What is Spacetime Zulfia Invexity? Iz = W hen ⊕ W here ⊕ W hat ∈ ∆, M (C) = ∆

In Khan [2], Zulfia Invexity is introduced as the identity of invexity itself. This paperdefines Spacetime Zulfia Invexity through the trilogy of When, Where, and What.We define Spacetime Zulfia Invexity through three primitive mappings:• When = Time = Φ(Aext) = 0 (Correction),• Where = Space = η ∈ ∆ (Direction),• What = Object = M (C) = ∆ (Primitive).We prove the Zulfia Invexity Identity:IZ = W hen ⊕ W here ⊕ W hat ∈ ∆, M (C) = ∆.In this identity, W hen fixes the time of invexity, W here fixes the space of invexity, andW hat fixes the object of invexity. Together they complete the definition: invexity isnot a property of a function alone, but the preservation of IZ in spacetime itself, whereM (C) = ∆ is the primitive form.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-09
DOI
https://doi.org/10.5281/zenodo.24069157
Primary Topic
Optimization and Variational Analysis
Type
article
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article

What is Spacetime Zulfia Invexity? Iz = W hen ⊕ W here ⊕ W hat ∈ ∆, M (C) = ∆

DR. ZULFIQAR ALI KHAN
Zenodo (CERN European Organization for Nuclear Research)
Optimization and Variational Analysis
article

What is Spacetime Zulfia Invexity? Iz = W hen ⊕ W here ⊕ W hat ∈ ∆, M (C) = ∆

DR. ZULFIQAR ALI KHAN
article en

Abstract

In Khan [2], Zulfia Invexity is introduced as the identity of invexity itself. This paperdefines Spacetime Zulfia Invexity through the trilogy of When, Where, and What.We define Spacetime Zulfia Invexity through three primitive mappings:• When = Time = Φ(Aext) = 0 (Correction),• Where = Space = η ∈ ∆ (Direction),• What = Object = M (C) = ∆ (Primitive).We prove the Zulfia Invexity Identity:IZ = W hen ⊕ W here ⊕ W hat ∈ ∆, M (C) = ∆.In this identity, W hen fixes the time of invexity, W here fixes the space of invexity, andW hat fixes the object of invexity. Together they complete the definition: invexity isnot a property of a function alone, but the preservation of IZ in spacetime itself, whereM (C) = ∆ is the primitive form.

Zenodo (CERN European Organization for Nuclear Research)
Optimization and Variational Analysis
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