Skip to main Communities My dashboard Log in Sign up There is a newer version of the record available. Published April 19, 2026 | Version 1.0 Preprint Open Gravity and Entanglement as Conjugate Variables: A Stokes-Type Conservation Law on Fl₁,₂(ℂ³) × ℂP¹ Authors/Creators Kirk, Harold D. Description This paper develops a geometric framework in which gravity and quantum entanglement arise as two canonical reductions of a single compact Kähler manifold: M = Fl₁,₂(ℂ³) × ℂP¹ Within this setting, a Stokes-type conservation law is proved relating bulk integrated content to a canonical boundary primitive, evolving synchronously under moment-map gradient flow. A Hodge-theoretic normalization uniquely fixes the primitive, allowing a sharp gravity–entanglement conjugacy conjecture to be posed invariantly. The framework further proposes: Gravity and entanglement are not separate phenomena requiring unification, but dual reductions of one geometric object. The Bekenstein–Hawking entropy coefficient 1/4 emerges as a structural projection ratio dim_ℝ m₁₃ / dim_ℝ M = 2/8, not a fitted constant. A massless spin-2 parity partner to the graviton is predicted, coupling selectively to entanglement-sector sources. Five experimental channels constrain it: parity-violating gravitational-wave polarization, quasi-normal mode doubling, correlated gravitational noise from The four-term Morse decomposition of α⁻¹ reproduces the measured fine-structure constant to 0.07 ppb (0.65σ) with no free parameters, using only the geometric invariants (8, 2, π) of M—an independent coefficient-level witness for the conjugacy. The information paradox, ER=EPR, AdS/CFT holography, decoherence, and wave–particle duality are reframed as further instances of the same Stokes-dual structure. The paper separates: Part I — Proven Core: conservation law, Hodge primitive, global volume preservation. Part II — Conjectural Extension: sharp conjugacy, partner mode, coefficient coherence. Part III — Interpretive Consequences: quantum gravity reframed as simultaneous necessity of both reductions. This work aims to provide a mathematically explicit geometric route linking gravitation, information, and symmetry structure. Files Kirk_2026_Gravity and Entanglement as Conjugate Variables_A Stokes-Type Conservation Law on Fl₁,₂(ℂ³) × ℂP¹.pdf Files (439.0 kB) Name Size Download all Kirk_2026_Gravity and Entanglement as Conjugate Variables_A Stokes-Type Conservation Law on Fl₁,₂(ℂ³) × ℂP¹.pdf md5:f379fb60502770b144a205818a4c8ba9 439.0 kB Preview Download Additional details Related works Is supplemented by Preprint: 10.5281/zenodo.18662524 (DOI) Preprint: 10.5281/zenodo.19296899 (DOI) Preprint: 10.5281/zenodo.19298041 (DOI) Preprint: 10.5281/zenodo.19117486 (DOI) Preprint: 10.5281/zenodo.19238002 (DOI) Dates Issued 2026-04-19 126 Views 132 Downloads Show more details All versions This version Views Total views 126 86 Downloads Total downloads 132 107 Data volume Total data volume 70.4 MB 53.8 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords quantum gravity entanglement gravity Kähler geometry flag manifold symplectic geometry Stokes theorem information paradox Bekenstein-Hawking entropy Fisher information geometric unification mathematical physics emergent spacetime CP¹ Fl₁,₂(ℂ³) ER=EPR AdS/CFT Page curve decoherence wave–particle duality Details DOI DOI Badge DOI 10.5281/zenodo.19655288 Markdown [](https://doi.org/10.5281/zenodo.19655288) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19655288.svg :target: https://doi.org/10.5281/zenodo.19655288 HTML <a href="https://doi.org/10.5281/zenodo.19655288"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19655288.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19655288.svg Target URL https://doi.org/10.5281/zenodo.19655288 Resource type Preprint Publisher Zenodo Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Copyright Copyright (c) 2026 Harold Kirk Citation Export Technical metadata Created April 19, 2026 Modified April 24, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies