{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:C6DAPK2QMCFYZB6DBZ7SEFR5NS","short_pith_number":"pith:C6DAPK2Q","canonical_record":{"source":{"id":"1308.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-01T08:43:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b17bd0049a2a55cedc1551480c388b3760510f9badc80d82fef9710c31f7bb77","abstract_canon_sha256":"6a545cc274f7e41cb13910d6978b9bb233f170913d599a62b5fdcae322e96f14"},"schema_version":"1.0"},"canonical_sha256":"178607ab50608b8c87c30e7f22163d6c8197bc90061c71342d899b8536048fc0","source":{"kind":"arxiv","id":"1308.0121","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0121","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0121v2","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0121","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"C6DAPK2QMCFY","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C6DAPK2QMCFYZB6D","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C6DAPK2Q","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:C6DAPK2QMCFYZB6DBZ7SEFR5NS","target":"record","payload":{"canonical_record":{"source":{"id":"1308.0121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-01T08:43:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b17bd0049a2a55cedc1551480c388b3760510f9badc80d82fef9710c31f7bb77","abstract_canon_sha256":"6a545cc274f7e41cb13910d6978b9bb233f170913d599a62b5fdcae322e96f14"},"schema_version":"1.0"},"canonical_sha256":"178607ab50608b8c87c30e7f22163d6c8197bc90061c71342d899b8536048fc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:32.411766Z","signature_b64":"+xC9FerkqPKdMnxknYgOe1xCKovf1HvFsYuZBxAAVf6LwAwzy5c09lTGOMQmPaYOm6kq4eKKhdI9zdCcU0y9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"178607ab50608b8c87c30e7f22163d6c8197bc90061c71342d899b8536048fc0","last_reissued_at":"2026-05-18T03:12:32.411000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:32.411000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.0121","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DCzhvyFjZSSMGIPuSuyYbLE0F+/L29D2lO43h/HeT8qp7NpQ/NCUdQl95mxTkzat4ZEpJzao+738TEGrjuUdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T17:23:31.266192Z"},"content_sha256":"2cbcbe211f243a2aeb7e081666228378c15863311d3fe63c5219df43cd78bfd0","schema_version":"1.0","event_id":"sha256:2cbcbe211f243a2aeb7e081666228378c15863311d3fe63c5219df43cd78bfd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:C6DAPK2QMCFYZB6DBZ7SEFR5NS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. Segar, N. Aizawa, Y. Kimura","submitted_at":"2013-08-01T08:43:21Z","abstract_excerpt":"l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of the conformal algebra. We derive hierarchies of partial differential equations which have invariance of the group generated by g{l}{d} with central extension as kinematical symmetry. This is done by developing a representation theory such as Verma modules, singular vectors of g{l}{d} and vector field representations for d = 1, 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0121","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FbbEfXr5dOJncCNCakfBzB9XZQlFNgQ2ZU1uDWCthPW0iBJzyc8BJdFOQ6Bxf4deIQ290gi8aWlbgRjUHgYtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T17:23:31.266559Z"},"content_sha256":"3303cc57bfbae4d28d66f81dbdef1c43d22d2d9eaed0e6d06537cb65e885e37b","schema_version":"1.0","event_id":"sha256:3303cc57bfbae4d28d66f81dbdef1c43d22d2d9eaed0e6d06537cb65e885e37b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS/bundle.json","state_url":"https://pith.science/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS/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":"2026-05-20T17:23:31Z","links":{"resolver":"https://pith.science/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS","bundle":"https://pith.science/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS/bundle.json","state":"https://pith.science/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6DAPK2QMCFYZB6DBZ7SEFR5NS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C6DAPK2QMCFYZB6DBZ7SEFR5NS","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":"6a545cc274f7e41cb13910d6978b9bb233f170913d599a62b5fdcae322e96f14","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-01T08:43:21Z","title_canon_sha256":"b17bd0049a2a55cedc1551480c388b3760510f9badc80d82fef9710c31f7bb77"},"schema_version":"1.0","source":{"id":"1308.0121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0121","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0121v2","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0121","created_at":"2026-05-18T03:12:32Z"},{"alias_kind":"pith_short_12","alias_value":"C6DAPK2QMCFY","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C6DAPK2QMCFYZB6D","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C6DAPK2Q","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:3303cc57bfbae4d28d66f81dbdef1c43d22d2d9eaed0e6d06537cb65e885e37b","target":"graph","created_at":"2026-05-18T03:12:32Z","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":"l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of the conformal algebra. We derive hierarchies of partial differential equations which have invariance of the group generated by g{l}{d} with central extension as kinematical symmetry. This is done by developing a representation theory such as Verma modules, singular vectors of g{l}{d} and vector field representations for d = 1, 2.","authors_text":"J. Segar, N. Aizawa, Y. Kimura","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-01T08:43:21Z","title":"Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0121","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":"sha256:2cbcbe211f243a2aeb7e081666228378c15863311d3fe63c5219df43cd78bfd0","target":"record","created_at":"2026-05-18T03:12:32Z","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":"6a545cc274f7e41cb13910d6978b9bb233f170913d599a62b5fdcae322e96f14","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-01T08:43:21Z","title_canon_sha256":"b17bd0049a2a55cedc1551480c388b3760510f9badc80d82fef9710c31f7bb77"},"schema_version":"1.0","source":{"id":"1308.0121","kind":"arxiv","version":2}},"canonical_sha256":"178607ab50608b8c87c30e7f22163d6c8197bc90061c71342d899b8536048fc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"178607ab50608b8c87c30e7f22163d6c8197bc90061c71342d899b8536048fc0","first_computed_at":"2026-05-18T03:12:32.411000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:32.411000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xC9FerkqPKdMnxknYgOe1xCKovf1HvFsYuZBxAAVf6LwAwzy5c09lTGOMQmPaYOm6kq4eKKhdI9zdCcU0y9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:32.411766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cbcbe211f243a2aeb7e081666228378c15863311d3fe63c5219df43cd78bfd0","sha256:3303cc57bfbae4d28d66f81dbdef1c43d22d2d9eaed0e6d06537cb65e885e37b"],"state_sha256":"08fd25b3719a544ac24abe7999c00b7c06c406be40cc7eddd9b7fba7e453c46a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ubdOSujpJ3iP4rTz6dZTjUh+u70iZrqAJrTlWz1zNW6pRlOuOWzq1sfJc7/R2hWd2zS0JRPPbhrvJ8UysroCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T17:23:31.268623Z","bundle_sha256":"49678c3d768f7d5e9c8010c9a06a9a99dd38fbb66affb9cdda6a669a6cf8cfe8"}}