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PreprintCC BY 4.0Zenodo

Topological Resolution of the Hodge Conjecture: Quantum-Geometric Cycle Quantization via 5D Information-Metric Manifolds

  • Ashok N. Bhaskarwar1
  • Isha Arora1
  • Google Gemini2
  1. 1Indian Institute of Technology Delhi
  2. 2Google (United States)
Open at sourcePDFDOICite

Abstract

This disclosure addresses the classical Hodge Conjecture for projective complex algebraic

varieties. By embedding complex manifolds into the five-dimensional information-metric

vacuum space M5 of the Cosmic Awareness Theory of Liquid Spacetime (CATLS) framework,

we demonstrate that rational de Rham cohomology classes of type (p, p) correspond strictly

to quantized stationary resonant states. We prove that the invariant saturation suture

constant Ceff forces continuous harmonic cycles to collapse into rational linear combinations of

algebraic cycles, establishing the validity of the Hodge conjecture as a fundamental topological

conservation law of liquid spacetime.

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Cite

BibTeXRIS
BibTeX
@misc{bhaskarwar2026topological,
  title = {{Topological Resolution of the Hodge Conjecture: Quantum-Geometric Cycle Quantization via 5D Information-Metric Manifolds}},
  author = {Ashok N. Bhaskarwar and Isha Arora and Google Gemini},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23469288},
  url = {https://zenodo.org/records/23469288},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Topological Resolution of the Hodge Conjecture: Quantum-Geometric Cycle Quantization via 5D Information-Metric Manifolds
AU  - Ashok N. Bhaskarwar
AU  - Isha Arora
AU  - Google Gemini
PY  - 2026
DA  - 2026/10/19
PB  - Zenodo
DO  - 10.5281/zenodo.23469288
UR  - https://zenodo.org/records/23469288
AB  - This disclosure addresses the classical Hodge Conjecture for projective complex algebraic  varieties. By embedding complex manifolds into the five-dimensional information-metric  vacuum space M5 of the Cosmic Awareness Theory of Liquid Spacetime (CATLS) framework,  we demonstrate that rational de Rham cohomology classes of type (p, p) correspond strictly  to quantized stationary resonant states. We prove that the invariant saturation suture  constant Ceff forces continuous harmonic cycles to collapse into rational linear combinations of  algebraic cycles, establishing the validity of the Hodge conjecture as a fundamental topological  conservation law of liquid spacetime.
ER  -