{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:42VLIAQY3CKDICDYYHEJXJWIYR","short_pith_number":"pith:42VLIAQY","canonical_record":{"source":{"id":"1510.02528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-10-08T23:43:43Z","cross_cats_sorted":[],"title_canon_sha256":"b9e7f6b6499ea7c0ccc6b439359b3cecdd8dde183b20a02992677fb1b70cf5a2","abstract_canon_sha256":"b71b1436638fafb7d3841fee1c37869fc8ef3447f71f632410d43cf39ba64f09"},"schema_version":"1.0"},"canonical_sha256":"e6aab40218d894340878c1c89ba6c8c46243c914546c283a4db647578989d18e","source":{"kind":"arxiv","id":"1510.02528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02528","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02528v1","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02528","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"42VLIAQY3CKD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42VLIAQY3CKDICDY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42VLIAQY","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:42VLIAQY3CKDICDYYHEJXJWIYR","target":"record","payload":{"canonical_record":{"source":{"id":"1510.02528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-10-08T23:43:43Z","cross_cats_sorted":[],"title_canon_sha256":"b9e7f6b6499ea7c0ccc6b439359b3cecdd8dde183b20a02992677fb1b70cf5a2","abstract_canon_sha256":"b71b1436638fafb7d3841fee1c37869fc8ef3447f71f632410d43cf39ba64f09"},"schema_version":"1.0"},"canonical_sha256":"e6aab40218d894340878c1c89ba6c8c46243c914546c283a4db647578989d18e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:42.181492Z","signature_b64":"oRMloQqsOosYTTwkzGXYlOQZhbSAFAuD/eek/oJIQg2myjT2saNEIjU18HR5ig9Ffg6QRFHckQ/I2q46b0uNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6aab40218d894340878c1c89ba6c8c46243c914546c283a4db647578989d18e","last_reissued_at":"2026-05-18T01:30:42.180787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:42.180787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.02528","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":"2026-05-18T01:30:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qa32pEn6UwzU5zVoM3J/srXYm5Lx5GVTWB+SnKVUGQmjjOVuvqWtJb1aW/j8VKTKUiJwBO5ivjObAbqUurYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:20:19.170811Z"},"content_sha256":"0dd1f853df5fe25eddd1bd795980103f113f55f9cf1d434e5191beeae6f62fd6","schema_version":"1.0","event_id":"sha256:0dd1f853df5fe25eddd1bd795980103f113f55f9cf1d434e5191beeae6f62fd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:42VLIAQY3CKDICDYYHEJXJWIYR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reply to the Comment by Zhang and Li [J. Math. Phys. 56, 084101, 2015] on the Paper [J. Math. Phys. {\\bf 56}, 032104, 2015]}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Avadh Saxena, Avinash Khare","submitted_at":"2015-10-08T23:43:43Z","abstract_excerpt":"In a recent paper Zhang and Li have doubted our claim that whenever a nonlinear equation has solutions in terms of the Jacobi elliptic functions $\\cn(x,m)$ and $\\dn(x,m)$, then the same nonlinear equation will necessarily also have solutions in terms of $\\dn(x,m) \\pm \\sqrt{m} \\cn(x,m)$. We point out the flaw in their argument and show why our assertion is indeed valid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02528","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":"2026-05-18T01:30:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QJ9U1l08rCC9YlWK3uTjjYga5YJF4WKxAJaqHbPhXcuB7ZjGgdqeP7G2MuwYYRKK93XJ6SzQvJSmCQk0RBP5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:20:19.171152Z"},"content_sha256":"725bb48a191b245c3cde1595abc669d2ba78023adc425edad4c8dd9640013d06","schema_version":"1.0","event_id":"sha256:725bb48a191b245c3cde1595abc669d2ba78023adc425edad4c8dd9640013d06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42VLIAQY3CKDICDYYHEJXJWIYR/bundle.json","state_url":"https://pith.science/pith/42VLIAQY3CKDICDYYHEJXJWIYR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42VLIAQY3CKDICDYYHEJXJWIYR/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":"2026-06-01T05:20:19Z","links":{"resolver":"https://pith.science/pith/42VLIAQY3CKDICDYYHEJXJWIYR","bundle":"https://pith.science/pith/42VLIAQY3CKDICDYYHEJXJWIYR/bundle.json","state":"https://pith.science/pith/42VLIAQY3CKDICDYYHEJXJWIYR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42VLIAQY3CKDICDYYHEJXJWIYR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:42VLIAQY3CKDICDYYHEJXJWIYR","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":"b71b1436638fafb7d3841fee1c37869fc8ef3447f71f632410d43cf39ba64f09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-10-08T23:43:43Z","title_canon_sha256":"b9e7f6b6499ea7c0ccc6b439359b3cecdd8dde183b20a02992677fb1b70cf5a2"},"schema_version":"1.0","source":{"id":"1510.02528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02528","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02528v1","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02528","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"42VLIAQY3CKD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"42VLIAQY3CKDICDY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"42VLIAQY","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:725bb48a191b245c3cde1595abc669d2ba78023adc425edad4c8dd9640013d06","target":"graph","created_at":"2026-05-18T01:30:42Z","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":"In a recent paper Zhang and Li have doubted our claim that whenever a nonlinear equation has solutions in terms of the Jacobi elliptic functions $\\cn(x,m)$ and $\\dn(x,m)$, then the same nonlinear equation will necessarily also have solutions in terms of $\\dn(x,m) \\pm \\sqrt{m} \\cn(x,m)$. We point out the flaw in their argument and show why our assertion is indeed valid.","authors_text":"Avadh Saxena, Avinash Khare","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-10-08T23:43:43Z","title":"Reply to the Comment by Zhang and Li [J. Math. Phys. 56, 084101, 2015] on the Paper [J. Math. Phys. {\\bf 56}, 032104, 2015]}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02528","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":"sha256:0dd1f853df5fe25eddd1bd795980103f113f55f9cf1d434e5191beeae6f62fd6","target":"record","created_at":"2026-05-18T01:30:42Z","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":"b71b1436638fafb7d3841fee1c37869fc8ef3447f71f632410d43cf39ba64f09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2015-10-08T23:43:43Z","title_canon_sha256":"b9e7f6b6499ea7c0ccc6b439359b3cecdd8dde183b20a02992677fb1b70cf5a2"},"schema_version":"1.0","source":{"id":"1510.02528","kind":"arxiv","version":1}},"canonical_sha256":"e6aab40218d894340878c1c89ba6c8c46243c914546c283a4db647578989d18e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6aab40218d894340878c1c89ba6c8c46243c914546c283a4db647578989d18e","first_computed_at":"2026-05-18T01:30:42.180787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.180787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oRMloQqsOosYTTwkzGXYlOQZhbSAFAuD/eek/oJIQg2myjT2saNEIjU18HR5ig9Ffg6QRFHckQ/I2q46b0uNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.181492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd1f853df5fe25eddd1bd795980103f113f55f9cf1d434e5191beeae6f62fd6","sha256:725bb48a191b245c3cde1595abc669d2ba78023adc425edad4c8dd9640013d06"],"state_sha256":"d0c6f32252f73e33ff4a6996126440d35e7f676206eb1bf32c650f742b53fe9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TLNFlbOwfGUZZEm2tj89AioxbYq/qUzURlSXTDAZZ7eRR3JDSedBzHhVoSja40K2Dsr5qc4XD4p5HEx8W0sIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:20:19.173038Z","bundle_sha256":"6b78610d7245f5be5359e8dc7b8b5fb630a403fd2377bec3ab61ca442a3a2dd0"}}