{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NL7WGA3A2NWJTTQR5IVLKWHDRQ","short_pith_number":"pith:NL7WGA3A","canonical_record":{"source":{"id":"1509.02899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-09-09T19:30:20Z","cross_cats_sorted":[],"title_canon_sha256":"410940fa270a4fa8fabd4b8e9620c72775586fae380c57c0e652f7409c35eb03","abstract_canon_sha256":"6fb30e2200fc508154881c6cc44a0a05dbd06736a4e4bce483d6769b44c91cc4"},"schema_version":"1.0"},"canonical_sha256":"6aff630360d36c99ce11ea2ab558e38c11e1b7155ea2a917f30bfbb0db422870","source":{"kind":"arxiv","id":"1509.02899","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02899","created_at":"2026-05-18T01:20:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02899v1","created_at":"2026-05-18T01:20:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02899","created_at":"2026-05-18T01:20:34Z"},{"alias_kind":"pith_short_12","alias_value":"NL7WGA3A2NWJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NL7WGA3A2NWJTTQR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NL7WGA3A","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NL7WGA3A2NWJTTQR5IVLKWHDRQ","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-09-09T19:30:20Z","cross_cats_sorted":[],"title_canon_sha256":"410940fa270a4fa8fabd4b8e9620c72775586fae380c57c0e652f7409c35eb03","abstract_canon_sha256":"6fb30e2200fc508154881c6cc44a0a05dbd06736a4e4bce483d6769b44c91cc4"},"schema_version":"1.0"},"canonical_sha256":"6aff630360d36c99ce11ea2ab558e38c11e1b7155ea2a917f30bfbb0db422870","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:34.261774Z","signature_b64":"oWVMRiVlWKI4N7PcY7PcexbN01U6VBNBMBntVe6s+f9DT7+am3c38OqWwr7gZuL7EyAv5P2/xBlEiJEZgUhgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6aff630360d36c99ce11ea2ab558e38c11e1b7155ea2a917f30bfbb0db422870","last_reissued_at":"2026-05-18T01:20:34.261290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:34.261290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02899","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":"2026-05-18T01:20:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2J2V6Y9ZPjIJxe4Ex8d+UJARqnm4UOj68pDvjaSm9m89OqL6Ju77jLqiep0wpa3v1yK9o/xVpFdgPEM42WpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:15:18.691225Z"},"content_sha256":"f2d58f40623bace91f9e56f6136dfd68db1bf9deba9dda92d8defe828fa9e386","schema_version":"1.0","event_id":"sha256:f2d58f40623bace91f9e56f6136dfd68db1bf9deba9dda92d8defe828fa9e386"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NL7WGA3A2NWJTTQR5IVLKWHDRQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Avadh Saxena, Avinash Khare","submitted_at":"2015-09-09T19:30:20Z","abstract_excerpt":"For a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of $\\sech x$, it also admits solutions in terms of the PT-invariant combinations $\\sech x \\pm i \\tanh x$. Further, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms $\\sech^2 x$, it also admits solutions in terms of the PT-invariant combinations $\\sech^2 x \\pm i \\sech x \\tanh x$. Besides, we show that similar results are also true in the periodic case inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02899","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":"2026-05-18T01:20:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyDkbrdvCfXYkC3wvaR2A8c8NivUnnc6VXri7MwyP8cSsIf0zNYxpzsOjAFMe0lqxwVQDzi3oy9T3gK7CpMlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:15:18.691591Z"},"content_sha256":"76de09ed4796ffaf78163f9cfa532aae881b85c74a6e51925097a0773f79ae40","schema_version":"1.0","event_id":"sha256:76de09ed4796ffaf78163f9cfa532aae881b85c74a6e51925097a0773f79ae40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ/bundle.json","state_url":"https://pith.science/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ/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":"2026-06-01T04:15:18Z","links":{"resolver":"https://pith.science/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ","bundle":"https://pith.science/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ/bundle.json","state":"https://pith.science/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NL7WGA3A2NWJTTQR5IVLKWHDRQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NL7WGA3A2NWJTTQR5IVLKWHDRQ","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":"6fb30e2200fc508154881c6cc44a0a05dbd06736a4e4bce483d6769b44c91cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-09-09T19:30:20Z","title_canon_sha256":"410940fa270a4fa8fabd4b8e9620c72775586fae380c57c0e652f7409c35eb03"},"schema_version":"1.0","source":{"id":"1509.02899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02899","created_at":"2026-05-18T01:20:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02899v1","created_at":"2026-05-18T01:20:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02899","created_at":"2026-05-18T01:20:34Z"},{"alias_kind":"pith_short_12","alias_value":"NL7WGA3A2NWJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NL7WGA3A2NWJTTQR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NL7WGA3A","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:76de09ed4796ffaf78163f9cfa532aae881b85c74a6e51925097a0773f79ae40","target":"graph","created_at":"2026-05-18T01:20:34Z","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 real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of $\\sech x$, it also admits solutions in terms of the PT-invariant combinations $\\sech x \\pm i \\tanh x$. Further, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms $\\sech^2 x$, it also admits solutions in terms of the PT-invariant combinations $\\sech^2 x \\pm i \\sech x \\tanh x$. Besides, we show that similar results are also true in the periodic case inv","authors_text":"Avadh Saxena, Avinash Khare","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-09-09T19:30:20Z","title":"Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02899","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:f2d58f40623bace91f9e56f6136dfd68db1bf9deba9dda92d8defe828fa9e386","target":"record","created_at":"2026-05-18T01:20:34Z","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":"6fb30e2200fc508154881c6cc44a0a05dbd06736a4e4bce483d6769b44c91cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-09-09T19:30:20Z","title_canon_sha256":"410940fa270a4fa8fabd4b8e9620c72775586fae380c57c0e652f7409c35eb03"},"schema_version":"1.0","source":{"id":"1509.02899","kind":"arxiv","version":1}},"canonical_sha256":"6aff630360d36c99ce11ea2ab558e38c11e1b7155ea2a917f30bfbb0db422870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6aff630360d36c99ce11ea2ab558e38c11e1b7155ea2a917f30bfbb0db422870","first_computed_at":"2026-05-18T01:20:34.261290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:34.261290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWVMRiVlWKI4N7PcY7PcexbN01U6VBNBMBntVe6s+f9DT7+am3c38OqWwr7gZuL7EyAv5P2/xBlEiJEZgUhgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:34.261774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2d58f40623bace91f9e56f6136dfd68db1bf9deba9dda92d8defe828fa9e386","sha256:76de09ed4796ffaf78163f9cfa532aae881b85c74a6e51925097a0773f79ae40"],"state_sha256":"350af7bffdef4b61160934c46ae37aebe935dbdfa114aedc0c9e6d01fb3304d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZbevb0v/lDhaDESSR4jH/VmqswVbVk3DM8UyKF/6Fli/auRFw/ZjY6vYaKCkyoyMAil7Vyne+ibVT9Ns83WAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:15:18.693994Z","bundle_sha256":"c856d37eb8465c27c70b0b680ee1c4ed3e259c93e4e2066826ea6663fa2492ec"}}