{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:SQKHGS2PJB7F5HTNGU4Y6YGPUO","short_pith_number":"pith:SQKHGS2P","canonical_record":{"source":{"id":"0912.1981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-10T13:30:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f943fa833cfb3fe4c7fab8b674a72394b6d0020266e200b13536a1b21cebce68","abstract_canon_sha256":"512f16b5925811df162531081985bf9b9c7171fe3614d65b9442b56f93ef0487"},"schema_version":"1.0"},"canonical_sha256":"9414734b4f487e5e9e6d35398f60cfa384fd94a37a16fce234d6d9c011299347","source":{"kind":"arxiv","id":"0912.1981","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:SQKHGS2PJB7F5HTNGU4Y6YGPUO","target":"record","payload":{"canonical_record":{"source":{"id":"0912.1981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-12-10T13:30:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f943fa833cfb3fe4c7fab8b674a72394b6d0020266e200b13536a1b21cebce68","abstract_canon_sha256":"512f16b5925811df162531081985bf9b9c7171fe3614d65b9442b56f93ef0487"},"schema_version":"1.0"},"canonical_sha256":"9414734b4f487e5e9e6d35398f60cfa384fd94a37a16fce234d6d9c011299347","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:08:56.289387Z","signature_b64":"NuTQQVNqbbnwstfscuJaNcwC1X5sSjLj3Y8WRC0brM1/yyVXXDyRGu4iyFUkq7V1tmc0U64ABd1/gmvtIhY6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9414734b4f487e5e9e6d35398f60cfa384fd94a37a16fce234d6d9c011299347","last_reissued_at":"2026-07-05T02:08:56.288833Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:08:56.288833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.1981","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:08:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"66kUm5FLhjHjnV02bnF55HlBBAqI33ulyhvvBGoNhovLF+DrkFQAC6Ldp9La1eHIWrLNIjh5EQe0nMezGNXkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T01:48:50.665860Z"},"content_sha256":"bb79f7ee07b6822ef5de5c493305631429267343f00183b2eb925dc594957776","schema_version":"1.0","event_id":"sha256:bb79f7ee07b6822ef5de5c493305631429267343f00183b2eb925dc594957776"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:SQKHGS2PJB7F5HTNGU4Y6YGPUO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On exact representations of the motions group of Galilean plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Dmitry Efimov, Igor Kostyakov, Vasiliy Kuratov","submitted_at":"2009-12-10T13:30:35Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1981","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0912.1981/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:08:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAa4z6JmL8nYuSAplzxkM/Y2oeaLdR35JO157jrYjoLMv/OzNk93eJTaShkKsW4MVN+ObqoMnL3nXAsP59/hDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T01:48:50.666230Z"},"content_sha256":"5554233b37ad6a47b8b23fb00e4f8795fde46e5b21bc03cec086169514880e38","schema_version":"1.0","event_id":"sha256:5554233b37ad6a47b8b23fb00e4f8795fde46e5b21bc03cec086169514880e38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO/bundle.json","state_url":"https://pith.science/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-09T01:48:50Z","links":{"resolver":"https://pith.science/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO","bundle":"https://pith.science/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO/bundle.json","state":"https://pith.science/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQKHGS2PJB7F5HTNGU4Y6YGPUO/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5J3NuZHastzgzDSiksJLvoI32AmCCHpk3OQemx8090CVoMyU63g7LopoijlkEXZcuOxKQSFufNb9WCOyXSZRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T01:48:50.668367Z","bundle_sha256":"a5f3a332a9a67e8e8f62f2517469bed5d8dfb13cd16a09a0b2b315aed6c299b2"}}