"What" is an Epit Mathematical Foundations of Epistemic Structure
Jason Perry
Source abstract
We introduce the epistemic unit (epit), a minimal formal structure for representing units of knowledge. Five axioms (EP1-EP5) define the epit as a tuple E = <(A,B,C), (R1,R2,R3), tau>: an ordered triad, a relation triple in {-1,0,+1}^3, and an iso-type tau = iso(R1,R2,R3) in {0,...,6}. This tuple is the unique minimal structure satisfying all five axioms (Theorem 1.2). The 27 relation triples partition under S3 into 7 iso-types (Proposition 2.2). From 20 pure concepts on a 4-simplex of five epistemic axes, the framework generates 536 depth-0 epits (Proposition 2.7). A constructor F: E^3 x Tour3 -> E produces a countably infinite, well-ordered space (Theorem 3.1) with growth N_n <= 1668^(3^n) (Proposition 3.6). A Gödel limit epit dalet_0, well-formed but undecidable, establishes necessary incompleteness (Proposition 4.4). The axiom system is satisfiable, independent, non-trivial, and relatively consistent with respect to ZFC (Proposition 5.1).
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