{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O2LN6D5MJV74VX3XIP24YOLNRF","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":"b45dab3972340fe7585f0544fd16697e109f59d7ebf3e538cbf949b7b63fcdf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-08T17:29:16Z","title_canon_sha256":"f1c154d970e04a2ebea0b380c4f8a2ba3f0d7c52cac0472e58a30325520eadcb"},"schema_version":"1.0","source":{"id":"1905.03226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03226","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03226v1","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03226","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"pith_short_12","alias_value":"O2LN6D5MJV74","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"O2LN6D5MJV74VX3X","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"O2LN6D5M","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:2aecb17bad13f74acdfb865fecd3548bf1abd494524bfa1adcaeb03d513dac30","target":"graph","created_at":"2026-05-17T23:46:42Z","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":"In this paper, we give a complete description of the language of geodesic words for the discrete Heisenberg group $H(\\mathbb{Z})$ with respect to the standard two-element generating set. More precisely, we prove that the only dead end elements in $H(\\mathbb{Z})$ are nontrivial elements of the commutator subgroup. We give a description of their geodesic representatives, which are called dead end words. The description is based on a minimal perimeter polyomino concept. Finally, we prove that any geodesic word in $H(\\mathbb{Z})$ is a prefix of a dead end word.","authors_text":"Ilya Alekseev, Ruslan Magdiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-08T17:29:16Z","title":"The language of geodesics for the discrete Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03226","kind":"arxiv","version":1},"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":"sha256:1483bf4a54970db4eeb66c03090b944b307b42f48408667684e732adbab51cec","target":"record","created_at":"2026-05-17T23:46:42Z","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":"b45dab3972340fe7585f0544fd16697e109f59d7ebf3e538cbf949b7b63fcdf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-05-08T17:29:16Z","title_canon_sha256":"f1c154d970e04a2ebea0b380c4f8a2ba3f0d7c52cac0472e58a30325520eadcb"},"schema_version":"1.0","source":{"id":"1905.03226","kind":"arxiv","version":1}},"canonical_sha256":"7696df0fac4d7fcadf7743f5cc396d897530ec490c799f014fd2bd57fef80064","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7696df0fac4d7fcadf7743f5cc396d897530ec490c799f014fd2bd57fef80064","first_computed_at":"2026-05-17T23:46:42.504769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:42.504769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IjyI5CxJO9WgzB4mBvhmZiw0jZBWLzsJRWttALZPQLClGu3J3DXzv46UGQFBQPFdL6aC8VJkZuiGedo0y7rqDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:42.505391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1483bf4a54970db4eeb66c03090b944b307b42f48408667684e732adbab51cec","sha256:2aecb17bad13f74acdfb865fecd3548bf1abd494524bfa1adcaeb03d513dac30"],"state_sha256":"45553eb8a3ab05513f3cb337f12d52d258690f5bb96b3116bfd856faaad9d1e4"}