{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OQDI3OIK3FOHJDCDOWLP33O4UJ","short_pith_number":"pith:OQDI3OIK","canonical_record":{"source":{"id":"1305.1095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T06:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"6430ccfa8d00e4f812b97391214c8f37350f8266207f5acfeaeb9e1e1401faf7","abstract_canon_sha256":"3c94da2a63a125808c2522923d0a4deb75771460c0bfd9edf45b5804905c0fa2"},"schema_version":"1.0"},"canonical_sha256":"74068db90ad95c748c437596fdeddca24831840620f20582e7b8fbfe9c429521","source":{"kind":"arxiv","id":"1305.1095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1095","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1095v1","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1095","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"OQDI3OIK3FOH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OQDI3OIK3FOHJDCD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OQDI3OIK","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OQDI3OIK3FOHJDCDOWLP33O4UJ","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T06:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"6430ccfa8d00e4f812b97391214c8f37350f8266207f5acfeaeb9e1e1401faf7","abstract_canon_sha256":"3c94da2a63a125808c2522923d0a4deb75771460c0bfd9edf45b5804905c0fa2"},"schema_version":"1.0"},"canonical_sha256":"74068db90ad95c748c437596fdeddca24831840620f20582e7b8fbfe9c429521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:59.878838Z","signature_b64":"w6FvythHYJhl9ixcCTH1LKESHurGcFOF9I6EfjFY/hQvObqkWFHX0ISwMu067vwcAhvCJHCFAYlBxjqxas/qAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74068db90ad95c748c437596fdeddca24831840620f20582e7b8fbfe9c429521","last_reissued_at":"2026-05-18T03:12:59.878176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:59.878176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1095","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":"2026-05-18T03:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XVAh/uUc+GSbbOMqXM1EBbqNZJzbOX5c2dXGH6Of347plemlii/S/8Zh698ehHcD3MYL2GKg6E5IzDO206mQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:36:35.739564Z"},"content_sha256":"327e79b12c50c5ce8f09ecd5c9363e53d84e436953c2438ce8463cb6a6169b9a","schema_version":"1.0","event_id":"sha256:327e79b12c50c5ce8f09ecd5c9363e53d84e436953c2438ce8463cb6a6169b9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OQDI3OIK3FOHJDCDOWLP33O4UJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniele Del Santo, Ferruccio Colombini, Francesco Fanelli, Guy M\\'etivier","submitted_at":"2013-05-06T06:45:51Z","abstract_excerpt":"In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension $N\\geq1$. We will suppose the coefficients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradifferential calculus with parameters will be the main tool to get energy estimates in Sobolev spaces and these estimates will present a time-dependent loss of derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1095","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":"2026-05-18T03:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k0VQtOOA7601oADDaqBw/Mv1H/5MMKASXmvUk15kiDOJu9rTxn24ccLX7yQVJBwv866GvGEZyDGe+gbL8Mf1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:36:35.739908Z"},"content_sha256":"2fe02d1cdc74ad76d36e8290d82f8462b87ae85a6878bd697c37430eb4502581","schema_version":"1.0","event_id":"sha256:2fe02d1cdc74ad76d36e8290d82f8462b87ae85a6878bd697c37430eb4502581"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ/bundle.json","state_url":"https://pith.science/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ/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":"2026-06-24T22:36:35Z","links":{"resolver":"https://pith.science/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ","bundle":"https://pith.science/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ/bundle.json","state":"https://pith.science/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQDI3OIK3FOHJDCDOWLP33O4UJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OQDI3OIK3FOHJDCDOWLP33O4UJ","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":"3c94da2a63a125808c2522923d0a4deb75771460c0bfd9edf45b5804905c0fa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T06:45:51Z","title_canon_sha256":"6430ccfa8d00e4f812b97391214c8f37350f8266207f5acfeaeb9e1e1401faf7"},"schema_version":"1.0","source":{"id":"1305.1095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1095","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1095v1","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1095","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"OQDI3OIK3FOH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OQDI3OIK3FOHJDCD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OQDI3OIK","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:2fe02d1cdc74ad76d36e8290d82f8462b87ae85a6878bd697c37430eb4502581","target":"graph","created_at":"2026-05-18T03:12:59Z","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 will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension $N\\geq1$. We will suppose the coefficients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradifferential calculus with parameters will be the main tool to get energy estimates in Sobolev spaces and these estimates will present a time-dependent loss of derivatives.","authors_text":"Daniele Del Santo, Ferruccio Colombini, Francesco Fanelli, Guy M\\'etivier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T06:45:51Z","title":"Time-dependent loss of derivatives for hyperbolic operators with non regular coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1095","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":"sha256:327e79b12c50c5ce8f09ecd5c9363e53d84e436953c2438ce8463cb6a6169b9a","target":"record","created_at":"2026-05-18T03:12:59Z","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":"3c94da2a63a125808c2522923d0a4deb75771460c0bfd9edf45b5804905c0fa2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-06T06:45:51Z","title_canon_sha256":"6430ccfa8d00e4f812b97391214c8f37350f8266207f5acfeaeb9e1e1401faf7"},"schema_version":"1.0","source":{"id":"1305.1095","kind":"arxiv","version":1}},"canonical_sha256":"74068db90ad95c748c437596fdeddca24831840620f20582e7b8fbfe9c429521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74068db90ad95c748c437596fdeddca24831840620f20582e7b8fbfe9c429521","first_computed_at":"2026-05-18T03:12:59.878176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:59.878176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w6FvythHYJhl9ixcCTH1LKESHurGcFOF9I6EfjFY/hQvObqkWFHX0ISwMu067vwcAhvCJHCFAYlBxjqxas/qAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:59.878838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:327e79b12c50c5ce8f09ecd5c9363e53d84e436953c2438ce8463cb6a6169b9a","sha256:2fe02d1cdc74ad76d36e8290d82f8462b87ae85a6878bd697c37430eb4502581"],"state_sha256":"6ad8b9097133dfa58eb82eb67f937352e297f03a45ca016078519d70eb11b38f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsQTs8zU5GhO8HVmUY6r5FeWHH2XXk6uGAx5IXZzRONdr1bOCSjeC/D/PuEI6QLAPxpxx5zgMbISO27dEUAXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:36:35.741959Z","bundle_sha256":"4377af2f1a695de652780c760e547f55a9e575260412b0e9db8ff5a79b46d557"}}