Skip to main Communities My dashboard Log in Sign up Published April 12, 2026 | Version v1 Preprint Open The Orbital Wall: Geometric Fixation and the Cartesian Diamond Horizon Authors/Creators Smith, Kyle MacLean 1 Show affiliations 1.
Haecceitate Universali Research Group Description Caveat emptor Abstract (English) We present a geometric demonstration of the Symmetric Diamond Tile Spiral, exploring how the discrete addressing of surface regions (Tiles) reveals the Cartesian plane as a bit-perfect realization of power-law scaling. Unlike legacy point-set calculus, our manifold is built upon a Mereological foundation where discrete triangular regions, or Tiles, are the primary primitives of information. Building upon the Scaling Law established in "Beyond the Polar Wall" (Zenodo: 17756193)—where the resolution D_n scales as log_d(D_n) = n—we unveil the Spiral Count z as the discrete enumeration of Unit Shards (D_0=1). We show that the manifold is anchored not to an infinitesimal origin point, but to a fixed physical Cork, which provides the boundary condition for deterministic halting. While traditional Cartesian (x,y) coordinates remain as a forensic trace, it is the integer z that surfaces the manifold's Positional Haeccity, where perfect squares (z^2) land with bit-perfect alignment along the Cardinal Horizon (Spokes 8 and 12), revealing the parity-driven rotation of the tiled geometry. Files orbital_wall_v1.pdf Files (1.2 MB) Name Size Download all orbital_wall_v1.pdf md5:66f2e80290cc69b7dcc10404fcbc3014 1.2 MB Preview Download Additional details References 10.5281/zenodo.19382689 (Beyond the Polar Wall: Global Remainder Tracking and Side-a Normalization for Bit-Perfect Orientation in 1-bit LLMs) 10.5281/zenodo.5803948 (The Vanishing Point Probabilities of Self-Referencing Copies) arXiv:2502.02617 (TurboQuant: Online Vector Quantization) arXiv:2407.16237 (PolarQuant: Polar Quantization for Low-Bit LLM Inference) arXiv:2310.11453 (BitNet: Is 1-bit Transformer All You Need?) 10.1109/ISSCC.2014.6757323 (Computing's energy problem - Horowitz 2014) arXiv:1602.07576 (Group Equivariant Convolutional Networks) 10.1007/JHEP07(2020)067 (Event Isotropy and Optimal Transport) arXiv:2602.09341 (Auditing Multi-Agent LLM Reasoning Trees) arXiv:2602.11865 (Intelligent AI Delegation) arXiv:2602.13567 (The Agent Kernel) 347 Views 222 Downloads Show more details All versions This version Views Total views 347 347 Downloads Total downloads 222 222 Data volume Total data volume 300.4 MB 300.4 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords Symmetric Diamond Tile Spiral Cartesian Diamond Power-law scaling Mereology Scaling Law Beyond the Polar Wall Spiral Count z Side-a Normalization Silver Ratio 16-phase lattice Geometric Fixation Deterministic Halting Quantum Stabilizer Details DOI DOI Badge DOI 10.5281/zenodo.19547514 Markdown [](https://doi.org/10.5281/zenodo.19547514) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19547514.svg :target: https://doi.org/10.5281/zenodo.19547514 HTML <a href="https://doi.org/10.5281/zenodo.19547514"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19547514.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19547514.svg Target URL https://doi.org/10.5281/zenodo.19547514 Resource type Preprint Publisher Zenodo Languages English 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 13, 2026 Modified August 13, 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