Mathematical Reconstruction and Calibration of a Candidate MD2 Operator on the Complex Projective Plane (CP2)
Abstract
This technical note presents a mathematical reconstruction and calibration of a candidate MD2 operator on the complex projective plane CP2.
The operator is formulated as a correspondence-induced map:
T(α) = π₂,(π₁α ∧ κ₂),
where X is a smooth compact complex manifold without boundary and κ₂ is a smooth closed differential form of degree 2n on X × X.
The note examines the induced action on cohomology and provides a calibration example on CP2, using the cohomology ring H*(CP2, Q) = Q[h]/(h³). For the specified kernel class, the induced map satisfies T = c₁h. The diagonal-class example is discussed as an identity correspondence.
The results establish a mathematically formulated candidate operator and a specific calibration example. They do not establish equivalence with the original MD2 formulation, a general mechanism proving algebraicity of Hodge classes, or a proof of the Hodge conjecture. The smoothness of the kernel and the estimates required for smoothness of the associated spectral construction must be treated according to the assumptions stated in the note.
This work is intended as a technical and mathematical reconstruction for further independent analysis and verification.
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BibTeX
@misc{artsybashev2026mathematical,
title = {{Mathematical Reconstruction and Calibration of a Candidate MD2 Operator on the Complex Projective Plane (CP2)}},
author = {ANDRII.A ARTSYBASHEV},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23572491},
url = {https://zenodo.org/records/23572491},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mathematical Reconstruction and Calibration of a Candidate MD2 Operator on the Complex Projective Plane (CP2)
AU - ANDRII.A ARTSYBASHEV
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23572491
UR - https://zenodo.org/records/23572491
AB - This technical note presents a mathematical reconstruction and calibration of a candidate MD2 operator on the complex projective plane CP2. The operator is formulated as a correspondence-induced map: T(α) = π₂,(π₁α ∧ κ₂), where X is a smooth compact complex manifold without boundary and κ₂ is a smooth closed differential form of degree 2n on X × X. The note examines the induced action on cohomology and provides a calibration example on CP2, using the cohomology ring H*(CP2, Q) = Q[h]/(h³). For the specified kernel class, the induced map satisfies T = c₁h. The diagonal-class example is discussed as an identity correspondence. The results establish a mathematically formulated candidate operator and a specific calibration example. They do not establish equivalence with the original MD2 formulation, a general mechanism proving algebraicity of Hodge classes, or a proof of the Hodge conjecture. The smoothness of the kernel and the estimates required for smoothness of the associated spectral construction must be treated according to the assumptions stated in the note. This work is intended as a technical and mathematical reconstruction for further independent analysis and verification.
ER -