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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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Volume 02, Issue 9

Published on: September 2026

CAUSAL RELATIVITY OF MULTI-ECHELON EVENTS: INVARIANT INTERVALS, LEAD-TIME CONES, AND FKF-COVARIANT DIAGNOSTICS

M. Waghmare R. Ingole N. Futane

Sant Gadge Baba Amravati University, Amravati, Maharashtra, India
DOI:https://doi.org/10.55041/ijcope.v2i9.239

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Abstract

Special-relativistic structure is not a metaphor pasted onto logistics. It is the minimal geometry in which a maximum propagation speed, a distinction between causal and rumoured events, and disagreement among clocks can be written without contradiction. Goods and messages in a multi-echelon network cannot outrun a finite lane speed. Receipt cannot precede release along a physical path. Planner clocks and dock clocks do not share a global simultaneity slice. This paper constructs an operational Minkowski plane whose time axis is a chosen frame clock and whose space axis is lane position scaled by the maximum admissible flow speed. Lead-time cones replace light cones. The invariant interval replaces raw coordinate delay as the quantity a digital twin should report. The distributional FKF transform is required to be covariant under the corresponding boosts and translations, so that a residue declared in one frame remains a residue in another. Charge-limited last-mile motion and append-only custody events sit inside the same causal order. The result is not a claim that warehouses curve spacetime. It is a claim that scoring delays as scalars in one privileged clock is the operational analogue of privileging a Newtonian now, and that the author’s prior lemmas already contain the objects needed to stop doing so.

Keywords: causal cone; invariant interval; relativity of simultaneity; FKF covariance; digital twin; lead time; supply-chain resilience.

How to Cite this Paper

Waghmare, M., Ingole, R. & Futane, N. (2026). Causal Relativity of Multi-Echelon Events: Invariant Intervals, Lead-Time Cones, and FKF-Covariant Diagnostics. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(9), 1-9. https://doi.org/10.55041/ijcope.v2i9.239

Waghmare, M., et al.. "Causal Relativity of Multi-Echelon Events: Invariant Intervals, Lead-Time Cones, and FKF-Covariant Diagnostics." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 9, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i9.239.

Waghmare, M.,R. Ingole, and N. Futane. "Causal Relativity of Multi-Echelon Events: Invariant Intervals, Lead-Time Cones, and FKF-Covariant Diagnostics." International Journal of Creative and Open Research in Engineering and Management 02, no. 9 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i9.239.

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  • •Published on: Sep 30 2026
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