{"paper":{"title":"Beyond the Space-Time Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Jerzy Kr\\'ol, Michael Heller","submitted_at":"2017-11-24T15:55:48Z","abstract_excerpt":"In General Relativity a space-time $M$ is regarded singular if there is an obstacle that prevents an incomplete curve in $M$ to be continued. Usually, such a space-time is completed to form $\\bar{M} = M \\cup \\partial M$ where $\\partial M$ is a singular boundary of $M$. The standard geometric tools on $M$ do not allow \"to cross the boundary\". However, the so-called Synthetic Differential Geometry (SDG), a categorical version of standard differential geometry based on intuitionistic logic, has at its disposal tools permitting doing so. Owing to the existence of infinitesimals one is able to pene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09027","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}