Two realizations of one complete service

2 Inherited benchmark and conditional assignment

On $x=(a_0,a_1,a_2,j_0,j_1)\in\B^5$, with little-endian indexing, retain

Thus $EF=GE$. All states and both inverse identities are checked exactly. The original public state is $x$; the recoded circuit reports $E^{-1}(z)$. Matching whole-state loads and enable operations preserve complete decoded traces, not merely one trajectory.

Under the inherited register doctrine, the original system has closed recurrent supports $\{a_0,a_1,a_2\}$ and $\{j_0,j_1\}$, with 8 and 4 predictive classes. All ten admissible connected groupings agree. The recoded essential graph is strongly connected; all 38 admissible groupings yield one five-register support with 32 classes. These are inherited conditional results, not observations of subjects [5, Section 4, P4].

Let $r_i^b$ denote an elementary overwrite of coordinate $i$. FRD-2 P2 characterizes bijections transporting these operations as signed permutations, and P3 transports the complete SPC-2 assignment when clocks, resources, records, preparations, and provenance are also matched [5, Section 3.2, P2–P3]. But $E$ does not transport this local algebra: changing $a_1$ can change both $z_1$ and $z_3$. The new work therefore seeks evidence for a chart rather than another covariance assertion.

Imported assignment contract.

The finite specialization fixes synchronous Boolean storage, the service tick and permitted preparations, essential-dependence routes, full successor-state records, resources, actual state, and operative provenance. It enumerates the doctrine's connected groupings and tests closure, executable covering return, predictive nontriviality, and certification; uncertified alternatives cannot simply be discarded when asserting whole-family agreement [4, Sections 2–4, FRD-01–FRD-04]. P3 transports the assignment only with those remaining fields matched. The response certificate below does not supply them. The accompanying dependency index locates the full hypotheses, extractor, and preserved failures [20].

The signed control is

CCI-1's official native-grain comparison selected IIT-2023 supports $\{a_1,a_2\}$ and $\{j_0,j_1\}$, each with $\varphi_s=2$, versus all five registers after $E$, again with $\varphi_s=2$. Its complete 2026 preset selected no positive complexes [6, Sections 2–4]. The original support disagreement is therefore already more precise than a difference of counts.