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On the Bibliometric Integrity of Scientific Literature: A Functional Analytic Approach to Self-Citation Dynamics 1

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Abstract

This paper provides a rigorous mathematical framework to evaluate the structural integrity of academic literature subject to self-citation. By modelling a research paper as an operator mapping existing scientific knowledge into an updated epistemic space, it utilises functional analytic tools to analyse the boundary conditions of legitimate self-referencing, thus proving that an excessive self-citation rate—specifically approaching the threshold of α = 0.75—collapses the underlying Banach space of global scientific discourse into a trivial, low-dimensional invariant subspace, effectively inducing an epistemic “echo chamber.” It establishes the existence of an optimal citation operator driven by the spectral properties that justify modern automated desk-rejection thresholds.

Keywords

Hilbert space; projection operators; bibliometrics; self-citation; spectral radius. 1

References

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