{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EJ4O5HSADXDFC7TMNYDZXESM3B","short_pith_number":"pith:EJ4O5HSA","canonical_record":{"source":{"id":"1403.5360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T04:35:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"aba5db89f2fd7a7d84c0cac46520bb920c552c040afc9fb8744f57c016a011e2","abstract_canon_sha256":"9ecb7a37f890d3fa2fe6c15ca23e1c48dd4d02b51940ee4b21737812db675755"},"schema_version":"1.0"},"canonical_sha256":"2278ee9e401dc6517e6c6e079b924cd87105d2cb0691db4a53a3426f4c1809ac","source":{"kind":"arxiv","id":"1403.5360","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5360","created_at":"2026-05-18T01:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5360v1","created_at":"2026-05-18T01:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5360","created_at":"2026-05-18T01:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"EJ4O5HSADXDF","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJ4O5HSADXDFC7TM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJ4O5HSA","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EJ4O5HSADXDFC7TMNYDZXESM3B","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T04:35:25Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"aba5db89f2fd7a7d84c0cac46520bb920c552c040afc9fb8744f57c016a011e2","abstract_canon_sha256":"9ecb7a37f890d3fa2fe6c15ca23e1c48dd4d02b51940ee4b21737812db675755"},"schema_version":"1.0"},"canonical_sha256":"2278ee9e401dc6517e6c6e079b924cd87105d2cb0691db4a53a3426f4c1809ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:52.721939Z","signature_b64":"M0ofKW93ywRhBSSp126Z/ABvDrI0Mhcpu3S05pN29A8Ft8bcUeNq5iLoP37m1VdH+eFUyYVMZntEhk8TBe6JCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2278ee9e401dc6517e6c6e079b924cd87105d2cb0691db4a53a3426f4c1809ac","last_reissued_at":"2026-05-18T01:43:52.721302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:52.721302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5360","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3FjmKJfhKXQfHdHSdyzcaPgP0Mu/sX8ie53LnZhaPTv4DYlPqh2oJ+3z09WW4jbuobIpzYJwvrpnyYHeZ4SCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:19:30.338052Z"},"content_sha256":"3896304f38e6b5b1b1641d8085e888f02dd4e154612f3ce486577e932a975a0a","schema_version":"1.0","event_id":"sha256:3896304f38e6b5b1b1641d8085e888f02dd4e154612f3ce486577e932a975a0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EJ4O5HSADXDFC7TMNYDZXESM3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Avadh Saxena, Avinash Khare","submitted_at":"2014-03-21T04:35:25Z","abstract_excerpt":"For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions $\\cn(x,m)$ and $\\dn(x,m)$ with modulus $m$, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schr\\\"odinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schr\\\"odinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schr\\\"o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5360","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zfw49p7O3wqiaD313Uko5MYUpw7WIPqiEHgUNSv3RZ2upVD6ct444np+6YI/wfJqwhJ5h60Eg1CBEPEjbsLNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:19:30.338420Z"},"content_sha256":"b6afd3517f4129b8a16bc1f43ff5dc09de61237642cab66a1c85bb6c2b8b0f6f","schema_version":"1.0","event_id":"sha256:b6afd3517f4129b8a16bc1f43ff5dc09de61237642cab66a1c85bb6c2b8b0f6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJ4O5HSADXDFC7TMNYDZXESM3B/bundle.json","state_url":"https://pith.science/pith/EJ4O5HSADXDFC7TMNYDZXESM3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJ4O5HSADXDFC7TMNYDZXESM3B/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T07:19:30Z","links":{"resolver":"https://pith.science/pith/EJ4O5HSADXDFC7TMNYDZXESM3B","bundle":"https://pith.science/pith/EJ4O5HSADXDFC7TMNYDZXESM3B/bundle.json","state":"https://pith.science/pith/EJ4O5HSADXDFC7TMNYDZXESM3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJ4O5HSADXDFC7TMNYDZXESM3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EJ4O5HSADXDFC7TMNYDZXESM3B","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":"9ecb7a37f890d3fa2fe6c15ca23e1c48dd4d02b51940ee4b21737812db675755","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T04:35:25Z","title_canon_sha256":"aba5db89f2fd7a7d84c0cac46520bb920c552c040afc9fb8744f57c016a011e2"},"schema_version":"1.0","source":{"id":"1403.5360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5360","created_at":"2026-05-18T01:43:52Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5360v1","created_at":"2026-05-18T01:43:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5360","created_at":"2026-05-18T01:43:52Z"},{"alias_kind":"pith_short_12","alias_value":"EJ4O5HSADXDF","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJ4O5HSADXDFC7TM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJ4O5HSA","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b6afd3517f4129b8a16bc1f43ff5dc09de61237642cab66a1c85bb6c2b8b0f6f","target":"graph","created_at":"2026-05-18T01:43:52Z","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":"For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions $\\cn(x,m)$ and $\\dn(x,m)$ with modulus $m$, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schr\\\"odinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schr\\\"odinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schr\\\"o","authors_text":"Avadh Saxena, Avinash Khare","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T04:35:25Z","title":"Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5360","kind":"arxiv","version":1},"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":"sha256:3896304f38e6b5b1b1641d8085e888f02dd4e154612f3ce486577e932a975a0a","target":"record","created_at":"2026-05-18T01:43:52Z","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":"9ecb7a37f890d3fa2fe6c15ca23e1c48dd4d02b51940ee4b21737812db675755","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-03-21T04:35:25Z","title_canon_sha256":"aba5db89f2fd7a7d84c0cac46520bb920c552c040afc9fb8744f57c016a011e2"},"schema_version":"1.0","source":{"id":"1403.5360","kind":"arxiv","version":1}},"canonical_sha256":"2278ee9e401dc6517e6c6e079b924cd87105d2cb0691db4a53a3426f4c1809ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2278ee9e401dc6517e6c6e079b924cd87105d2cb0691db4a53a3426f4c1809ac","first_computed_at":"2026-05-18T01:43:52.721302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:52.721302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M0ofKW93ywRhBSSp126Z/ABvDrI0Mhcpu3S05pN29A8Ft8bcUeNq5iLoP37m1VdH+eFUyYVMZntEhk8TBe6JCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:52.721939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3896304f38e6b5b1b1641d8085e888f02dd4e154612f3ce486577e932a975a0a","sha256:b6afd3517f4129b8a16bc1f43ff5dc09de61237642cab66a1c85bb6c2b8b0f6f"],"state_sha256":"7d38688055c66c25e32e3e1e0230fd4ab04e1f5a7b56a15536ac021b79a407ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktHz4ZdGvwuDMg8qIGE6yvP73xgTQOmiVe2Jj6f/OHS0uEUc9oYZf7UQk0Tmet61rct1ifsl8uvh6NUmakI4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:19:30.340368Z","bundle_sha256":"7472db83055f40fc5ca39f7161c14e5068674b439b1887a07fec57ec5f318ebe"}}