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Library / First Principles Framework (FPF) - Core Conceptual Specification
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B.1.3:4.2 - The operator family (companion flavours)

To keep design vs run clean (A.15), Γ_epist has two companion flavours that share the same algebra but answer different semantic questions. Their declarations contain only the values on which the result depends. A performer, local system-role kind, or assignment is therefore not an operator argument: the same fold can be specified before staffing and can be applied in Work performed by different Systems without changing its result semantics.

When one particular operation application matters, use A.6.1 for that application and its argument and result bindings. A practitioner sentence may still say “the engineer compiled the guidance”. If no particular dated U.Work claim is current, that ordinary sentence needs no classification or assignment apparatus. If one is current, recover every actual performer System’s A.13 core and independently admit the Work under A.15.1 from its performance history, enacted Method, temporal extent, and containing System. Add F.6 afterward only when precise assignment-bound attribution is current. A short B.1.3 projection may omit an assignment identifier unused by its receiver only when every relation it consumes remains recoverable. An operation result binding says which value the application returned; it establishes neither production nor first existence of that value, publication, release, acceptance, nor a carrier. Open A.15.PROD or the publication patterns only when one of those separate questions is current.

Synthesis (design-time semantic fold). Compose exact input epistemes into a draft aggregate.

Γ_epist^synth : ( D_know : DependencyGraph< U.Episteme > ) → U.Episteme
  • Domain. D_know designates exact source epistemes and the governed ConstituentOf, UsageOf, ReferenceTo, evidences, derivesFrom, and collection-specific belongs-to relations that obtain among them, together with the mappings used by the fold. The graph represents those objects and relations; it does not make them obtain.
  • Result. One synthesized episteme whose claim content, exact EntityOfConcern, and effective reference scheme satisfy C.2.1. Its ClaimGraph integrates the retained content; provenance and SCR keep contributing sources and carriers traceable. State its formal basis, scope, and supported conclusion with limitations. Calculate an aggregate R only where B.3 and C.2.2 establish the input meanings, scales, and dependency model. Otherwise keep support separate and return a bounded reasoned synthesis. Neither a higher formality level nor an axiomatic mode requires an invented numerical score or an irrelevant empirical study.

Compilation (target-scheme fold). Map one synthesized episteme into one exact target reference scheme.

Γ_epist^compile : ( E_synth    : U.Episteme,
                    TargetScheme : U.ReferenceScheme ) → U.Episteme
  • Domain. One synthesized episteme and the exact target reference scheme used to read the compiled claims—for example, the scheme used by a journal, standard, or program specification. For every meaning that crosses semantic contexts, the fold also relies on exact source and receiving SchemeSenseCell values, an obtaining F.9 Bridge, and a separately stated bounded-use claim; any relied-on use must pass A.10 or B.3.
  • Result. One compiled, target-scheme episteme with explicit mapping and loss information and a C.2.1 identity determined by its claim content, exact EntityOfConcern, and effective reference scheme. The result is not thereby a publication, release, carrier, or accepted artifact.

Relationship to Γ_ctx / Γ_time. If the knowledge fold explicitly depends on argument order (for example, a derivation), the internal fold uses Γ_ctx for the sequence. If a temporal storyline matters, first identify each exact episteme and any obtaining C.2.1 edition relation; then use B.1.4/Γ_time to aggregate only the recovered temporal restrictions, relation order, or applicability windows required by the use. Γ_epist composes exact selected episteme inputs, not a label-defined current slice. If the result changes claim content, EntityOfConcern, or effective reference scheme, C.2.1 identifies another episteme. Use B.2 only when exact construction facts leave a separate existing-whole versus candidate-new-whole question.