{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2JT7PFWLN6SEEPJ4YEKH2TSN6B","short_pith_number":"pith:2JT7PFWL","schema_version":"1.0","canonical_sha256":"d267f796cb6fa4423d3cc1147d4e4df052ad5d6a55afa6e8fe8b27f0caa393f1","source":{"kind":"arxiv","id":"1107.4877","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear self-adjointness and conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Nail H. Ibragimov","submitted_at":"2011-07-25T09:52:35Z","abstract_excerpt":"The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced earlier by the author. It is shown that the equations possessing the nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint. For example, the heat equation "},"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":"1107.4877","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-25T09:52:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1931fd9657114f8068ac4b701a89c373a88ec8c388f713ce4e913515ea38ce34","abstract_canon_sha256":"1f973c3f47963d66a044f975e1e58d9486d1038e051a2bb64da0382c5feb5c85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:10.705046Z","signature_b64":"yITje2x9YZTO1cbufUtPPCfOzFuDXGsPvEq6IoJ7V0fhn28wy1vqsqLDQi1+LsvzeaewG+eM4WQ+p+s6rzAJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d267f796cb6fa4423d3cc1147d4e4df052ad5d6a55afa6e8fe8b27f0caa393f1","last_reissued_at":"2026-05-18T02:01:10.704120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:10.704120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear self-adjointness and conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Nail H. Ibragimov","submitted_at":"2011-07-25T09:52:35Z","abstract_excerpt":"The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced earlier by the author. It is shown that the equations possessing the nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint. For example, the heat equation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4877","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":"1107.4877","created_at":"2026-05-18T02:01:10.704287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.4877v1","created_at":"2026-05-18T02:01:10.704287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4877","created_at":"2026-05-18T02:01:10.704287+00:00"},{"alias_kind":"pith_short_12","alias_value":"2JT7PFWLN6SE","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2JT7PFWLN6SEEPJ4","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2JT7PFWL","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/2JT7PFWLN6SEEPJ4YEKH2TSN6B","json":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B.json","graph_json":"https://pith.science/api/pith-number/2JT7PFWLN6SEEPJ4YEKH2TSN6B/graph.json","events_json":"https://pith.science/api/pith-number/2JT7PFWLN6SEEPJ4YEKH2TSN6B/events.json","paper":"https://pith.science/paper/2JT7PFWL"},"agent_actions":{"view_html":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B","download_json":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B.json","view_paper":"https://pith.science/paper/2JT7PFWL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.4877&json=true","fetch_graph":"https://pith.science/api/pith-number/2JT7PFWLN6SEEPJ4YEKH2TSN6B/graph.json","fetch_events":"https://pith.science/api/pith-number/2JT7PFWLN6SEEPJ4YEKH2TSN6B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B/action/storage_attestation","attest_author":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B/action/author_attestation","sign_citation":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B/action/citation_signature","submit_replication":"https://pith.science/pith/2JT7PFWLN6SEEPJ4YEKH2TSN6B/action/replication_record"}},"created_at":"2026-05-18T02:01:10.704287+00:00","updated_at":"2026-05-18T02:01:10.704287+00:00"}