{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XVANOJ3Z6AAAA5CHOQR3COAPXO","short_pith_number":"pith:XVANOJ3Z","canonical_record":{"source":{"id":"1704.05013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-17T16:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"bdf764ae482c350f8b55df2732ba9b129649c6c1cd2684b9a35f07f61c0e9837","abstract_canon_sha256":"e629a531f3514bd71a94af6a4078cd24c7cb3d3cea32f84b3cb381785d0848a2"},"schema_version":"1.0"},"canonical_sha256":"bd40d72779f0000074477423b1380fbb8baf8c18eb676baa540fed285acdc2b2","source":{"kind":"arxiv","id":"1704.05013","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05013","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05013v2","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05013","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"XVANOJ3Z6AAA","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"pith_short_16","alias_value":"XVANOJ3Z6AAAA5CH","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"pith_short_8","alias_value":"XVANOJ3Z","created_at":"2026-07-05T04:30:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XVANOJ3Z6AAAA5CHOQR3COAPXO","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-17T16:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"bdf764ae482c350f8b55df2732ba9b129649c6c1cd2684b9a35f07f61c0e9837","abstract_canon_sha256":"e629a531f3514bd71a94af6a4078cd24c7cb3d3cea32f84b3cb381785d0848a2"},"schema_version":"1.0"},"canonical_sha256":"bd40d72779f0000074477423b1380fbb8baf8c18eb676baa540fed285acdc2b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:30:49.073136Z","signature_b64":"Udq31si5Cp8BXvx/7DQR+jKUX1wxc8O3mKNRGLOMfB+PYK4FeZZQc6OoFWP80br02PjApozbbUaGXcLYNTb9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd40d72779f0000074477423b1380fbb8baf8c18eb676baa540fed285acdc2b2","last_reissued_at":"2026-07-05T04:30:49.072655Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:30:49.072655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05013","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":"2026-07-05T04:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y8rk5kq7W+D51Bgqx+PPrIoO4YvHSKoYC2Wr77Ws8JPyiKj713jY2psW822iOr1RNjJybXXa8XiPWvYN2903Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:25:17.302435Z"},"content_sha256":"ba4e873e398870f89c97494db8a35f4e925e59dacaf5aaf26795b8bc54c100fc","schema_version":"1.0","event_id":"sha256:ba4e873e398870f89c97494db8a35f4e925e59dacaf5aaf26795b8bc54c100fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XVANOJ3Z6AAAA5CHOQR3COAPXO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chenmin Sun","submitted_at":"2017-04-17T16:16:52Z","abstract_excerpt":"In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter $\\alpha\\in (0, 1)$. When $\\frac{1}{2}<\\alpha<1$,we prove the global well-posedness in $H^s(\\mathbb{R})$ with $s>-\\frac{1}{4}$, while for $0<\\alpha<\\frac{1}{2}$, we obtain global well-posedness in $H^s(\\mathbb{R})$ with $s>-\\frac{5}{8}$. We have adapted the linear-nonlinear decomposition and resonance decomposition technique in different range of $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05013","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1704.05013/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IpCwrhVfgaoI7/uc9GseedgXAjf66HR5q8aEgf8jSIGg7hVOzra5vxsBnM+paGE4YkvLhh/RlLWEkJ4d7lnPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T00:25:17.302979Z"},"content_sha256":"f38f4216a2f3e0f3d33b6510811a42363a823049323a304d9656ac43eb22d484","schema_version":"1.0","event_id":"sha256:f38f4216a2f3e0f3d33b6510811a42363a823049323a304d9656ac43eb22d484"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO/bundle.json","state_url":"https://pith.science/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO/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":"2026-08-07T00:25:17Z","links":{"resolver":"https://pith.science/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO","bundle":"https://pith.science/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO/bundle.json","state":"https://pith.science/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVANOJ3Z6AAAA5CHOQR3COAPXO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XVANOJ3Z6AAAA5CHOQR3COAPXO","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":"e629a531f3514bd71a94af6a4078cd24c7cb3d3cea32f84b3cb381785d0848a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-17T16:16:52Z","title_canon_sha256":"bdf764ae482c350f8b55df2732ba9b129649c6c1cd2684b9a35f07f61c0e9837"},"schema_version":"1.0","source":{"id":"1704.05013","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05013","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05013v2","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05013","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"XVANOJ3Z6AAA","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"pith_short_16","alias_value":"XVANOJ3Z6AAAA5CH","created_at":"2026-07-05T04:30:49Z"},{"alias_kind":"pith_short_8","alias_value":"XVANOJ3Z","created_at":"2026-07-05T04:30:49Z"}],"graph_snapshots":[{"event_id":"sha256:f38f4216a2f3e0f3d33b6510811a42363a823049323a304d9656ac43eb22d484","target":"graph","created_at":"2026-07-05T04:30:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1704.05013/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we study the low-regularity Cauchy problem of a one dimensional quadratic Schrodinger system with coupled parameter $\\alpha\\in (0, 1)$. When $\\frac{1}{2}<\\alpha<1$,we prove the global well-posedness in $H^s(\\mathbb{R})$ with $s>-\\frac{1}{4}$, while for $0<\\alpha<\\frac{1}{2}$, we obtain global well-posedness in $H^s(\\mathbb{R})$ with $s>-\\frac{5}{8}$. We have adapted the linear-nonlinear decomposition and resonance decomposition technique in different range of $\\alpha$.","authors_text":"Chenmin Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-17T16:16:52Z","title":"On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05013","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:ba4e873e398870f89c97494db8a35f4e925e59dacaf5aaf26795b8bc54c100fc","target":"record","created_at":"2026-07-05T04:30:49Z","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":"e629a531f3514bd71a94af6a4078cd24c7cb3d3cea32f84b3cb381785d0848a2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-17T16:16:52Z","title_canon_sha256":"bdf764ae482c350f8b55df2732ba9b129649c6c1cd2684b9a35f07f61c0e9837"},"schema_version":"1.0","source":{"id":"1704.05013","kind":"arxiv","version":2}},"canonical_sha256":"bd40d72779f0000074477423b1380fbb8baf8c18eb676baa540fed285acdc2b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd40d72779f0000074477423b1380fbb8baf8c18eb676baa540fed285acdc2b2","first_computed_at":"2026-07-05T04:30:49.072655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:30:49.072655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Udq31si5Cp8BXvx/7DQR+jKUX1wxc8O3mKNRGLOMfB+PYK4FeZZQc6OoFWP80br02PjApozbbUaGXcLYNTb9Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:30:49.073136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05013","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba4e873e398870f89c97494db8a35f4e925e59dacaf5aaf26795b8bc54c100fc","sha256:f38f4216a2f3e0f3d33b6510811a42363a823049323a304d9656ac43eb22d484"],"state_sha256":"54c56059bd3475a76836638cca7db52d8a54511defeee7700e6b220bea53da1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rj2ytcmUdoAMl39ON4bS6rpe0c/UADt/93h1X5opQu5NuusOoVCMC6iGwdNIt/mgj5tIUUn6I+mbHj/9EUKSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T00:25:17.306232Z","bundle_sha256":"742be56b37a92ace10c0077c5b1a5ee623e24de007c97ff5eae68e04a5a08868"}}