Formative dependence and experiential admission

A developmental recipe is not automatically a universal origin rule

A local interpretation recipe and a historical admission rule must be assessed separately. This appendix holds the nominated local and unit conditions fixed, including any developed reasoning and actual-uptake requirements. The problem is consistency and selection of experiential assignments, not a consciousness detector.

B.1 Unanchored assignments

Let $L\subseteq V$ be locally qualifying activities. Write $u\to v$ for an eligible formative contribution from another unit, and define

$$\operatorname{Post}_L(E)=\{v\in L:\exists u\in E,\ u\to v\}.$$

The biconditional experiencing-contributor recipe requires

$$E=\operatorname{Post}_L(E).\tag{23}$$

A necessary-only rule instead says $E\subseteq\operatorname{Post}_L(E)$. It still requires an admitted predecessor for every admitted activity. Either rule excludes nonempty admission on well-founded ancestry. Only equality also requires every locally qualifying successor of an admitted contributor to be admitted. For $a\leftrightarrow b$ and $b\to c$, $E=\{a,b\}$ is a necessary-only solution strictly contained in $\operatorname{Post}_L(E)=\{a,b,c\}$.

Proposition B.1: existence, uniqueness and finite classification. Empty admission always solves (23). If ancestry inside a hypothetical nonempty solution is well founded, there is no such solution and empty admission is unique. On a finite graph, all solutions are forward-reachability closures of unions of cyclic strongly connected components in the graph induced by $L$. Nonempty admission exists exactly when that graph has a cycle. Empty admission is unique exactly when it is acyclic. Exactly one nonempty solution exists exactly when there is one cyclic SCC, with empty admission still present.

Proof. $\operatorname{Post}_L(\varnothing)=\varnothing$. A nonempty well-founded solution has a minimal member, contradicting its required admitted predecessor. In a finite fixed point, forward closure holds and every member has a predecessor. Repeatedly following predecessors reaches a cycle, so every member is reachable from a cycle inside the set. Forward closure includes its SCC and qualifying successors. Conversely the forward closure of any selected cyclic SCCs is closed under successors, and every member has a predecessor on a cycle or the path from one. It is therefore fixed. One cyclic SCC gives only its closure besides empty. With at least two, choose a terminal cyclic SCC in the condensation's cyclic reachability order; its closure omits another cyclic SCC, whose addition makes another nonempty fixed point.

The greatest finite solution consists of qualifying successors of qualifying cycles, equivalently vertices whose backward path stays entirely in $L$ and reaches a cycle. Descending iteration from $L$ computes it. A nonqualifying intermediate cannot transmit the justification. These are elementary monotone fixed-point consequences [47].

The incompatible combination is universal already-experiencing formative dependence, well-founded experiential ancestry and at least one experience. Temporal precedence need not be well founded on infinite domains, although finite strictly ordered event models are. On integers with $n-1\to n$, empty and all-vertex admission both solve the recipe without a cycle. Infinite ancestry removes a first element but supplies neither historical evidence nor a reason to select the nonempty assignment. Selecting the greatest fixed point adds a constitutive rule rather than deriving admission.

B.2 Independent anchors and nonrecursive formation

Let $B\subseteq L$ contain independently admitted activities. The anchored rule explicitly changes the condition:

$$E=B\cup\operatorname{Post}_L(E).$$

Write $\mathcal R(S)$ for forward closure within $L$, including zero-length paths.

Proposition B.2: anchored scope. On a finite graph, the solutions are precisely $\mathcal R(B\cup C)$ for unions $C$ of cyclic SCCs. The least is $\mathcal R(B)$ and is unique exactly when the graph induced on $L\setminus\mathcal R(B)$ is acyclic. On a well-founded formative relation the unique anchored solution is $\mathcal R(B)$.

Proof. A fixed point contains $B$ and is forward closed, hence contains $\mathcal R(B)$. A member outside that closure cannot have a predecessor inside it. In a finite excess, predecessor iteration reaches a cycle there, yielding the stated representation. Conversely those closures satisfy the equation. A residual cycle makes a larger solution; no residual cycle leaves only the least. On well-founded ancestry, a minimal excess member can have a predecessor neither inside nor outside the closure, a contradiction.

An adult independently assumed to experience is thus a conditional anchor, not a product of the unanchored rule. Section 4 does not derive a universal origin by assuming its example. Thin fundamental awareness is not silently promoted to an individuated experiential anchor.

Another possible formulation requires relational development without experiential admission of every contributor:

$$D_{\mathrm{rel}}(A,J):=\exists B\ne A\;\operatorname{CausalFormation}(B\to\operatorname{Scaffold}_A\text{ operative in }J).$$

Combined with reasoning and local/unit requirements, it is a scoped proposed constitution for reasoning-organized episodes. It changes the contributor premise. Mandatory relational formation applies only if this variant is chosen; it is not established universally and is not conjoined here to SPC-2. Human language, broader conceptual inference and uptake remain separate. Agrammatic adult calculation can survive severe acquired grammatical loss, but does not prove developmental independence from language [49]. Social-learning benefit also does not prove universal experiential-contributor necessity [14].

B.3 Mutual learning without circular experiential justification

Two organizations can acquire a particular reasoning scaffold together without inserting consciousness predicates into learning equations. Give them all sixteen binary truth functions. One sees grounded examples $00\mapsto0,01\mapsto1$; the other $10\mapsto1,11\mapsto0$. Each has four consistent hypotheses. Positive-delay exchange supplies all four examples and uniquely identifies XOR. Induction on novel left-associated bit expressions yields $\sum_i x_i\bmod2$. Three through nine leaves provide $1016$ enumerated cases. Withhold the other's evidence and four candidates remain under the same protocol.

Initial concepts, grounding, memory, labels, inference architecture and composition capacity are counted. The model learns one scaffold, not all reasoning from nothing. It does not establish that early contributors lack all possible experience. It supplies the nonrecursive developmental predicate without a consciousness threshold. Under the unchanged well-founded experiencing-contributor recipe, universal assignment stays empty.

Feedback across extended activities does not repair that obstruction. $A_{t_1}\to B_{t_2}$ and $B_{t_3}\to A_{t_4}$ with $t_1\lt t_2\lt t_3\lt t_4$ remain causally ordered even if their encompassing intervals form a two-cycle. If each contributing token must already experience, well-founded obstruction remains. If later qualification admits an entire earlier interval, that adds a whole-interval admission principle. A physical feedback cycle is not automatically a cycle of experiential justification.

Having experience, interpreting an occurrence and explicitly defining or reporting it are therefore different. The adult temporal construction uses actual interpretation while leaving universal admission, complete character and nested/larger bearers distinct. The source-to-functional-use results are independent of every assignment choice examined here.