{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WM7AT6TIYZAUDCF26VO5TFOD7D","short_pith_number":"pith:WM7AT6TI","canonical_record":{"source":{"id":"1404.7581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T03:04:31Z","cross_cats_sorted":[],"title_canon_sha256":"256ea3e1a104a2372f984d101bb926abd160290aef4662aec0cfb6f5c3feaa80","abstract_canon_sha256":"0410239f9929f936833dcf0173f5171954b2e5f2eb360d19d959c515c95ac52e"},"schema_version":"1.0"},"canonical_sha256":"b33e09fa68c6414188baf55dd995c3f8c6157dd032e2d6032a7166e20cf8492c","source":{"kind":"arxiv","id":"1404.7581","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7581","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7581v2","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7581","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"WM7AT6TIYZAU","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WM7AT6TIYZAUDCF2","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WM7AT6TI","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WM7AT6TIYZAUDCF26VO5TFOD7D","target":"record","payload":{"canonical_record":{"source":{"id":"1404.7581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T03:04:31Z","cross_cats_sorted":[],"title_canon_sha256":"256ea3e1a104a2372f984d101bb926abd160290aef4662aec0cfb6f5c3feaa80","abstract_canon_sha256":"0410239f9929f936833dcf0173f5171954b2e5f2eb360d19d959c515c95ac52e"},"schema_version":"1.0"},"canonical_sha256":"b33e09fa68c6414188baf55dd995c3f8c6157dd032e2d6032a7166e20cf8492c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:18.267884Z","signature_b64":"yFtji18+kMKcSGy5GBrWZQIYLihCToq0FN9MKuu8kSu1qPPrhpKHxqs0P18MOXOIuInw4vGg5gdtXvLY7X3dAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b33e09fa68c6414188baf55dd995c3f8c6157dd032e2d6032a7166e20cf8492c","last_reissued_at":"2026-05-18T02:40:18.267308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:18.267308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.7581","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":"2026-05-18T02:40:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x4iup+zQA0ArDRzGm2cx9Og+PQcubP5+7Wh0k8dAVkDG4Z1a7MYSZObvsDtCdWouteqPZqXmqnc81fllgxWIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:57:19.343165Z"},"content_sha256":"06fd8add123a67ce2476a2f6b211dab63e931345b74f3dc367b759dd70a132bb","schema_version":"1.0","event_id":"sha256:06fd8add123a67ce2476a2f6b211dab63e931345b74f3dc367b759dd70a132bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WM7AT6TIYZAUDCF26VO5TFOD7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global bounds for the cubic nonlinear Schr\\\"odinger equation (NLS) in one space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Tataru, Mihaela Ifrim","submitted_at":"2014-04-30T03:04:31Z","abstract_excerpt":"This article is concerned with the small data problem for the cubic nonlinear Schr\\\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global solutions exist for data which is small in $H^{0,1}$. In the same setting we also discuss the related problems of obtaining a modified scattering expansion for the solution, as well as asymptotic completeness."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7581","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":"2026-05-18T02:40:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Whx9RTQ8HIaJVpIcuOl5nEqlai7iZOgAOl9D7tI0W7H9TqWlppXK/Rtovk9cdu3v+x9z/t7+tBbwNsJlLI/rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:57:19.343808Z"},"content_sha256":"5f5a61f80ed6779b84058b2e5280d98ccb1dbb56cd76bb99e8dcef6a85a077b6","schema_version":"1.0","event_id":"sha256:5f5a61f80ed6779b84058b2e5280d98ccb1dbb56cd76bb99e8dcef6a85a077b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WM7AT6TIYZAUDCF26VO5TFOD7D/bundle.json","state_url":"https://pith.science/pith/WM7AT6TIYZAUDCF26VO5TFOD7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WM7AT6TIYZAUDCF26VO5TFOD7D/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":"2026-05-22T04:57:19Z","links":{"resolver":"https://pith.science/pith/WM7AT6TIYZAUDCF26VO5TFOD7D","bundle":"https://pith.science/pith/WM7AT6TIYZAUDCF26VO5TFOD7D/bundle.json","state":"https://pith.science/pith/WM7AT6TIYZAUDCF26VO5TFOD7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WM7AT6TIYZAUDCF26VO5TFOD7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WM7AT6TIYZAUDCF26VO5TFOD7D","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":"0410239f9929f936833dcf0173f5171954b2e5f2eb360d19d959c515c95ac52e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T03:04:31Z","title_canon_sha256":"256ea3e1a104a2372f984d101bb926abd160290aef4662aec0cfb6f5c3feaa80"},"schema_version":"1.0","source":{"id":"1404.7581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7581","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7581v2","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7581","created_at":"2026-05-18T02:40:18Z"},{"alias_kind":"pith_short_12","alias_value":"WM7AT6TIYZAU","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WM7AT6TIYZAUDCF2","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WM7AT6TI","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:5f5a61f80ed6779b84058b2e5280d98ccb1dbb56cd76bb99e8dcef6a85a077b6","target":"graph","created_at":"2026-05-18T02:40:18Z","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":"This article is concerned with the small data problem for the cubic nonlinear Schr\\\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global solutions exist for data which is small in $H^{0,1}$. In the same setting we also discuss the related problems of obtaining a modified scattering expansion for the solution, as well as asymptotic completeness.","authors_text":"Daniel Tataru, Mihaela Ifrim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T03:04:31Z","title":"Global bounds for the cubic nonlinear Schr\\\"odinger equation (NLS) in one space dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7581","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":"sha256:06fd8add123a67ce2476a2f6b211dab63e931345b74f3dc367b759dd70a132bb","target":"record","created_at":"2026-05-18T02:40:18Z","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":"0410239f9929f936833dcf0173f5171954b2e5f2eb360d19d959c515c95ac52e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-30T03:04:31Z","title_canon_sha256":"256ea3e1a104a2372f984d101bb926abd160290aef4662aec0cfb6f5c3feaa80"},"schema_version":"1.0","source":{"id":"1404.7581","kind":"arxiv","version":2}},"canonical_sha256":"b33e09fa68c6414188baf55dd995c3f8c6157dd032e2d6032a7166e20cf8492c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b33e09fa68c6414188baf55dd995c3f8c6157dd032e2d6032a7166e20cf8492c","first_computed_at":"2026-05-18T02:40:18.267308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:18.267308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yFtji18+kMKcSGy5GBrWZQIYLihCToq0FN9MKuu8kSu1qPPrhpKHxqs0P18MOXOIuInw4vGg5gdtXvLY7X3dAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:18.267884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06fd8add123a67ce2476a2f6b211dab63e931345b74f3dc367b759dd70a132bb","sha256:5f5a61f80ed6779b84058b2e5280d98ccb1dbb56cd76bb99e8dcef6a85a077b6"],"state_sha256":"577e1a6159f5a7d0b823815efd364e51b1ca2e027fc3c2b68701494c3b4fd0bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLMK9IqiVjhYUGJY79UZzsy/TxqRE/2EpI8fRj9yYYSKxsgHtGpxT/eSbT36heJZiuGnjUcrbm0lLtWhly0MBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T04:57:19.347701Z","bundle_sha256":"cfd2552bebde7e5a192c32bf285d001fe65b0273826ec916a14b4e08918a644b"}}