{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:K5EV22Q5BHUC7SKZQFVZNMGQS4","short_pith_number":"pith:K5EV22Q5","canonical_record":{"source":{"id":"1107.2565","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T14:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"c5edac789b4666dd0f940753b4008b33d80302b41253a27c1ed43404747d7906","abstract_canon_sha256":"db4f12fecd209f1b276734c576f200478ca13db2851cb055c1a8a10e398f22f1"},"schema_version":"1.0"},"canonical_sha256":"57495d6a1d09e82fc959816b96b0d09729465833f1cc38aa07ef46423e421b3e","source":{"kind":"arxiv","id":"1107.2565","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2565","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2565v2","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2565","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"K5EV22Q5BHUC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5EV22Q5BHUC7SKZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5EV22Q5","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:K5EV22Q5BHUC7SKZQFVZNMGQS4","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2565","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T14:51:20Z","cross_cats_sorted":[],"title_canon_sha256":"c5edac789b4666dd0f940753b4008b33d80302b41253a27c1ed43404747d7906","abstract_canon_sha256":"db4f12fecd209f1b276734c576f200478ca13db2851cb055c1a8a10e398f22f1"},"schema_version":"1.0"},"canonical_sha256":"57495d6a1d09e82fc959816b96b0d09729465833f1cc38aa07ef46423e421b3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:34.095627Z","signature_b64":"b9yQaCnpDBMz6W9ecl+OGnA8b6b3/tHCx7JOmkjZf29ivJK8iOCVcFpord0xXIrOn/iBA7qK+SDzTC7dhMaKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57495d6a1d09e82fc959816b96b0d09729465833f1cc38aa07ef46423e421b3e","last_reissued_at":"2026-05-18T03:42:34.095160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:34.095160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2565","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":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggBkt6mYI7qVoVyaNVrnOT/v2gqxxP9IX5S+XyiYqzWpg8AH4QJ2w68IGNL2zNEVVGu9qIDhlsyIVA3qJEzDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:08:07.033884Z"},"content_sha256":"abb18cafb49320b16702e170a8ec817b2cfda8471433e066439f8f3b96d33693","schema_version":"1.0","event_id":"sha256:abb18cafb49320b16702e170a8ec817b2cfda8471433e066439f8f3b96d33693"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:K5EV22Q5BHUC7SKZQFVZNMGQS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the well-posedness of weakly hyperbolic equations with time dependent coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudia Garetto, Michael Ruzhansky","submitted_at":"2011-07-13T14:51:20Z","abstract_excerpt":"In this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lower order terms and the number of multiple roots. We also derive the corresponding well-posedness results in the space of Gevrey Beurling ultradistributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2565","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":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YuUNn3AiXDGABQVjDJiTe5lvs4fS++gNXAlMpcCWw9b1ohmJlZ7f+wIOvAGVQp3hY7SQ2LdpvRIug/Vv5uRpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:08:07.034227Z"},"content_sha256":"5a68b768581f1496bf475acbf0e26005485e3347d8c727daeab5c8b6cf81172b","schema_version":"1.0","event_id":"sha256:5a68b768581f1496bf475acbf0e26005485e3347d8c727daeab5c8b6cf81172b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4/bundle.json","state_url":"https://pith.science/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4/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":"2026-06-25T03:08:07Z","links":{"resolver":"https://pith.science/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4","bundle":"https://pith.science/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4/bundle.json","state":"https://pith.science/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5EV22Q5BHUC7SKZQFVZNMGQS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K5EV22Q5BHUC7SKZQFVZNMGQS4","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":"db4f12fecd209f1b276734c576f200478ca13db2851cb055c1a8a10e398f22f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T14:51:20Z","title_canon_sha256":"c5edac789b4666dd0f940753b4008b33d80302b41253a27c1ed43404747d7906"},"schema_version":"1.0","source":{"id":"1107.2565","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2565","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2565v2","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2565","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"K5EV22Q5BHUC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5EV22Q5BHUC7SKZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5EV22Q5","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:5a68b768581f1496bf475acbf0e26005485e3347d8c727daeab5c8b6cf81172b","target":"graph","created_at":"2026-05-18T03:42:34Z","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 analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lower order terms and the number of multiple roots. We also derive the corresponding well-posedness results in the space of Gevrey Beurling ultradistributions.","authors_text":"Claudia Garetto, Michael Ruzhansky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T14:51:20Z","title":"On the well-posedness of weakly hyperbolic equations with time dependent coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2565","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:abb18cafb49320b16702e170a8ec817b2cfda8471433e066439f8f3b96d33693","target":"record","created_at":"2026-05-18T03:42:34Z","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":"db4f12fecd209f1b276734c576f200478ca13db2851cb055c1a8a10e398f22f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T14:51:20Z","title_canon_sha256":"c5edac789b4666dd0f940753b4008b33d80302b41253a27c1ed43404747d7906"},"schema_version":"1.0","source":{"id":"1107.2565","kind":"arxiv","version":2}},"canonical_sha256":"57495d6a1d09e82fc959816b96b0d09729465833f1cc38aa07ef46423e421b3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57495d6a1d09e82fc959816b96b0d09729465833f1cc38aa07ef46423e421b3e","first_computed_at":"2026-05-18T03:42:34.095160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:34.095160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b9yQaCnpDBMz6W9ecl+OGnA8b6b3/tHCx7JOmkjZf29ivJK8iOCVcFpord0xXIrOn/iBA7qK+SDzTC7dhMaKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:34.095627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2565","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abb18cafb49320b16702e170a8ec817b2cfda8471433e066439f8f3b96d33693","sha256:5a68b768581f1496bf475acbf0e26005485e3347d8c727daeab5c8b6cf81172b"],"state_sha256":"be28645a82488eab4d285edf5fd79fa295fc9a151fdd8ab61a8300cbc846a607"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0pDYN9de0CVqMm27eRBkrSt6CbuCXYIL2QoO5iLxvuBmfD4mumbtRXm46Yd2TwAjlzP/LXnwsnbZ05Dzqm8Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T03:08:07.036224Z","bundle_sha256":"5e1c8d9c6de6a61e662449e7ac7e6283573cab68e440c0635b2c91d33540b2d2"}}