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Library / First Principles Framework (FPF) - Core Conceptual Specification
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A.7:5.6 - Formal inclusion, world-side collection, and collective System

  • Mathematical or representation inclusion — say that an element is in a set, a value fills a tuple place, or a value lies in a coordinate domain under the applicable mathematical statement. Keep the statement with its defining mathematical rule; use C.29 for an actual mathematical-lens use and A.19 when a characteristic scale or coordinate is current. No world-side belongs-to relation follows.

  • World-side collection — identify the collection and use its subject-specific belongs-to rule. That rule says who or what may belong, when belonging begins and ends, whether it may recur, and how past belonging is stated. Belonging alone establishes neither parthood nor holonhood, but it does not prohibit a separately grounded constructive part relation.

  • Collective System — treat a team or other grouping as an acting System only after the candidate passes all six A.1 matters. A list, formal set, catalogue, or belongs-to statement does not establish that result.

  • Use the direct relation for every stronger claim:

    • ComponentOf — mechanical or structural part in systems.
    • ConstituentOf — logical or content part in epistemes.
    • PortionOf — quantitative portion with conserved extensives.
    • PhaseOf — temporal part of the same carrier over a proper interval.
    • System-role assignment — a System is the HolderSystemSlot value in one obtaining occurrence of a directly admitted U.SystemRoleAssignment species.

Normative guard: Formal inclusion establishes no world-side belonging. Collection belonging establishes neither constructive parthood nor holonhood and does not make either impossible. If a grouping is claimed to act, test it against all six A.1 matters. Add a local system-role kind, assignment, Method, Work, or constructive part relation only when that separate claim obtains.