{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XVV7NDUALCOIKKJEJOVXPDW7EJ","short_pith_number":"pith:XVV7NDUA","canonical_record":{"source":{"id":"1512.02107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-11-25T15:51:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"02b1f67597a24419840f6aa0f16adcb9232d9b5fe1cdb7f7c42cd54fae980f67","abstract_canon_sha256":"21a8d93479ed6206d29c1d4b76d2ead4bfd6da41e5569702b418afd8f37bdd40"},"schema_version":"1.0"},"canonical_sha256":"bd6bf68e80589c8529244bab778edf2258e264672d9c6bcdfcb143e1d4352a4d","source":{"kind":"arxiv","id":"1512.02107","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02107","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02107v1","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02107","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"XVV7NDUALCOI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XVV7NDUALCOIKKJE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XVV7NDUA","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XVV7NDUALCOIKKJEJOVXPDW7EJ","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-11-25T15:51:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"02b1f67597a24419840f6aa0f16adcb9232d9b5fe1cdb7f7c42cd54fae980f67","abstract_canon_sha256":"21a8d93479ed6206d29c1d4b76d2ead4bfd6da41e5569702b418afd8f37bdd40"},"schema_version":"1.0"},"canonical_sha256":"bd6bf68e80589c8529244bab778edf2258e264672d9c6bcdfcb143e1d4352a4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:09.597217Z","signature_b64":"aNQkhSJ40+zFQNDepx2YHyBAKpbiPbXLcfCylHhza0JjjitVGKNbsoindPVizIZTc4Lz4hJcfHQyFs/xihrADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd6bf68e80589c8529244bab778edf2258e264672d9c6bcdfcb143e1d4352a4d","last_reissued_at":"2026-05-18T01:25:09.596667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:09.596667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02107","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dG+PbCxMB3OjDsvSJ/AlQOKMzEcYUqV+WfSGjagDU9Oqip6mFbjK6wFFdGvvqWPw2+7oDaQKnw3of/hyILOkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:39:15.064362Z"},"content_sha256":"3b0bf9cc911caed1eb9f71cabd41e449dbe0637248d1b01f02aede527b7c8940","schema_version":"1.0","event_id":"sha256:3b0bf9cc911caed1eb9f71cabd41e449dbe0637248d1b01f02aede527b7c8940"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XVV7NDUALCOIKKJEJOVXPDW7EJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex singularities and PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.flu-dyn","authors_text":"F. Gargano, M. Sammartino, R.E.Caflisch, V. Sciacca","submitted_at":"2015-11-25T15:51:23Z","abstract_excerpt":"In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02107","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d/p3BNzWxGF4VjROiRB+xDM+/up1vowoXe4nP/dk7dOMVHX//C8bz5xNFG1u+A8iKw/O7QIJcjPz6kqtS75YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:39:15.064980Z"},"content_sha256":"0aebc20ff74935631688ec4521b7fbf93b42da132c3a7bf2f7b53d7918852a77","schema_version":"1.0","event_id":"sha256:0aebc20ff74935631688ec4521b7fbf93b42da132c3a7bf2f7b53d7918852a77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ/bundle.json","state_url":"https://pith.science/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ/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":"2026-05-28T16:39:15Z","links":{"resolver":"https://pith.science/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ","bundle":"https://pith.science/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ/bundle.json","state":"https://pith.science/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVV7NDUALCOIKKJEJOVXPDW7EJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XVV7NDUALCOIKKJEJOVXPDW7EJ","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":"21a8d93479ed6206d29c1d4b76d2ead4bfd6da41e5569702b418afd8f37bdd40","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-11-25T15:51:23Z","title_canon_sha256":"02b1f67597a24419840f6aa0f16adcb9232d9b5fe1cdb7f7c42cd54fae980f67"},"schema_version":"1.0","source":{"id":"1512.02107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02107","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02107v1","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02107","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"XVV7NDUALCOI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XVV7NDUALCOIKKJE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XVV7NDUA","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:0aebc20ff74935631688ec4521b7fbf93b42da132c3a7bf2f7b53d7918852a77","target":"graph","created_at":"2026-05-18T01:25:09Z","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 give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation,","authors_text":"F. Gargano, M. Sammartino, R.E.Caflisch, V. Sciacca","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-11-25T15:51:23Z","title":"Complex singularities and PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02107","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":"sha256:3b0bf9cc911caed1eb9f71cabd41e449dbe0637248d1b01f02aede527b7c8940","target":"record","created_at":"2026-05-18T01:25:09Z","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":"21a8d93479ed6206d29c1d4b76d2ead4bfd6da41e5569702b418afd8f37bdd40","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-11-25T15:51:23Z","title_canon_sha256":"02b1f67597a24419840f6aa0f16adcb9232d9b5fe1cdb7f7c42cd54fae980f67"},"schema_version":"1.0","source":{"id":"1512.02107","kind":"arxiv","version":1}},"canonical_sha256":"bd6bf68e80589c8529244bab778edf2258e264672d9c6bcdfcb143e1d4352a4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd6bf68e80589c8529244bab778edf2258e264672d9c6bcdfcb143e1d4352a4d","first_computed_at":"2026-05-18T01:25:09.596667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:09.596667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aNQkhSJ40+zFQNDepx2YHyBAKpbiPbXLcfCylHhza0JjjitVGKNbsoindPVizIZTc4Lz4hJcfHQyFs/xihrADA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:09.597217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b0bf9cc911caed1eb9f71cabd41e449dbe0637248d1b01f02aede527b7c8940","sha256:0aebc20ff74935631688ec4521b7fbf93b42da132c3a7bf2f7b53d7918852a77"],"state_sha256":"366fe5dce10305a1cb3fd544ca2e4c133c34e550ddd41eb93be52f312e14053b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"70lxbQ/OSNCkr3RD7tSvD8Eq7WxS3kqQDyozn3bxxjl3vBHAj+yHW1ig+tixt3mC095YKmqjXCTkXTRQ0Ph6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:39:15.068299Z","bundle_sha256":"1e59ece971e74acbfc095ad9cbe8f8197c84d83903fe16aa9bdacfc29a3686cd"}}