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Library / First Principles Framework (FPF) - Core Conceptual Specification
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C.2:4.3 - Composition (Γ_epist) and propagation

Let Γ_epist compose exact epistemes {Eᵢ} for one declared claim and use. B.1.3 supplies the synthesis/compilation Method; B.3 and C.2.2 govern warrant and scale discipline.

  • R (Reliability). First distinguish indispensable premises, alternative sufficient arguments, complementary evidence, different scope slices, and counterevidence. Identify duplicated data and shared assumptions or bias. A numerical fold requires warranted input meanings, compatible scales, dependencies, and a receiving model. Neither series nor parallel syntax supplies a default minimum or maximum, and there is no universal cap at the best support line. Where no common model is justified, retain separate contributions and limitations in a bounded reasoned synthesis.
  • F (Formality). F(Γ) = minᵢ F(Eᵢ) over the essential formal constituents of the claim. This is an ordinal formality statement, not an R calculation. Raise F by the actual ΔF move; neither an axiomatic mode nor a line=formal tag converts F into empirical warrant.
  • G (ClaimScope). Required premises compose only on their overlapping scope. Distinct supported slices may form SpanUnion({G_path}) under A.2.6 and C.2.2’s type-before-scope rule; retain their support separately and drop unsupported regions. A new source does not by itself generalise the claim. Scope change remains an explicit ΔG± move.
  • CL (Congruence). Keep each traversed mapping and the ordered meaning of its declared CL visible. A chain minimum is usable where that relation’s congruence rule justifies it. A notation, scope-translation, kind, plane, source-local, model-use, or evidence-reuse relation contributes only its own warranted loss. A numerical Φ needs its receiving model; a monotone table or clipped output does not supply one.

For example, two necessary independent conditions with probabilities 0.9 each have conjunction probability 0.81, not minimum 0.9. Conversely, a limited complementary source need not reduce the support already available. A credible contrary result changes the affected conclusion. A theorem A ⇒ P remains valid as a formal result while evidence violating A can defeat its use as assurance of an actual system.

Γ remains defined on holons and respects the core’s identity and boundary discipline. Its support account establishes neither a new action permission nor the worth of acquiring further evidence.