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We consider the case when the fundamental matrix of the principal symbol of $P$ at $\\rho$ has a couple of non-vanishing real eigenvalues. Such operators are called {\\it effectively hyperbolic}. V. Ivrii introduced the conjecture that every effectively hyperbolic operator is {\\it strongly hyperbolic}, that is the Cauchy problem for $P + Q$ is locally well posed for any lower ord"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.0950","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-05T07:25:11Z","cross_cats_sorted":[],"title_canon_sha256":"a9512a9e009bc81c1f0ac118df9a7ffd39425a4327562ee006df46c7cc1c2818","abstract_canon_sha256":"97ad4bc08f7705143b6b38d7aed979f89f0ad336ab6f4254f8ee0deaafc7ba0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:16.985466Z","signature_b64":"pCe07k72Q/Nx4i76s+aOApwe3os7cIQ2vVYv40MUX4eg57KUltgOqRcE57l0cTLtoeVLxbWZv2DydTSCpT9hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c55a9529b5d92b2f5ec727c170efe8dc5e916ccb7ff09956ce6abda14c5d319a","last_reissued_at":"2026-05-18T01:33:16.984791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:16.984791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cauchy problem for effectively hyperbolic operators with triple characteristics of variable multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Bove, Enrico Bernardi, Vesselin Petkov","submitted_at":"2013-03-05T07:25:11Z","abstract_excerpt":"We study a class of third order hyperbolic operators $P$ in $G = \\{(t, x):0 \\leq t \\leq T, x \\in U \\Subset {\\mathbb R}^{n}\\}$ with triple characteristics at $\\rho = (0, x_0, \\xi), \\xi \\in {\\mathbb R}^n \\setminus \\{0\\}$. We consider the case when the fundamental matrix of the principal symbol of $P$ at $\\rho$ has a couple of non-vanishing real eigenvalues. Such operators are called {\\it effectively hyperbolic}. V. Ivrii introduced the conjecture that every effectively hyperbolic operator is {\\it strongly hyperbolic}, that is the Cauchy problem for $P + Q$ is locally well posed for any lower ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0950","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.0950","created_at":"2026-05-18T01:33:16.984875+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.0950v4","created_at":"2026-05-18T01:33:16.984875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0950","created_at":"2026-05-18T01:33:16.984875+00:00"},{"alias_kind":"pith_short_12","alias_value":"YVNJKKNV3EVS","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YVNJKKNV3EVS6XWH","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YVNJKKNV","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R","json":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R.json","graph_json":"https://pith.science/api/pith-number/YVNJKKNV3EVS6XWHE7AXB37I3R/graph.json","events_json":"https://pith.science/api/pith-number/YVNJKKNV3EVS6XWHE7AXB37I3R/events.json","paper":"https://pith.science/paper/YVNJKKNV"},"agent_actions":{"view_html":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R","download_json":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R.json","view_paper":"https://pith.science/paper/YVNJKKNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.0950&json=true","fetch_graph":"https://pith.science/api/pith-number/YVNJKKNV3EVS6XWHE7AXB37I3R/graph.json","fetch_events":"https://pith.science/api/pith-number/YVNJKKNV3EVS6XWHE7AXB37I3R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R/action/storage_attestation","attest_author":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R/action/author_attestation","sign_citation":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R/action/citation_signature","submit_replication":"https://pith.science/pith/YVNJKKNV3EVS6XWHE7AXB37I3R/action/replication_record"}},"created_at":"2026-05-18T01:33:16.984875+00:00","updated_at":"2026-05-18T01:33:16.984875+00:00"}