{"id":21435539,"url":"https://github.com/mountain/aeg-paper","last_synced_at":"2026-02-23T00:35:19.954Z","repository":{"id":136938675,"uuid":"560027460","full_name":"mountain/aeg-paper","owner":"mountain","description":"a paper about Arithmetic Expression Geometry (AEG), a new way to think about computation, analysis, and geometry","archived":false,"fork":false,"pushed_at":"2025-12-27T13:28:11.000Z","size":12312,"stargazers_count":11,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"main","last_synced_at":"2025-12-29T09:04:07.038Z","etag":null,"topics":["arithmetic-expression-geometry","geometry"],"latest_commit_sha":null,"homepage":"https://onecorner.org/curiosity/aegeom/","language":"TeX","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"cc0-1.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/mountain.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2022-10-31T15:34:52.000Z","updated_at":"2025-12-27T13:28:15.000Z","dependencies_parsed_at":"2025-12-18T12:06:11.727Z","dependency_job_id":null,"html_url":"https://github.com/mountain/aeg-paper","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/mountain/aeg-paper","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mountain%2Faeg-paper","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mountain%2Faeg-paper/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mountain%2Faeg-paper/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mountain%2Faeg-paper/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mountain","download_url":"https://codeload.github.com/mountain/aeg-paper/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mountain%2Faeg-paper/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29733119,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-22T20:09:16.275Z","status":"ssl_error","status_checked_at":"2026-02-22T20:09:13.750Z","response_time":110,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["arithmetic-expression-geometry","geometry"],"created_at":"2024-11-22T23:44:33.467Z","updated_at":"2026-02-23T00:35:19.926Z","avatar_url":"https://github.com/mountain.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"# aeg-paper\n\n[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.16938960.svg)](https://doi.org/10.5281/zenodo.16938960)\n\nThis paper introduces a novel geometric framework for studying arithmetic expressions, \nestablishing a rigorous connection between algebraic operations and hyperbolic geometry.\nWe formalize arithmetic expressions as syntactic structures and demonstrate how they can be embedded into continuous geometric spaces where addition and multiplication correspond to movements along orthogonal directions.\nCentral to our approach is a flow equation that governs how expression values propagate through this geometric space.\nWe construct the first kind arithmetic expression space $\\mathfrak{E}_1$ on the upper half-plane with a hyperbolic metric,\nwhere the assignment function satisfies the flow equation and serves as an eigenfunction of the Laplacian.\nThis construction reveals that arithmetic torsion—the non-commutativity of addition and multiplication—directly\ncorresponds to geometric area, analogous to how curvature measures deviation from flatness.\nThe paper establishes arithmetic expressions as geometric objects with intrinsic invariants,\nopening new avenues for exploring the interplay between computation and geometry.\n\n\n## Building the PDF\n\nEnsure that `pdflatex` and `bibtex` are available. Then run:\n\n```bash\n./build.sh\n```\n\n### Building with Docker\n\nIf a TeX environment is not installed locally, use Docker:\n\n```bash\ndocker build -t aeg-paper .\ndocker run --rm -v $(pwd):/work aeg-paper\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmountain%2Faeg-paper","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmountain%2Faeg-paper","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmountain%2Faeg-paper/lists"}