{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CJE3U2TBOXUB46PYKNH3BLYQDQ","short_pith_number":"pith:CJE3U2TB","canonical_record":{"source":{"id":"1204.4468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-19T20:35:54Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"b3868902b80e4687435d6d7617cb885c02b8edf3cca2a6058ef3b39d2a64584f","abstract_canon_sha256":"1096c9136c5e78a6c7bfdd480bb2c7b73801ca7b3cac48e6ed78f8c119b7b47c"},"schema_version":"1.0"},"canonical_sha256":"1249ba6a6175e81e79f8534fb0af101c2b45bb1fd4cc7336e0f714d023adb83d","source":{"kind":"arxiv","id":"1204.4468","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4468","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4468v3","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4468","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"CJE3U2TBOXUB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CJE3U2TBOXUB46PY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CJE3U2TB","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CJE3U2TBOXUB46PYKNH3BLYQDQ","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-19T20:35:54Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"b3868902b80e4687435d6d7617cb885c02b8edf3cca2a6058ef3b39d2a64584f","abstract_canon_sha256":"1096c9136c5e78a6c7bfdd480bb2c7b73801ca7b3cac48e6ed78f8c119b7b47c"},"schema_version":"1.0"},"canonical_sha256":"1249ba6a6175e81e79f8534fb0af101c2b45bb1fd4cc7336e0f714d023adb83d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:15.275661Z","signature_b64":"yBJJR5yhyFj3BH9Cr8ImI/170Qw0czHrd3v9xe089wDxWUgWbz/mLPVt7qNf/PD2ABzCMn3KHIB0y2d2+QQ2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1249ba6a6175e81e79f8534fb0af101c2b45bb1fd4cc7336e0f714d023adb83d","last_reissued_at":"2026-05-18T03:44:15.274961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:15.274961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4468","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDv5IXfY2BKxIxM9iS3VMGwQcF/rQ5dXNN+OtmJCC2oXuFaDQLs7/vC5OduaDYj84xy4SHibXt5/MsmkQmSACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:51:09.856251Z"},"content_sha256":"7399572fdb8367be1f22cf87748093652f9fd16d540d9581c99d7170563c2d9c","schema_version":"1.0","event_id":"sha256:7399572fdb8367be1f22cf87748093652f9fd16d540d9581c99d7170563c2d9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CJE3U2TBOXUB46PYKNH3BLYQDQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-Posedness and averaging of NLS with time-periodic dispersion management","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"math.AP","authors_text":"Christof Sparber, Jean-Claude Saut, Paolo Antonelli","submitted_at":"2012-04-19T20:35:54Z","abstract_excerpt":"We consider the Cauchy problem for dispersion managed nonlinear Schroedinger equations, where the dispersion map is assumed to be periodic and piecewise constant in time. We establish local and global well-posedness results and the possibility of finite time blow-up. In addition, we shall study the scaling limit of fast dispersion management and establish convergence to an effective model with averaged dispersion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4468","kind":"arxiv","version":3},"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":"2026-05-18T03:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xWhMI9ATtV/2lYwjQuUHBARO4wC9+9lT0VlE+jsfCASR3XGM1BHIiA2BnF2qXd0F1qamsWm8ZNRc5WZRLa7tCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:51:09.856643Z"},"content_sha256":"4953dc1cab30bb5e843f2e0313b894fae9ff725c359b6af2a76a46ad77ac2e06","schema_version":"1.0","event_id":"sha256:4953dc1cab30bb5e843f2e0313b894fae9ff725c359b6af2a76a46ad77ac2e06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ/bundle.json","state_url":"https://pith.science/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ/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":"2026-06-12T09:51:09Z","links":{"resolver":"https://pith.science/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ","bundle":"https://pith.science/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ/bundle.json","state":"https://pith.science/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJE3U2TBOXUB46PYKNH3BLYQDQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CJE3U2TBOXUB46PYKNH3BLYQDQ","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":"1096c9136c5e78a6c7bfdd480bb2c7b73801ca7b3cac48e6ed78f8c119b7b47c","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-19T20:35:54Z","title_canon_sha256":"b3868902b80e4687435d6d7617cb885c02b8edf3cca2a6058ef3b39d2a64584f"},"schema_version":"1.0","source":{"id":"1204.4468","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4468","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4468v3","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4468","created_at":"2026-05-18T03:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"CJE3U2TBOXUB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CJE3U2TBOXUB46PY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CJE3U2TB","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:4953dc1cab30bb5e843f2e0313b894fae9ff725c359b6af2a76a46ad77ac2e06","target":"graph","created_at":"2026-05-18T03:44:15Z","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 consider the Cauchy problem for dispersion managed nonlinear Schroedinger equations, where the dispersion map is assumed to be periodic and piecewise constant in time. We establish local and global well-posedness results and the possibility of finite time blow-up. In addition, we shall study the scaling limit of fast dispersion management and establish convergence to an effective model with averaged dispersion.","authors_text":"Christof Sparber, Jean-Claude Saut, Paolo Antonelli","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-19T20:35:54Z","title":"Well-Posedness and averaging of NLS with time-periodic dispersion management"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4468","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":"sha256:7399572fdb8367be1f22cf87748093652f9fd16d540d9581c99d7170563c2d9c","target":"record","created_at":"2026-05-18T03:44:15Z","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":"1096c9136c5e78a6c7bfdd480bb2c7b73801ca7b3cac48e6ed78f8c119b7b47c","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-19T20:35:54Z","title_canon_sha256":"b3868902b80e4687435d6d7617cb885c02b8edf3cca2a6058ef3b39d2a64584f"},"schema_version":"1.0","source":{"id":"1204.4468","kind":"arxiv","version":3}},"canonical_sha256":"1249ba6a6175e81e79f8534fb0af101c2b45bb1fd4cc7336e0f714d023adb83d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1249ba6a6175e81e79f8534fb0af101c2b45bb1fd4cc7336e0f714d023adb83d","first_computed_at":"2026-05-18T03:44:15.274961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:15.274961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yBJJR5yhyFj3BH9Cr8ImI/170Qw0czHrd3v9xe089wDxWUgWbz/mLPVt7qNf/PD2ABzCMn3KHIB0y2d2+QQ2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:15.275661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4468","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7399572fdb8367be1f22cf87748093652f9fd16d540d9581c99d7170563c2d9c","sha256:4953dc1cab30bb5e843f2e0313b894fae9ff725c359b6af2a76a46ad77ac2e06"],"state_sha256":"153bc0d24b78a434475833d4e5e24ee7eb9c08c2df20a2d28c3a9c9d80855572"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bwh5KpAVYuwgNKwihhOgP3AEgM3HrFTBoQwWtS/sj+k7FgOjwl8jDaG6Wa9TgR0YojDXnz7zq7f3vRQ/msBDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:51:09.858726Z","bundle_sha256":"81ed9c0b5684c8cd015af3f95bf9a6a24650b005a9afd7e044e9ab8f2d3aba57"}}