{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:3KELJX6GUHXFQCB7WWL4MCKEEP","short_pith_number":"pith:3KELJX6G","schema_version":"1.0","canonical_sha256":"da88b4dfc6a1ee58083fb597c6094423e5930fc5eac2464a3948545f287fe344","source":{"kind":"arxiv","id":"1109.4543","version":1},"attestation_state":"computed","paper":{"title":"On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Georgi G. Grahovski, Rossen I. Ivanov, Vladimir S. Gerdjikov","submitted_at":"2011-09-21T14:34:55Z","abstract_excerpt":"Non-holonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called \"squared solutions\" (squared eigenfunctions). Such deformations are equivalent to perturbed models with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV equation. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV hierarchy with generic self-consistent sources are analyzed. This allows one to formulate a set of conditions on the perturbation ter"},"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":"1109.4543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-09-21T14:34:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0457f1c1fc97251a07b93e7616732f6bb4137304bb31d217cd5fdd57d2480e17","abstract_canon_sha256":"18d9133bb4ad1c7e66d3fe15a951d2af156ab02aa1d403d18c9a319bd5b9ca29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:56.827687Z","signature_b64":"kl7w3F70wuIDYUAdvwjPZvy6B9zb6+vbwDvssIXUCJpZcnzL8dI8EKVU8x3VHpwTvZG8204KbKtn0Nx5TQrfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da88b4dfc6a1ee58083fb597c6094423e5930fc5eac2464a3948545f287fe344","last_reissued_at":"2026-05-18T04:03:56.827196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:56.827196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Georgi G. Grahovski, Rossen I. Ivanov, Vladimir S. Gerdjikov","submitted_at":"2011-09-21T14:34:55Z","abstract_excerpt":"Non-holonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called \"squared solutions\" (squared eigenfunctions). Such deformations are equivalent to perturbed models with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV equation. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV hierarchy with generic self-consistent sources are analyzed. This allows one to formulate a set of conditions on the perturbation ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4543","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":"1109.4543","created_at":"2026-05-18T04:03:56.827264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.4543v1","created_at":"2026-05-18T04:03:56.827264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4543","created_at":"2026-05-18T04:03:56.827264+00:00"},{"alias_kind":"pith_short_12","alias_value":"3KELJX6GUHXF","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"3KELJX6GUHXFQCB7","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"3KELJX6G","created_at":"2026-05-18T12:26:18.847500+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/3KELJX6GUHXFQCB7WWL4MCKEEP","json":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP.json","graph_json":"https://pith.science/api/pith-number/3KELJX6GUHXFQCB7WWL4MCKEEP/graph.json","events_json":"https://pith.science/api/pith-number/3KELJX6GUHXFQCB7WWL4MCKEEP/events.json","paper":"https://pith.science/paper/3KELJX6G"},"agent_actions":{"view_html":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP","download_json":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP.json","view_paper":"https://pith.science/paper/3KELJX6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.4543&json=true","fetch_graph":"https://pith.science/api/pith-number/3KELJX6GUHXFQCB7WWL4MCKEEP/graph.json","fetch_events":"https://pith.science/api/pith-number/3KELJX6GUHXFQCB7WWL4MCKEEP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP/action/storage_attestation","attest_author":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP/action/author_attestation","sign_citation":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP/action/citation_signature","submit_replication":"https://pith.science/pith/3KELJX6GUHXFQCB7WWL4MCKEEP/action/replication_record"}},"created_at":"2026-05-18T04:03:56.827264+00:00","updated_at":"2026-05-18T04:03:56.827264+00:00"}