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International Journal of Creative and Open Research in Engineering and Management

A Peer-Reviewed, Open-Access International Journal Supporting Multidisciplinary Research, Digital Publishing Standards, DOI Registration, and Academic Indexing.
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ISSN: 3108-1754 (Online)
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Peer Review: Double Blind
Volume 02, Issue 10

Published on: October 2026

GEOMETRY OF LEAD-TIME SPECTRA: BULLWHIP AS CURVATURE ON A CONSTRAINED MANIFOLD

Tale A V. A. Sharma Gupta A

Department of Mathematics, Smt. Narsamma Arts, Commerce and Science college, Amravati 444606
DOI:https://doi.org/10.55041/ijcope.v2i10.010

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Abstract

A lead-time spectrum is usually read as a gain: a peak means amplification, and bullwhip is the height of that peak. This paper reads the spectrum as a curve on a constrained manifold. Positivity, unit mass, and shift invariance are the constraints. Bullwhip is the curvature of the curve, not the value of the chart coordinate. The two-sided FKF transform supplies the chart and nothing else. A change of damper or window moves the coordinates and does not, by itself, change the curvature. Residues weight an identified covector. A null pole is a gap, not a flat spectrum. Curves illustrate the spectrum, the constraint, the curvature score against a gain score, the chart, the residues, the recovery objection, and concentrated modal energy. Twins and ledgers should publish the curvature and the chart hash, not a gain taken from one coordinate.

Keywords: lead-time spectrum; constrained manifold; bullwhip curvature; FKF chart; shift invariance; residue covector.

How to Cite this Paper

A, T., Sharma, V. A. & A, G. (2026). Geometry of Lead-Time Spectra: Bullwhip as Curvature on a Constrained Manifold. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(10), 1-9. https://doi.org/10.55041/ijcope.v2i10.010

A, Tale, et al.. "Geometry of Lead-Time Spectra: Bullwhip as Curvature on a Constrained Manifold." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 10, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i10.010.

A, Tale,V. Sharma, and Gupta A. "Geometry of Lead-Time Spectra: Bullwhip as Curvature on a Constrained Manifold." International Journal of Creative and Open Research in Engineering and Management 02, no. 10 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i10.010.

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  • •Published on: Oct 08 2026
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