoding. They do not enter A2 merely because an investigator records them. A grounded report channel factors through the core's predictive class at each fixed boundary/channel context, as established in Chapter 16. Its phenomenal expression is transported by A2's identification. No independent psychophysical decoder remains adjustable.

Grounding is a sufficiency requirement, not a completeness or truthfulness requirement. Two different phenomenal states can yield the same constant report, and apparatus noise can erase distinctions. A family separates all phenomenal states only under the additional report-completeness premise. Conversely, a physical instrument that separates two states in one predictive class is not a grounded report of that class under the declared law. It remains an ordinary physical observation with a determined probability; it cannot be promoted to a phenomenal decoder without changing the law or the realization.

A0, A1, A2, and A3 perform different jobs: fundamental ontological attribution, localized admission and individuation, relational organization, and episode identity. The physical realization supplies event and report probabilities. This division makes the ontological interpretation explicit while leaving no report mechanism to be chosen after the desired conclusion is known.

17.7 The constitutive choice

The designation SPC-2 marks substantive commitments. Relative to SPC-1, it fixes a separate endogenous grammar, uses one compatible all-finite predictive structure instead of a nominated finite-horizon assignment, requires predictive transition congruence on its finite intrinsic domain, detects minimal joint-output dependence in its physical influence structure, and admits nonbranching process continuation through support turnover. External report maps are independently grounded rather than included automatically in the phenomenal test family. These choices preserve the source-aspect architecture while defining a more explicit manifestation law. They are not deductions that every admissible consciousness theory must share.