Chapter 54: The Complete Dependency Chain

This chapter is an audit. It traces the complete logical path from the seven axioms K0–K6 of Book I through every definition, lemma, and theorem of Books I and II to the Central Theorem O(τ³) ≅ A_spec(𝕃) (the relevant theorem, II.T40). The dependency is organized as a directed acyclic graph (the relevant definition, II.D62) whose unique sources are the axioms and whose unique sink is the Central Theorem. The Complete Dependency Chain (Remark [rem:complete-dependency], II.R17) then verifies that every step in this graph is earned from within the τ-framework: no topology was imported, no geometry was assumed, no transcendentals were postulated, no complex analysis was borrowed, no set theory was presupposed, and no category-theoretic axioms were adopted without proof. This chapter is both a reference map and a proof of intellectual honesty.