{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SYXP4TSX6NSO6PFZIT5N6ONWEL","short_pith_number":"pith:SYXP4TSX","canonical_record":{"source":{"id":"1804.03544","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-09T11:41:04Z","cross_cats_sorted":["math.FA","math.GR"],"title_canon_sha256":"b82829d4d4055d929611755c02407a64d663c2a959b28b296008e2717a42d695","abstract_canon_sha256":"6048f1fd8edb8dd608e0134057dcb0c7a4510fb5673c7afc9cd840bde302445d"},"schema_version":"1.0"},"canonical_sha256":"962efe4e57f364ef3cb944fadf39b622ca4767ed2a54e2412b2979b0611404f6","source":{"kind":"arxiv","id":"1804.03544","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03544","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03544v2","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03544","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"SYXP4TSX6NSO","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SYXP4TSX6NSO6PFZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SYXP4TSX","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SYXP4TSX6NSO6PFZIT5N6ONWEL","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03544","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-09T11:41:04Z","cross_cats_sorted":["math.FA","math.GR"],"title_canon_sha256":"b82829d4d4055d929611755c02407a64d663c2a959b28b296008e2717a42d695","abstract_canon_sha256":"6048f1fd8edb8dd608e0134057dcb0c7a4510fb5673c7afc9cd840bde302445d"},"schema_version":"1.0"},"canonical_sha256":"962efe4e57f364ef3cb944fadf39b622ca4767ed2a54e2412b2979b0611404f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:02.753579Z","signature_b64":"SJRSdcsuvzOri1wV504Y2Oq1NhyqH15iJU9YICvzVk8KVHyGc9c9pBqiYJsqRszI35tovIhqFmjEJmTzfvZwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"962efe4e57f364ef3cb944fadf39b622ca4767ed2a54e2412b2979b0611404f6","last_reissued_at":"2026-05-18T00:15:02.752863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:02.752863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03544","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":"2026-05-18T00:15:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bL4vOY3tYA/iI/VUWnzACaf7vrjmqrbU3+pTOYzkwYU2YJ5vB4Cv9VE4HwuOcQ1iAlYotG+JIwl7y3OHT/9qCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:49:03.421668Z"},"content_sha256":"e020221fb82d395391bfba80c36f47e40b6f07c08bbf932267c8faf1919ab23d","schema_version":"1.0","event_id":"sha256:e020221fb82d395391bfba80c36f47e40b6f07c08bbf932267c8faf1919ab23d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SYXP4TSX6NSO6PFZIT5N6ONWEL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wave equations on graded groups and hypoelliptic Gevrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.AP","authors_text":"Chiara Alba Taranto","submitted_at":"2018-04-09T11:41:04Z","abstract_excerpt":"The overall goal of this dissertation is to investigate certain classical results from harmonic analysis, replacing the Euclidean setting, the abelian structure and the elliptic Laplace operator with a non-commutative environment and hypoelliptic operators.\n  More specifically, we consider wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups with time-dependent non-negative propagation speeds that are H\\\"older-regular or even more so. The corresponding Euclidean problem has been extensively studied in the `80s and some additional results have been recently "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03544","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":"2026-05-18T00:15:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MvhfePg6Mt+fRaFEHd3F2T84mgTeGz6qQRrym2wlZPyF64Gwrot3ipgXzwCZ8EpzkFBPyCcY/xIIHi9y49TZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:49:03.423860Z"},"content_sha256":"bb133c21a0b4ebf9e89d876a4e59580777e696f118b968fec73999102eba4423","schema_version":"1.0","event_id":"sha256:bb133c21a0b4ebf9e89d876a4e59580777e696f118b968fec73999102eba4423"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL/bundle.json","state_url":"https://pith.science/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL/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":"2026-08-17T08:49:03Z","links":{"resolver":"https://pith.science/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL","bundle":"https://pith.science/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL/bundle.json","state":"https://pith.science/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYXP4TSX6NSO6PFZIT5N6ONWEL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SYXP4TSX6NSO6PFZIT5N6ONWEL","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":"6048f1fd8edb8dd608e0134057dcb0c7a4510fb5673c7afc9cd840bde302445d","cross_cats_sorted":["math.FA","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-09T11:41:04Z","title_canon_sha256":"b82829d4d4055d929611755c02407a64d663c2a959b28b296008e2717a42d695"},"schema_version":"1.0","source":{"id":"1804.03544","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03544","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03544v2","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03544","created_at":"2026-05-18T00:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"SYXP4TSX6NSO","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SYXP4TSX6NSO6PFZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SYXP4TSX","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:bb133c21a0b4ebf9e89d876a4e59580777e696f118b968fec73999102eba4423","target":"graph","created_at":"2026-05-18T00:15:02Z","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":"The overall goal of this dissertation is to investigate certain classical results from harmonic analysis, replacing the Euclidean setting, the abelian structure and the elliptic Laplace operator with a non-commutative environment and hypoelliptic operators.\n  More specifically, we consider wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups with time-dependent non-negative propagation speeds that are H\\\"older-regular or even more so. The corresponding Euclidean problem has been extensively studied in the `80s and some additional results have been recently ","authors_text":"Chiara Alba Taranto","cross_cats":["math.FA","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-09T11:41:04Z","title":"Wave equations on graded groups and hypoelliptic Gevrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03544","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:e020221fb82d395391bfba80c36f47e40b6f07c08bbf932267c8faf1919ab23d","target":"record","created_at":"2026-05-18T00:15:02Z","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":"6048f1fd8edb8dd608e0134057dcb0c7a4510fb5673c7afc9cd840bde302445d","cross_cats_sorted":["math.FA","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-09T11:41:04Z","title_canon_sha256":"b82829d4d4055d929611755c02407a64d663c2a959b28b296008e2717a42d695"},"schema_version":"1.0","source":{"id":"1804.03544","kind":"arxiv","version":2}},"canonical_sha256":"962efe4e57f364ef3cb944fadf39b622ca4767ed2a54e2412b2979b0611404f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"962efe4e57f364ef3cb944fadf39b622ca4767ed2a54e2412b2979b0611404f6","first_computed_at":"2026-05-18T00:15:02.752863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:02.752863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SJRSdcsuvzOri1wV504Y2Oq1NhyqH15iJU9YICvzVk8KVHyGc9c9pBqiYJsqRszI35tovIhqFmjEJmTzfvZwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:02.753579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03544","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e020221fb82d395391bfba80c36f47e40b6f07c08bbf932267c8faf1919ab23d","sha256:bb133c21a0b4ebf9e89d876a4e59580777e696f118b968fec73999102eba4423"],"state_sha256":"3faceee0482fb07f4ecd5725f6d8b05f9619b67b6f8f87255d34b47ad34002e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LcqxNv0gOpDXp0DyW3nXw90j6rUb0LjAy16s+OUP8pClUa1H1WawJdcvU7khIi+0ZM2BMDLiMnhWg81Z8k1oBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T08:49:03.484621Z","bundle_sha256":"6320f118f7938bf1488f4e5a12df6ecde171444dc0a0da637f78e6c616b2a833"}}