{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ND5YEWJ3H5SVVSJXX6KXETPAQV","short_pith_number":"pith:ND5YEWJ3","canonical_record":{"source":{"id":"1211.7195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T09:23:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1744bcadb2c09c97b5b6281bd71f358fd085ab107b42e0ee72ba519ed29c38b7","abstract_canon_sha256":"584d94171b9ca20a2e23364cfda2d475e535510576285c89ff252066e1d6320c"},"schema_version":"1.0"},"canonical_sha256":"68fb82593b3f655ac937bf95724de0854c47e22581459fd736bbfd23d1f83738","source":{"kind":"arxiv","id":"1211.7195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7195","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7195v2","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7195","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"ND5YEWJ3H5SV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ND5YEWJ3H5SVVSJX","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ND5YEWJ3","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ND5YEWJ3H5SVVSJXX6KXETPAQV","target":"record","payload":{"canonical_record":{"source":{"id":"1211.7195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T09:23:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1744bcadb2c09c97b5b6281bd71f358fd085ab107b42e0ee72ba519ed29c38b7","abstract_canon_sha256":"584d94171b9ca20a2e23364cfda2d475e535510576285c89ff252066e1d6320c"},"schema_version":"1.0"},"canonical_sha256":"68fb82593b3f655ac937bf95724de0854c47e22581459fd736bbfd23d1f83738","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:43.603800Z","signature_b64":"pC88vVnQ3eVhjnfO3ttcYr2s+bvVWQq47vfQ41pz56TuGiczJSt0xxhnaE8M3nk8uFwyP+e+OSptuAPjEFwkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68fb82593b3f655ac937bf95724de0854c47e22581459fd736bbfd23d1f83738","last_reissued_at":"2026-05-18T03:15:43.603381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:43.603381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.7195","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXnmI3C39VPg7EmYmmOOAGzcThiHjqfRvleSR6C1gCaslsPhdEFZ1MjNIPfT0OdInuqZ5R8gshGSkacWeJfsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:27:35.875002Z"},"content_sha256":"bfc3c8b7caec2ac263f389f75c82e373ca7875fd66a35c2ef8b303c724a2351b","schema_version":"1.0","event_id":"sha256:bfc3c8b7caec2ac263f389f75c82e373ca7875fd66a35c2ef8b303c724a2351b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ND5YEWJ3H5SVVSJXX6KXETPAQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A nonlinear Landau-Zener formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Clotilde Fermanian Kammerer (LAMA), R\\'emi Carles (I3M)","submitted_at":"2012-11-30T09:23:28Z","abstract_excerpt":"We consider a system of two coupled ordinary differential equations which appears as an envelope equation in Bose-Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We show how the nonlinear system may appear from different physical models. We focus our attention on the large time behavior of the solution. We show the existence of a nonlinear scattering operator, which is reminiscent of long range scattering for the nonlinear Schrodinger equation, and which can be compared with its linear counterpart."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7195","kind":"arxiv","version":2},"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":"2026-05-18T03:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mx4nl6vCcbXDRfUvTTdWdwWShMb8gnmU3eTrg9yfKZU2ZbmxbJRlJTTnZMKV7o+809IxhYwlX+yhmrB4roB1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:27:35.875365Z"},"content_sha256":"a4a4987a324856a5d8467e15ca6fe6ab4423cabb75ff87d80ca74f57b8e51385","schema_version":"1.0","event_id":"sha256:a4a4987a324856a5d8467e15ca6fe6ab4423cabb75ff87d80ca74f57b8e51385"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV/bundle.json","state_url":"https://pith.science/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV/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":"2026-06-24T22:27:35Z","links":{"resolver":"https://pith.science/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV","bundle":"https://pith.science/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV/bundle.json","state":"https://pith.science/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ND5YEWJ3H5SVVSJXX6KXETPAQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ND5YEWJ3H5SVVSJXX6KXETPAQV","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":"584d94171b9ca20a2e23364cfda2d475e535510576285c89ff252066e1d6320c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T09:23:28Z","title_canon_sha256":"1744bcadb2c09c97b5b6281bd71f358fd085ab107b42e0ee72ba519ed29c38b7"},"schema_version":"1.0","source":{"id":"1211.7195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7195","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7195v2","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7195","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"ND5YEWJ3H5SV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ND5YEWJ3H5SVVSJX","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ND5YEWJ3","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:a4a4987a324856a5d8467e15ca6fe6ab4423cabb75ff87d80ca74f57b8e51385","target":"graph","created_at":"2026-05-18T03:15:43Z","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 a system of two coupled ordinary differential equations which appears as an envelope equation in Bose-Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We show how the nonlinear system may appear from different physical models. We focus our attention on the large time behavior of the solution. We show the existence of a nonlinear scattering operator, which is reminiscent of long range scattering for the nonlinear Schrodinger equation, and which can be compared with its linear counterpart.","authors_text":"Clotilde Fermanian Kammerer (LAMA), R\\'emi Carles (I3M)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T09:23:28Z","title":"A nonlinear Landau-Zener formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7195","kind":"arxiv","version":2},"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:bfc3c8b7caec2ac263f389f75c82e373ca7875fd66a35c2ef8b303c724a2351b","target":"record","created_at":"2026-05-18T03:15:43Z","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":"584d94171b9ca20a2e23364cfda2d475e535510576285c89ff252066e1d6320c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-30T09:23:28Z","title_canon_sha256":"1744bcadb2c09c97b5b6281bd71f358fd085ab107b42e0ee72ba519ed29c38b7"},"schema_version":"1.0","source":{"id":"1211.7195","kind":"arxiv","version":2}},"canonical_sha256":"68fb82593b3f655ac937bf95724de0854c47e22581459fd736bbfd23d1f83738","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68fb82593b3f655ac937bf95724de0854c47e22581459fd736bbfd23d1f83738","first_computed_at":"2026-05-18T03:15:43.603381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:43.603381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pC88vVnQ3eVhjnfO3ttcYr2s+bvVWQq47vfQ41pz56TuGiczJSt0xxhnaE8M3nk8uFwyP+e+OSptuAPjEFwkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:43.603800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfc3c8b7caec2ac263f389f75c82e373ca7875fd66a35c2ef8b303c724a2351b","sha256:a4a4987a324856a5d8467e15ca6fe6ab4423cabb75ff87d80ca74f57b8e51385"],"state_sha256":"d18c73e85c09af10780727c226cf245ceae96b84fc22549287b6740a3356e33d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0Iuy/M8XbmEBYpO2kmLOKfn8QxWU8iHebwIY9Os/NXDdY6GSj7TV7G2jaHnCaxSHsKpoVvwLRXx799qhOebCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:27:35.877360Z","bundle_sha256":"ecbe354c1049d53377366ead33b2e3e28c1730807cccf55b1d8a05590b463b48"}}