J
plain-language theorem explainer
The definition introduces the J-cost functional J(x) = (x + x^{-1})/2 - 1 on the reals. Researchers deriving double-entry ledger structure from J-symmetry in the Ledger Forcing module would cite this as the base cost measure. The definition is a direct noncomputable algebraic expression chosen to match the T5 J-uniqueness condition.
Claim. The cost functional is defined by $J(x) = (x + x^{-1})/2 - 1$ for $x : ℝ$.
background
The Ledger Forcing module proves that J-symmetry forces double-entry ledger structure, per the module documentation. The J functional acts as the central cost measure whose symmetry properties are developed in sibling declarations such as J_symmetric and reciprocity. Upstream results supply supporting lists including seven plot families, eight kinship systems, seven ore classes, seven Greek modes, and a MetaRealizationCert structure for self-reference axioms.
proof idea
This is a definition rather than a theorem. It consists of a direct assignment of the algebraic expression (x + x^{-1})/2 - 1 with no lemmas, tactics, or reduction steps.
why it matters
This definition anchors the Ledger Forcing module and realizes the J-uniqueness at T5 of the UnifiedForcingChain. It supplies the cost functional needed to derive reciprocity and balanced lists that enforce double-entry structure. The declaration touches the framework step linking J-symmetry to ledger axioms but leaves open how this extends to the full phi-ladder and physical constants.
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