Powered by OpenAIRE graph
Found an issue? Give us feedback
ZENODOarrow_drop_down
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
versions View all 4 versions
addClaim

Structural Addresses: Continuous Proximity, Discrete Membership, and Compatible Markers in Inheritance Systems

Authors: De Jesus, Elias;

Structural Addresses: Continuous Proximity, Discrete Membership, and Compatible Markers in Inheritance Systems

Abstract

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.

Keywords

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

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!