{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7PT7ISQUATXUCISKQA3XAKQ36E","short_pith_number":"pith:7PT7ISQU","schema_version":"1.0","canonical_sha256":"fbe7f44a1404ef41224a8037702a1bf10d1b36921a9fd36f9ec2d811922905da","source":{"kind":"arxiv","id":"1010.2933","version":1},"attestation_state":"computed","paper":{"title":"Lax Equations, Singularities and Riemann-Hilbert Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Ant\\'onio F. dos Santos, Pedro F. dos Santos","submitted_at":"2010-10-14T14:23:24Z","abstract_excerpt":"The existence of singularities of the solution for a class of Lax equations is investigated using a development of the fac- torization method first proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the existence of a singularity at a point t = ti is directly related to the property that the ker- nel of a certain Toeplitz operator (whose symbol depends on t) be non-trivial. The investigation of this question involves the factor- ization on a Riemann surface of a scalar function closely related to the above-mentioned operator. An example is presented and the set of singula"},"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":"1010.2933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-10-14T14:23:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"201957cc92ee7f3378e4354417e11018e5fbfa00877c14a7f5d8d5a9c9982041","abstract_canon_sha256":"9721d144fa48a7de4bcc94ac5c7ccaa5ee45b7bcb7b8ff25d9039a385511b7fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:18.844940Z","signature_b64":"WQ9EvlDezVodnZZ/AziUpgBylj7+/tope3RxwzL3MBPp1YUS2fpn/DPkJ1cOWNLeU9M7AkZo1SI0EfYHE2iBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbe7f44a1404ef41224a8037702a1bf10d1b36921a9fd36f9ec2d811922905da","last_reissued_at":"2026-05-18T04:39:18.844381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:18.844381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lax Equations, Singularities and Riemann-Hilbert Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Ant\\'onio F. dos Santos, Pedro F. dos Santos","submitted_at":"2010-10-14T14:23:24Z","abstract_excerpt":"The existence of singularities of the solution for a class of Lax equations is investigated using a development of the fac- torization method first proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the existence of a singularity at a point t = ti is directly related to the property that the ker- nel of a certain Toeplitz operator (whose symbol depends on t) be non-trivial. The investigation of this question involves the factor- ization on a Riemann surface of a scalar function closely related to the above-mentioned operator. An example is presented and the set of singula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2933","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1010.2933","created_at":"2026-05-18T04:39:18.844453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.2933v1","created_at":"2026-05-18T04:39:18.844453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2933","created_at":"2026-05-18T04:39:18.844453+00:00"},{"alias_kind":"pith_short_12","alias_value":"7PT7ISQUATXU","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"7PT7ISQUATXUCISK","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"7PT7ISQU","created_at":"2026-05-18T12:26:05.355336+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/7PT7ISQUATXUCISKQA3XAKQ36E","json":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E.json","graph_json":"https://pith.science/api/pith-number/7PT7ISQUATXUCISKQA3XAKQ36E/graph.json","events_json":"https://pith.science/api/pith-number/7PT7ISQUATXUCISKQA3XAKQ36E/events.json","paper":"https://pith.science/paper/7PT7ISQU"},"agent_actions":{"view_html":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E","download_json":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E.json","view_paper":"https://pith.science/paper/7PT7ISQU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.2933&json=true","fetch_graph":"https://pith.science/api/pith-number/7PT7ISQUATXUCISKQA3XAKQ36E/graph.json","fetch_events":"https://pith.science/api/pith-number/7PT7ISQUATXUCISKQA3XAKQ36E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E/action/storage_attestation","attest_author":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E/action/author_attestation","sign_citation":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E/action/citation_signature","submit_replication":"https://pith.science/pith/7PT7ISQUATXUCISKQA3XAKQ36E/action/replication_record"}},"created_at":"2026-05-18T04:39:18.844453+00:00","updated_at":"2026-05-18T04:39:18.844453+00:00"}