WUCC & BVP Axioms & Mathematical Derivations

Thisdocument rebuilds the R3 manuscript of the WUCC & BVP framework as an R4consistent revision. Every defect identified in the R4 audit is repaired: the dimensionalassignments are made self-consistent in1+1dimensions, the kink sector and charge conventions are statedc orrectly, the triadic sector is reclassified under an explicit postulate,the induced-geometry construction is given consistent units and a correct rank statement,and the restoring-force identity is corrected in both sign convention and couplingfactor.Allassumptions that R3 used implicitly are numbered as postulates P1–P7.Every claim carriesone of the status tags [M](mathematically correct as written), [A](correc tonly under thestated assumptions), [P] (matches a standard known result),or [H] (physical hypothesis,unverified).The document contains no experimental orobservational evidence,and none isadded here.