{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KMEMOWDIWFYPP5SV5GOGJMAMAA","short_pith_number":"pith:KMEMOWDI","canonical_record":{"source":{"id":"1403.1370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T08:01:44Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a981f8ab82ba6f0afec7ed8a6014eadbf701e96cb957ffe1e0fd084240076fb6","abstract_canon_sha256":"d377972e25696a2569e2efd76b8c0efbc833c2acdee6c02d7c2d466e0089f52c"},"schema_version":"1.0"},"canonical_sha256":"5308c75868b170f7f655e99c64b00c001d5ce46dc7678d0fb2b593296653e72a","source":{"kind":"arxiv","id":"1403.1370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1370","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1370v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1370","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"KMEMOWDIWFYP","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KMEMOWDIWFYPP5SV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KMEMOWDI","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KMEMOWDIWFYPP5SV5GOGJMAMAA","target":"record","payload":{"canonical_record":{"source":{"id":"1403.1370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T08:01:44Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a981f8ab82ba6f0afec7ed8a6014eadbf701e96cb957ffe1e0fd084240076fb6","abstract_canon_sha256":"d377972e25696a2569e2efd76b8c0efbc833c2acdee6c02d7c2d466e0089f52c"},"schema_version":"1.0"},"canonical_sha256":"5308c75868b170f7f655e99c64b00c001d5ce46dc7678d0fb2b593296653e72a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:08.458853Z","signature_b64":"UddQdyQxVKEiN6ZY8FgXJyN0Zrv+C+TXI2TMTN9tEmR6YJkUXukZ/YQMV45RKLWEbJ2VMCuUpVHpCnhnlDghBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5308c75868b170f7f655e99c64b00c001d5ce46dc7678d0fb2b593296653e72a","last_reissued_at":"2026-05-18T01:30:08.458188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:08.458188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.1370","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmhKUTao1ZU31WsII1GXKXGexPnG7d4YgRIBIHbxTQswiKqwSZI5TV5xU3x5gdig3UbpP0xJREPAtCVzwf6cDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:28:14.543601Z"},"content_sha256":"940df367604727314de6050f4635085e6c1716a03fa67f04f81affcfd089adbc","schema_version":"1.0","event_id":"sha256:940df367604727314de6050f4635085e6c1716a03fa67f04f81affcfd089adbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KMEMOWDIWFYPP5SV5GOGJMAMAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wave equation for sums of squares on compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Claudia Garetto, Michael Ruzhansky","submitted_at":"2014-03-06T08:01:44Z","abstract_excerpt":"In this paper we investigate the well-posedness of the Cauchy problem for the wave equation for sums of squares of vector fields on compact Lie groups. We obtain the loss of regularity for solutions to the Cauchy problem in local Sobolev spaces depending on the order to which the H\\\"ormander condition is satisfied, but no loss in globally defined spaces. We also establish Gevrey well-posedness for equations with irregular coefficients and/or multiple characteristics. As in the Sobolev spaces, if formulated in local coordinates, we observe well-posedness with the loss of local Gevrey order depe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1370","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":""},"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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zT9rCUCQSG9uKIo+MQjcfqQIHgrbPEAgKOMWgoahSM2S25ck5bpg4ZO+P0v5e9bCiSHMgEUl7kGxunf5IoJGAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:28:14.543950Z"},"content_sha256":"977ebf7e7d380625e0cf248425f3e75875dd8caee5352248c3111e9e2aa23e14","schema_version":"1.0","event_id":"sha256:977ebf7e7d380625e0cf248425f3e75875dd8caee5352248c3111e9e2aa23e14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA/bundle.json","state_url":"https://pith.science/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA/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":"2026-06-04T21:28:14Z","links":{"resolver":"https://pith.science/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA","bundle":"https://pith.science/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA/bundle.json","state":"https://pith.science/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMEMOWDIWFYPP5SV5GOGJMAMAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KMEMOWDIWFYPP5SV5GOGJMAMAA","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":"d377972e25696a2569e2efd76b8c0efbc833c2acdee6c02d7c2d466e0089f52c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T08:01:44Z","title_canon_sha256":"a981f8ab82ba6f0afec7ed8a6014eadbf701e96cb957ffe1e0fd084240076fb6"},"schema_version":"1.0","source":{"id":"1403.1370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1370","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1370v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1370","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"KMEMOWDIWFYP","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KMEMOWDIWFYPP5SV","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KMEMOWDI","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:977ebf7e7d380625e0cf248425f3e75875dd8caee5352248c3111e9e2aa23e14","target":"graph","created_at":"2026-05-18T01:30:08Z","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 investigate the well-posedness of the Cauchy problem for the wave equation for sums of squares of vector fields on compact Lie groups. We obtain the loss of regularity for solutions to the Cauchy problem in local Sobolev spaces depending on the order to which the H\\\"ormander condition is satisfied, but no loss in globally defined spaces. We also establish Gevrey well-posedness for equations with irregular coefficients and/or multiple characteristics. As in the Sobolev spaces, if formulated in local coordinates, we observe well-posedness with the loss of local Gevrey order depe","authors_text":"Claudia Garetto, Michael Ruzhansky","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T08:01:44Z","title":"Wave equation for sums of squares on compact Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1370","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":"sha256:940df367604727314de6050f4635085e6c1716a03fa67f04f81affcfd089adbc","target":"record","created_at":"2026-05-18T01:30:08Z","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":"d377972e25696a2569e2efd76b8c0efbc833c2acdee6c02d7c2d466e0089f52c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-06T08:01:44Z","title_canon_sha256":"a981f8ab82ba6f0afec7ed8a6014eadbf701e96cb957ffe1e0fd084240076fb6"},"schema_version":"1.0","source":{"id":"1403.1370","kind":"arxiv","version":1}},"canonical_sha256":"5308c75868b170f7f655e99c64b00c001d5ce46dc7678d0fb2b593296653e72a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5308c75868b170f7f655e99c64b00c001d5ce46dc7678d0fb2b593296653e72a","first_computed_at":"2026-05-18T01:30:08.458188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:08.458188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UddQdyQxVKEiN6ZY8FgXJyN0Zrv+C+TXI2TMTN9tEmR6YJkUXukZ/YQMV45RKLWEbJ2VMCuUpVHpCnhnlDghBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:08.458853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:940df367604727314de6050f4635085e6c1716a03fa67f04f81affcfd089adbc","sha256:977ebf7e7d380625e0cf248425f3e75875dd8caee5352248c3111e9e2aa23e14"],"state_sha256":"45cbb2333d4cf685d4f04f35ca333cbcec04a2e58ea50ad0c94305c52fa0d1c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xof+7+xr6YZ5jf92MaN/V4+dP7h/IOCvkcp6Tdp+zVi82zbfO47sq4Ht7H69LxPWoLvk7X2RqgcDzVheTaYYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:28:14.545922Z","bundle_sha256":"38f708e7d189773faf24f44d07483bd2039416288a60d97876bc780cda941bb8"}}