{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ODT3BACYWQC45FAJU5OTQKWDEW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"72ba05765932ba44f8a62b8003895048755f020f90c092ac2b341519d4ef9683","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-04T18:07:36Z","title_canon_sha256":"49d7955dd53572bd93276324387c5d87c191333eedd4931980668acb420b0a62"},"schema_version":"1.0","source":{"id":"1402.0815","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0815","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0815v2","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0815","created_at":"2026-05-18T03:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"ODT3BACYWQC4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"ODT3BACYWQC45FAJ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"ODT3BACY","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:9ff7698cfb7dc31770f92ff0f8d338943604eb31aafd3477db95570d3bcbae09","target":"graph","created_at":"2026-05-18T03:00:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We show that the following algorithmic problem is decidable: given a $2$-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in $\\mathbf{R}^3$? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold $X$ into the 3-sphere $S^3$. The main step, which allows us to simplify $X$ and recurse, is in proving that if $X$ can be embedded in $S^3$, then there is also an embedding in which $X$ has a short meridian, i.e., an essential curve in the boundary of $X$ bounding a disk in $S^3\\setminus X$ with length bou","authors_text":"Eric Sedgwick, Ji\\v{r}\\'i Matou\\v{s}ek, Martin Tancer, Uli Wagner","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-04T18:07:36Z","title":"Embeddability in the 3-sphere is decidable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0815","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9586fd5a36d93a62483ef3189bea8b4d6d605ea911b0a5c8bfe87d6c02ffbde0","target":"record","created_at":"2026-05-18T03:00:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"72ba05765932ba44f8a62b8003895048755f020f90c092ac2b341519d4ef9683","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-04T18:07:36Z","title_canon_sha256":"49d7955dd53572bd93276324387c5d87c191333eedd4931980668acb420b0a62"},"schema_version":"1.0","source":{"id":"1402.0815","kind":"arxiv","version":2}},"canonical_sha256":"70e7b08058b405ce9409a75d382ac325b949e3c9dfad19b763b61508dc7d418c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70e7b08058b405ce9409a75d382ac325b949e3c9dfad19b763b61508dc7d418c","first_computed_at":"2026-05-18T03:00:02.452356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:02.452356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0sxdXfSVC4CorH4qqvrFp0PEwz0erbkCammmvbenHX7Wlb9BSe6v12Fj5rUhd9ukJXNW1cq2q9GMoTVTuJHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:02.452891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0815","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9586fd5a36d93a62483ef3189bea8b4d6d605ea911b0a5c8bfe87d6c02ffbde0","sha256:9ff7698cfb7dc31770f92ff0f8d338943604eb31aafd3477db95570d3bcbae09"],"state_sha256":"a1915dd7f52e6eb842075651a1bedab13308b2c3652027d404a546d0f71e691e"}