2012.01005
THE TAKAGI CURVE AND THE β-CANTOR FUNCTION FROM MECHANICAL LAWS
Javier Rodríguez-Cuadrado, Jesús San Martín
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s core limits for vertical and horizontal displacements and the emergence of a Takagi curve and Ct-terms match the model’s derivations. However, the paper overstates the identification of each Ct with an inverse β–Cantor function without stating the necessary restriction t<1/2 (equivalently β∈(0,1)); it also states the Takagi ‘fractal dimension’ DΨ=log(a/4)/log 2 without qualifying that the graph dimension is 1 when a≤4. The model’s solution includes these missing hypotheses and gives a clean argument showing the P-dependent term vanishes, so the limits exist without any special cancellation.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper’s analytical derivations connecting a hierarchical elastic tree to a Takagi curve and to Ct-type series (interpreted as inverse β–Cantor functions) are sound and illuminating. However, two missing qualifications reduce correctness: the inverse β–Cantor identification requires t<1/2 (β∈(0,1)), and the Takagi graph’s dimension is 1 when a≤4. These clarifications are straightforward to add and do not alter the main contributions.