{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ETUWXNEOASEQTXP5YGM2RXEJYW","short_pith_number":"pith:ETUWXNEO","canonical_record":{"source":{"id":"1411.2895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-11T17:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"ad229bde641cd9fa88b04651ef10783b48989e3945aadcdcd88111fc4e506ff8","abstract_canon_sha256":"fe8e9eea6bffb5dd4901df6a211e6cdc54315ef32438444c78d289962d727c24"},"schema_version":"1.0"},"canonical_sha256":"24e96bb48e048909ddfdc199a8dc89c5bb162343283811dc3ae75f5531bf414c","source":{"kind":"arxiv","id":"1411.2895","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2895","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2895v1","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2895","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"ETUWXNEOASEQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"ETUWXNEOASEQTXP5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"ETUWXNEO","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ETUWXNEOASEQTXP5YGM2RXEJYW","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2895","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-11T17:36:59Z","cross_cats_sorted":[],"title_canon_sha256":"ad229bde641cd9fa88b04651ef10783b48989e3945aadcdcd88111fc4e506ff8","abstract_canon_sha256":"fe8e9eea6bffb5dd4901df6a211e6cdc54315ef32438444c78d289962d727c24"},"schema_version":"1.0"},"canonical_sha256":"24e96bb48e048909ddfdc199a8dc89c5bb162343283811dc3ae75f5531bf414c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:31.558695Z","signature_b64":"92a2jEtEJSS7R9a2bGBgxv0erdBKNGgjkEOMHAyKhuIiDdDb/xYKU3P0Ef47qm20/hwKPH68Q9wKJQfc18+tBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24e96bb48e048909ddfdc199a8dc89c5bb162343283811dc3ae75f5531bf414c","last_reissued_at":"2026-05-18T01:41:31.557969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:31.557969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2895","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":"2026-05-18T01:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNR4dhJKhvNH0MQCE+VZ/j2veX/Vn6kL72taZTvH4/iVRT9tvq9qpbGQbwwxtqK0qOf2teah0NCGk92P5z6WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:47:48.619331Z"},"content_sha256":"602a56fd541ad007def2c19bfb2c3ab420331bcfd11158ab895491b2a8d44674","schema_version":"1.0","event_id":"sha256:602a56fd541ad007def2c19bfb2c3ab420331bcfd11158ab895491b2a8d44674"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ETUWXNEOASEQTXP5YGM2RXEJYW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence of solutions to coupled ${\\cal PT}$-symmetric nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dmitry A. Zezyulin, Dmitry E. Pelinovsky, Vladimir V. Konotop","submitted_at":"2014-11-11T17:36:59Z","abstract_excerpt":"We study a system of two coupled nonlinear Schr\\\"{o}dinger equations, where one equation includes gain and the other one includes losses. Strengths of the gain and the loss are equal, i.e., the resulting system is parity-time (${\\cal PT}$) symmetric. The model includes both linear and nonlinear couplings, such that when all nonlinear coefficients are equal, the system represents the ${\\cal PT}$-generalization of the Manakov model. In the one-dimensional case, we prove the existence of a global solution to the Cauchy problem in energy space $H^1$, such that the $H^1$-norm of the global solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2895","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":"2026-05-18T01:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eBJVy0GsqwAaNXd8x1rN+XFcXY22tGNmUOsVsWaFE+V1XHU33tJjfLo6KOAmVSTS8M3y575WO1IRfYzEMzEPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:47:48.620010Z"},"content_sha256":"d8648325464e840ac5bd80a92eaa921875d859c5f6bc514ad76932b1cf91b624","schema_version":"1.0","event_id":"sha256:d8648325464e840ac5bd80a92eaa921875d859c5f6bc514ad76932b1cf91b624"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ETUWXNEOASEQTXP5YGM2RXEJYW/bundle.json","state_url":"https://pith.science/pith/ETUWXNEOASEQTXP5YGM2RXEJYW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ETUWXNEOASEQTXP5YGM2RXEJYW/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":"2026-05-27T19:47:48Z","links":{"resolver":"https://pith.science/pith/ETUWXNEOASEQTXP5YGM2RXEJYW","bundle":"https://pith.science/pith/ETUWXNEOASEQTXP5YGM2RXEJYW/bundle.json","state":"https://pith.science/pith/ETUWXNEOASEQTXP5YGM2RXEJYW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ETUWXNEOASEQTXP5YGM2RXEJYW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ETUWXNEOASEQTXP5YGM2RXEJYW","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":"fe8e9eea6bffb5dd4901df6a211e6cdc54315ef32438444c78d289962d727c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-11T17:36:59Z","title_canon_sha256":"ad229bde641cd9fa88b04651ef10783b48989e3945aadcdcd88111fc4e506ff8"},"schema_version":"1.0","source":{"id":"1411.2895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2895","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2895v1","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2895","created_at":"2026-05-18T01:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"ETUWXNEOASEQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"ETUWXNEOASEQTXP5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"ETUWXNEO","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:d8648325464e840ac5bd80a92eaa921875d859c5f6bc514ad76932b1cf91b624","target":"graph","created_at":"2026-05-18T01:41:31Z","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":"We study a system of two coupled nonlinear Schr\\\"{o}dinger equations, where one equation includes gain and the other one includes losses. Strengths of the gain and the loss are equal, i.e., the resulting system is parity-time (${\\cal PT}$) symmetric. The model includes both linear and nonlinear couplings, such that when all nonlinear coefficients are equal, the system represents the ${\\cal PT}$-generalization of the Manakov model. In the one-dimensional case, we prove the existence of a global solution to the Cauchy problem in energy space $H^1$, such that the $H^1$-norm of the global solution","authors_text":"Dmitry A. Zezyulin, Dmitry E. Pelinovsky, Vladimir V. Konotop","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-11T17:36:59Z","title":"Global existence of solutions to coupled ${\\cal PT}$-symmetric nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2895","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":"sha256:602a56fd541ad007def2c19bfb2c3ab420331bcfd11158ab895491b2a8d44674","target":"record","created_at":"2026-05-18T01:41:31Z","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":"fe8e9eea6bffb5dd4901df6a211e6cdc54315ef32438444c78d289962d727c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-11T17:36:59Z","title_canon_sha256":"ad229bde641cd9fa88b04651ef10783b48989e3945aadcdcd88111fc4e506ff8"},"schema_version":"1.0","source":{"id":"1411.2895","kind":"arxiv","version":1}},"canonical_sha256":"24e96bb48e048909ddfdc199a8dc89c5bb162343283811dc3ae75f5531bf414c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24e96bb48e048909ddfdc199a8dc89c5bb162343283811dc3ae75f5531bf414c","first_computed_at":"2026-05-18T01:41:31.557969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:31.557969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"92a2jEtEJSS7R9a2bGBgxv0erdBKNGgjkEOMHAyKhuIiDdDb/xYKU3P0Ef47qm20/hwKPH68Q9wKJQfc18+tBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:31.558695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:602a56fd541ad007def2c19bfb2c3ab420331bcfd11158ab895491b2a8d44674","sha256:d8648325464e840ac5bd80a92eaa921875d859c5f6bc514ad76932b1cf91b624"],"state_sha256":"014729aaf61f0311b696c2291272c250a399fdc180b7bc899be62c0f71afb4b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+BU7zAH56BcbnYm5yT+RrMggxh8LSsz5yfMZc2yLPsm+TxKy700cktsyG2K+JdiiTSFjagE+ZgRKMkYWsTLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:47:48.624883Z","bundle_sha256":"922b475512ad43b497a29c50f9eb663012ccc78bfdaa6172213f83fe1a85343f"}}