
This technical note develops a methodology for locating and classifying objects in analytic, arithmetic, and inherited families by separating two different tasks: continuous navigation and exact structural identification. A structural address is written as \operatorname{Addr}(x)=\bigl(\Sigma_c(x),\delta(x)\bigr), where the continuous signature \Sigma_c provides local proximity information and the discrete invariant \delta determines exact stratum membership. The note shows that continuous signatures provide reliable local coordinates only where the signature map is a local embedding, while exact membership is recoverable from continuous data only when the discrete invariant factors through the continuous signature. For inherited systems, a marker supports well-defined reduced dynamics precisely when its fibers are compatible with the inheritance map; closure of the reduced dynamics and separation of structural classes are shown to be independent requirements. The framework is illustrated with three controls. In the detuned Ramanujan 1/\pi family, the parameter moves through one fixed hypergeometric local system: the observable varies analytically, the convergence rate changes monotonically, and the exact value at D=396 is not signaled by a local analytic extremum. In the beta/gamma family J(s)=\frac{\Gamma(s+1)^2}{\Gamma(2s+2)}, continuous parameter proximity is shown to differ from exact gamma-period relations, with reflection and multiplication identities providing discrete structural relations that are not captured by raw parameter distance alone. A minimal four-state inheritance model then exhibits markers that close but fail to separate, markers that separate but fail to close, and a composite marker that satisfies both requirements. The note is methodological rather than theorem-driven: its contribution is the synthesis of classical tools into a structural-address framework for surveying continuous neighborhoods, identifying exact strata, and testing whether reduced markers remain compatible under inheritance.
structural address; continuous signature; discrete invariant; structural stratum; local embedding; period map; hypergeometric function; gamma values; complex multiplication; factor map; inheritance system; congruence relation; Markov lumpability; coarse-graining; model reduction; false neighbors; structural navigation
structural address; continuous signature; discrete invariant; structural stratum; local embedding; period map; hypergeometric function; gamma values; complex multiplication; factor map; inheritance system; congruence relation; Markov lumpability; coarse-graining; model reduction; false neighbors; structural navigation
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