Skip to main Communities My dashboard Log in Sign up Theoretical Physics There is a newer version of the record available. Published April 18, 2026 | Version v2 Preprint Open No Free Parameters --- The Fixed Point Law Authors/Creators Kreder III, Karl J (Contact person) Description We take the exact self-reproduction equation T_K(Σ) = K as primitive. Nothing analytically or geometrically precedes this requirement. The point of the theory is that admissibility, overlap structure, induced geometry, and normalization are selected by the existence of a kernel that closes on itself. A kernel satisfying this exact self-consistency requirement is called a Distinguished Reproducing Kernel (DRK). We study the realized hyperbolic class in which the closure obstruction can be computed explicitly. In that class, the weighted closure fails exact reproduction by a purely scalar obstruction. We compute that obstruction exactly, identify its residue with boundary contact volume, and reformulate the same asymptotics intrinsically using contrast-ball truncations. Any uncancelled scalar residue yields T_K = cK with c ≠ 1 and therefore violates the primitive fixed-point equation. Exact non-projective closure consequently forces all normalization channels to collapse into one unified exact normalization package. This unified exact normalization forces complex dimension 2 and canonical holomorphic sectional curvature −1. On the exact complex-hyperbolic branch in complex dimension 2, the raw kernel diagonal is K(z,z) = c_K(1−||z||²)^−3, while the canonically normalized metric representative is g_* = 2 ∂∂̄(−log(1−||z||²)). It follows that the realized geometry selected by the equation is the canonically normalized complex hyperbolic plane CH², hence real dimension 4. Files No_Free_Parameters-4.pdf Files (236.2 kB) Name Size Download all No_Free_Parameters-4.pdf md5:c4155cddef7c41dbc92cd0bd74e19d43 236.2 kB Preview Download 2K Views 592 Downloads Show more details All versions This version Views Total views 2,328 64 Downloads Total downloads 592 168 Data volume Total data volume 172.1 MB 42.0 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Details DOI DOI Badge DOI 10.5281/zenodo.19645764 Markdown [](https://doi.org/10.5281/zenodo.19645764) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19645764.svg :target: https://doi.org/10.5281/zenodo.19645764 HTML <a href="https://doi.org/10.5281/zenodo.19645764"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19645764.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19645764.svg Target URL https://doi.org/10.5281/zenodo.19645764 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 18, 2026 Modified April 18, 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