Minimal Axioms of Causal Inheritance: An Axiomatic Construction from Update Identity to Structural Generation

Minimal Axioms of Causal Inheritance presents a parameter-free axiomatic construction in which two structural channels preserve an identical parent-to-child update law. The minimal causal conditions select q=2,⁼q+1=3. From the derived pair (q,q⁾, the structural sequences X(n,s)=q^ qⁿ+s,(n):=X(n,0), and Y(n)=qⁿ⁺¹-1. are generated. Their normalized product map is P(n)=X(n)Y(n)/q^. At the distinguished arguments $1$, q, and q², (P(1),P(q),P(q²))=(6,28,496). which coincide with the first three even perfect numbers. Version 1.0 reorganizes the downstream construction so that the structural ratios R and S are defined directly from the generated $X/Y$ hierarchy: R=X(q)^/X(1)=13/6, S=Y(q²)/X(q⁾=31/24, The second relation gives the compact terminal ratio q/S=X(q²)/Y(q²)=48/31. The product-map expressions remain as exact equivalent closure representations, R=q+1/P(1), S=P(q²)P(1)qP(1), and R-S=P(q)qP(1)-1=7/8. rather than as the primary definitions of R and S. The resulting logical structure is causal inheritance(q,q⁾(X,Y). with the two downstream constructions (X,Y) P,(X,Y)(R,S). The framework is formulated at a pre-observational structural layer (L1). No observational constant is used to determine q, q^, X, Y, P, R, or S.