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Library / First Principles Framework (FPF) - Core Conceptual Specification
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A.6.3:4.7 - Preserve composition and replay

The selected formal substrate supplies the identities, admitted compositions, and arrow equivalence. For fixed source epistemes, rules, reference semantics, correspondence dependencies, and configuration:

  • identity viewing preserves the same C.2.1 episteme;
  • composing f : X -> Y with g : Y -> Z gives the admitted composite compose(g,f) : X -> Z under A.6.2 P3;
  • if a separately declared construction operation is deterministic, replay with the same admitted inputs yields the same receiving C.2.1 identity discriminators;
  • random seeds, model editions, external service state, or timing that can change Y are explicit inputs to the work or declaration, not hidden meta;
  • a normalization repeat claim identifies n_X : X -> Y and the next arrow n_Y : Y -> Z, establishes Z = Y under C.2.1, and witnesses compose(n_Y,n_X) ≃ n_X under the declared arrow equivalence. One X -> Y arrow is self-composable only when X = Y.

A composition requires the exact middle episteme to match. A claim that two routes yield the same receiving episteme requires equality of all three C.2.1 identity discriminators; representation equivalence alone does not establish that identity. The repeat claim requires a fixture or proof under A.6.2 P4.