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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Fractal Non-Closure

Authors: Close, Larsen James;

Fractal Non-Closure

Abstract

Fractals make non-closure visible because under magnification, the non-attainment of a terminal witness is more than mere absence. Smooth objects close under zoom by yielding a tangent element. Exactly self-similar objects close by return. The target fractal case does neither: the instance under magnification does not settle to one form or one finite orbit. What may stabilize instead is a law of instancing: a scenery distribution, invariant measure, or statistical pattern one level up. The asymmetric commuting square is the minimal grammar for this situation. It certifies lawful reading across loss, but it does not say which distinctions a reading has retained; the one-point reading commutes with everything while retaining no distinction. Fractal non-closure therefore names three tasks: identify the closure not attained under magnification, identify the law-level closure that may replace it, and state the domain’s collapse condition so that the resulting law remains informative for that domain.

Keywords

invariant measures, ergodic theory, self-similarity, non-closure, tangent measures, magnification, scenery flow, philosophy of mathematics, dynamical systems, fractal geometry, factor systems, commuting square, renormalization

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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
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