{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K5JL5F7CXVXFBHB46YTGIF7XRO","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":"016c3522e01934224521e1ff0dffda534e86653e0fed8699897f5adfaa1fe105","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-23T10:29:12Z","title_canon_sha256":"b86928466f3b58689a87ae8b5073ecfb4ada6f7050ec101cb7c8d48e49e927be"},"schema_version":"1.0","source":{"id":"1812.09685","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09685","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09685v3","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09685","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"pith_short_12","alias_value":"K5JL5F7CXVXF","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K5JL5F7CXVXFBHB4","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K5JL5F7C","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:b05e47dc03a9aa6918ab208bf8964794dabeb8bda713a88689a0744b197d583d","target":"graph","created_at":"2026-05-17T23:42:48Z","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":"Regarding $N$-soliton solutions, the trigonometric type, the hyperbolic type, and the exponential type solutions are well studied. While for the elliptic type solution, we know only the one-soliton solution so far. Using the commutative B\\\"{a}cklund transformation, we have succeeded in constructing the KdV static elliptic $N$-soliton solution, which means that we have constructed infinitely many solutions for the $\\wp$-function type differential equation.","authors_text":"Kazuyasu Shigemoto, Masahito Hayashi, Takuya Tsukioka","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-23T10:29:12Z","title":"The Static Elliptic $N$-soliton Solutions of the KdV Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09685","kind":"arxiv","version":3},"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":"sha256:29d2ad0ad2c00b7dce14067f2948aca08fd468da052b62e95fdc4d20ad82c715","target":"record","created_at":"2026-05-17T23:42:48Z","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":"016c3522e01934224521e1ff0dffda534e86653e0fed8699897f5adfaa1fe105","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-23T10:29:12Z","title_canon_sha256":"b86928466f3b58689a87ae8b5073ecfb4ada6f7050ec101cb7c8d48e49e927be"},"schema_version":"1.0","source":{"id":"1812.09685","kind":"arxiv","version":3}},"canonical_sha256":"5752be97e2bd6e509c3cf6266417f78bac35cd87ba1eeb2895cdb9149a40dd62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5752be97e2bd6e509c3cf6266417f78bac35cd87ba1eeb2895cdb9149a40dd62","first_computed_at":"2026-05-17T23:42:48.606781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:48.606781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vY5U+F7uN5GmOHCL3i4xfEM2aK1C5aghMOM7WI9LP8Lozyi0CKofRFDlz7Wbw5yYQzWMlx9kegxXFjNg9+CSBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:48.607264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09685","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29d2ad0ad2c00b7dce14067f2948aca08fd468da052b62e95fdc4d20ad82c715","sha256:b05e47dc03a9aa6918ab208bf8964794dabeb8bda713a88689a0744b197d583d"],"state_sha256":"6c13465f036386b9818597a50c93947e1ba6f4def35c3e42e9bc9af0208ca597"}