{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SQKHGS2PJB7F5HTNGU4Y6YGPUO","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":"512f16b5925811df162531081985bf9b9c7171fe3614d65b9442b56f93ef0487","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-10T13:30:35Z","title_canon_sha256":"f943fa833cfb3fe4c7fab8b674a72394b6d0020266e200b13536a1b21cebce68"},"schema_version":"1.0","source":{"id":"0912.1981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1981","created_at":"2026-07-05T02:08:56Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1981v1","created_at":"2026-07-05T02:08:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1981","created_at":"2026-07-05T02:08:56Z"},{"alias_kind":"pith_short_12","alias_value":"SQKHGS2PJB7F","created_at":"2026-07-05T02:08:56Z"},{"alias_kind":"pith_short_16","alias_value":"SQKHGS2PJB7F5HTN","created_at":"2026-07-05T02:08:56Z"},{"alias_kind":"pith_short_8","alias_value":"SQKHGS2P","created_at":"2026-07-05T02:08:56Z"}],"graph_snapshots":[{"event_id":"sha256:5554233b37ad6a47b8b23fb00e4f8795fde46e5b21bc03cec086169514880e38","target":"graph","created_at":"2026-07-05T02:08:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0912.1981/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Pimenov algebra with two generators is defined and some of its properties are shown. Some exact matrix over the Pimenov algebra representations of the motions group of Galilean plane (the Galilean group) are considered. A geometric interpretation of them is giving. We consider also a exact representation of the Galilean group by elements of Grassmann algebra.","authors_text":"Dmitry Efimov, Igor Kostyakov, Vasiliy Kuratov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-10T13:30:35Z","title":"On exact representations of the motions group of Galilean plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1981","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:bb79f7ee07b6822ef5de5c493305631429267343f00183b2eb925dc594957776","target":"record","created_at":"2026-07-05T02:08:56Z","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":"512f16b5925811df162531081985bf9b9c7171fe3614d65b9442b56f93ef0487","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-10T13:30:35Z","title_canon_sha256":"f943fa833cfb3fe4c7fab8b674a72394b6d0020266e200b13536a1b21cebce68"},"schema_version":"1.0","source":{"id":"0912.1981","kind":"arxiv","version":1}},"canonical_sha256":"9414734b4f487e5e9e6d35398f60cfa384fd94a37a16fce234d6d9c011299347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9414734b4f487e5e9e6d35398f60cfa384fd94a37a16fce234d6d9c011299347","first_computed_at":"2026-07-05T02:08:56.288833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:08:56.288833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NuTQQVNqbbnwstfscuJaNcwC1X5sSjLj3Y8WRC0brM1/yyVXXDyRGu4iyFUkq7V1tmc0U64ABd1/gmvtIhY6Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:08:56.289387Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb79f7ee07b6822ef5de5c493305631429267343f00183b2eb925dc594957776","sha256:5554233b37ad6a47b8b23fb00e4f8795fde46e5b21bc03cec086169514880e38"],"state_sha256":"637e78e2d6ae13d624523300c5e802deaadd883983916c80f7c1d1f19cb461f7"}