{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GKNNGZYFUJMTUDLTOO52KZGVA6","short_pith_number":"pith:GKNNGZYF","schema_version":"1.0","canonical_sha256":"329ad36705a2593a0d7373bba564d507b4e7c56ae7a6f5e5a05ee0b80e7dff86","source":{"kind":"arxiv","id":"2411.17364","version":1},"attestation_state":"computed","paper":{"title":"Concentric-ring patterns of higher-order lumps in the Kadomtsev--Petviashvili I equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Bo Yang, Jianke Yang","submitted_at":"2024-11-26T12:13:16Z","abstract_excerpt":"Large-time patterns of general higher-order lump solutions in the KP-I equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial $(x, y)$ plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian-Hermit polynomial, together with possible funda"},"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":"2411.17364","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2024-11-26T12:13:16Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"1adedfd55969d8c13152d1aabcf1fc109910d788265b0418be28e5b55b9915b2","abstract_canon_sha256":"1e357458e5c8b86b085783306529206800d2a8a3071d816a7591c832035f56a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:46.337022Z","signature_b64":"QQdG7bMjt52r6igevhG+RGzlKOZAzcXyYe9An1UOaKmVTGMaR8qG8UOk/p6SBcw56eebLF5q6WrB4FZGkZI1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"329ad36705a2593a0d7373bba564d507b4e7c56ae7a6f5e5a05ee0b80e7dff86","last_reissued_at":"2026-07-05T09:40:46.336516Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:46.336516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentric-ring patterns of higher-order lumps in the Kadomtsev--Petviashvili I equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Bo Yang, Jianke Yang","submitted_at":"2024-11-26T12:13:16Z","abstract_excerpt":"Large-time patterns of general higher-order lump solutions in the KP-I equation are investigated. It is shown that when the index vector of the general lump solution is a sequence of consecutive odd integers starting from one, the large-time pattern in the spatial $(x, y)$ plane generically would comprise fundamental lumps uniformly distributed on concentric rings. For other index vectors, the large-time pattern would comprise fundamental lumps in the outer region as described analytically by the nonzero-root structure of the associated Wronskian-Hermit polynomial, together with possible funda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17364","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17364/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.17364","created_at":"2026-07-05T09:40:46.336574+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.17364v1","created_at":"2026-07-05T09:40:46.336574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17364","created_at":"2026-07-05T09:40:46.336574+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKNNGZYFUJMT","created_at":"2026-07-05T09:40:46.336574+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKNNGZYFUJMTUDLT","created_at":"2026-07-05T09:40:46.336574+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKNNGZYF","created_at":"2026-07-05T09:40:46.336574+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/GKNNGZYFUJMTUDLTOO52KZGVA6","json":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6.json","graph_json":"https://pith.science/api/pith-number/GKNNGZYFUJMTUDLTOO52KZGVA6/graph.json","events_json":"https://pith.science/api/pith-number/GKNNGZYFUJMTUDLTOO52KZGVA6/events.json","paper":"https://pith.science/paper/GKNNGZYF"},"agent_actions":{"view_html":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6","download_json":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6.json","view_paper":"https://pith.science/paper/GKNNGZYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.17364&json=true","fetch_graph":"https://pith.science/api/pith-number/GKNNGZYFUJMTUDLTOO52KZGVA6/graph.json","fetch_events":"https://pith.science/api/pith-number/GKNNGZYFUJMTUDLTOO52KZGVA6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6/action/storage_attestation","attest_author":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6/action/author_attestation","sign_citation":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6/action/citation_signature","submit_replication":"https://pith.science/pith/GKNNGZYFUJMTUDLTOO52KZGVA6/action/replication_record"}},"created_at":"2026-07-05T09:40:46.336574+00:00","updated_at":"2026-07-05T09:40:46.336574+00:00"}