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Library / First Principles Framework (FPF) - Core Conceptual Specification
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C.3.2:7 - Extension as Representation

Materialize KindExtension(k, slice) only when a named query, quantification, comparison, review, or publication needs the current true-candidate set.

  • Pin the signature edition even though the compact name shows only k and slice.
  • State the candidate domain without inventing U.EntitySet.
  • Include exactly admissible candidates whose judgment is true. Keep unknown and not-applicable distinct when the receiver needs those exclusions explained.
  • Treat braces, rows, indexes, or database results as representations. They create neither a collection holon, A.14 membership occurrence, direct classification relation, nor criterion condition.
  • Use C.29 when the represented set changes a claim-bearing use; otherwise the extension may remain a local calculation.

Candidate state or a later slice can change an extension without changing the signature or kind. An extension row cannot repair an inconsistent declaration or subkind fact.