Gravitational Structure from the Distinguished Reproducing Kernel | Zenodo Skip to main Communities My dashboard Log in Sign up Published April 23, 2026 | Version v1 Preprint Open Gravitational Structure from the Distinguished Reproducing Kernel Authors/Creators Kreder III, Karl J (Contact person) Description Taking as upstream input the Distinguished Reproducing Kernel fixed-point law, which forces the realized branch together with its exact normalization package, this paper develops the gravitational specialization of the exact-normalized semiclassical branch. Starting from the semiclassical Hamilton–Jacobi structure already derived upstream, the paper shows that any admissible gravitational theory must arise by a closure-compatible restriction of the realized branch. The quadratic term of the restricted phase law is shown to be uniquely inherited from the realized branch and to carry no residual scalar normalization freedom. When the closure-compatible sector is realized in metric variables, every ultralocal diffeomorphism-covariant quadratic Hamiltonian density is forced into the DeWitt-type family. Exact closure of the full constraint system then fixes the remaining trace-weight parameter uniquely to the Einstein value. The theorem-level outputs are the existence of a closure-compatible gravitational restriction of the semiclassical branch, the uniqueness of the induced quadratic form on that sector, the DeWitt-type classification of ultralocal diffeomorphism-covariant quadratic forms, the constraint-closure selection of the Einstein value, and the resulting Einstein-sector gravitational Hamilton–Jacobi equation. Files Gravitational_Structure.pdf Files (250.9 kB) Name Size Download all Gravitational_Structure.pdf md5:c3e3ca328192eed6f30c342c00ee1a7d 250.9 kB Preview Download 38 Views 25 Downloads Show more details All versions This version Views Total views 38 38 Downloads Total downloads 25 25 Data volume Total data volume 7.0 MB 7.0 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Details DOI DOI Badge DOI 10.5281/zenodo.19708823 Markdown [](https://doi.org/10.5281/zenodo.19708823) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19708823.svg :target: https://doi.org/10.5281/zenodo.19708823 HTML <a href="https://doi.org/10.5281/zenodo.19708823"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19708823.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19708823.svg Target URL https://doi.org/10.5281/zenodo.19708823 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 Citation Export Technical metadata Created April 23, 2026 Modified April 23, 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