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Library / First Principles Framework (FPF) - Core Conceptual Specification
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A.6.2:4.1 - Informal definition

Definition. An effect-free episteme morphism is a local mathematical arrow f : X -> Y between two exact epistemes. Under its selected formal substrate, it states how claim content, the EntityOfConcern, and any material reference or representation scheme correspond. Its content is this mathematical relation and its laws. Any Work, mechanism application, or episteme creation is a separate fact under its direct governor.

This is a local mathematical class defined here in the selected formal substrate, not an admitted durable U-kind. The pattern keeps the short name EFEM for that class. A reusable A.6.0 FormalSubstrate signature may declare its vocabulary and P0-P5 laws, but that signature episteme is not the class and is not one arrow.

An arrow in this class:

  • has exact domain and codomain epistemes identified under C.2.1;
  • is effect-free: no Work, mechanism application, system change, or carrier mutation follows from the arrow;
  • states the exact conservativity rule it claims;
  • obeys the declared identity and composition laws; and
  • is classified locally by EntityOfConcernChangeMode as preserve or retarget.

Within the selected formal substrate, one arrow is identified by its exact domain, codomain, arrow rule or designator, and declared formal equivalence. Two arrows can have the same endpoints and still be different. Changing a claim about whether the same arrow is suitable for another use does not reidentify the arrow.

The ordinary FPF objects remain separate:

  • f is the local mathematical arrow;
  • the A.6.0 FormalSubstrate signature is a C.2.1 episteme declaring reusable vocabulary and laws for the arrow family;
  • a C.2.1 bounded-use assertion q about f is another episteme; its ClaimGraph states the invariant, visible loss, named receiving use, conditions, and affirmative or negative polarity;
  • a current-case judgement separately compares exact facts with q and returns satisfies, fails, or cannot decide;
  • an operation application and any Work that computes, authors, or changes an episteme are identified only when they actually occur.

The A.6.3 viewing branch has endpoint epistemes about the same EntityOfConcern. The A.6.4 retargeting branch has endpoints about independently different entities and adds the separate bounded-use assertion q and current-case judgement defined above.