{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5GP7TSUAVNBTKB7PNW5HHFY4Q7","short_pith_number":"pith:5GP7TSUA","canonical_record":{"source":{"id":"1010.0040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-01T00:20:53Z","cross_cats_sorted":[],"title_canon_sha256":"1b9d1be54008e16c2a8d1d349885d9a7ec29faa82e5c367c9e2a25e7d1e951ba","abstract_canon_sha256":"6734f887ea0b4846165f5648eb3da7f5a1bcfc726fd75261868267acd69efc27"},"schema_version":"1.0"},"canonical_sha256":"e99ff9ca80ab433507ef6dba73971c87ea02b989c543e5cba0c1eccdfc89127a","source":{"kind":"arxiv","id":"1010.0040","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0040","created_at":"2026-05-18T04:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0040v2","created_at":"2026-05-18T04:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0040","created_at":"2026-05-18T04:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"5GP7TSUAVNBT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5GP7TSUAVNBTKB7P","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5GP7TSUA","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5GP7TSUAVNBTKB7PNW5HHFY4Q7","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-01T00:20:53Z","cross_cats_sorted":[],"title_canon_sha256":"1b9d1be54008e16c2a8d1d349885d9a7ec29faa82e5c367c9e2a25e7d1e951ba","abstract_canon_sha256":"6734f887ea0b4846165f5648eb3da7f5a1bcfc726fd75261868267acd69efc27"},"schema_version":"1.0"},"canonical_sha256":"e99ff9ca80ab433507ef6dba73971c87ea02b989c543e5cba0c1eccdfc89127a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:23.126870Z","signature_b64":"Kuch30JItp2U0ahcucb7zlCDXIH0NrrcXkFxKlBWyjZFVvLjv7nbZ0EF6zyCDMV7/jnc8jzEdXgm3erkEHogDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e99ff9ca80ab433507ef6dba73971c87ea02b989c543e5cba0c1eccdfc89127a","last_reissued_at":"2026-05-18T04:26:23.126394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:23.126394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0040","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":"2026-05-18T04:26:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VbOZDtM2uiBxt5+S/iXqswVztCgitqjXWCKcUsIiPZbifhjUxnIVPr2yz+8T54WSKWzDJWikcTEAuZCV8cStDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:07:45.267579Z"},"content_sha256":"bec80ddaf151b4d1d173b18fd37c481549795dde4db2768c0b7e16913c738bdf","schema_version":"1.0","event_id":"sha256:bec80ddaf151b4d1d173b18fd37c481549795dde4db2768c0b7e16913c738bdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5GP7TSUAVNBTKB7PNW5HHFY4Q7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr\\\"odinger equation when $d = 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2010-10-01T00:20:53Z","abstract_excerpt":"In this paper we prove that the defocusing, quintic nonlinear Schr\\\"odinger initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R})$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in [11]. Since we are considering an $L^{2}$ - critical initial value problem we will localize to low frequencies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0040","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":"2026-05-18T04:26:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B1wA0zZHdZdrsq+7KloaoryqZ1JZ2urDiE6iryUCcTOz9KNR0AYXDkKhPjKBlcB8kPZZcVYXZIKFhsI80GTMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:07:45.267921Z"},"content_sha256":"d322cf9428adefb4e4980acd87c2249b87fcf9acb8988c51b54fddeac53d1e67","schema_version":"1.0","event_id":"sha256:d322cf9428adefb4e4980acd87c2249b87fcf9acb8988c51b54fddeac53d1e67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7/bundle.json","state_url":"https://pith.science/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7/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":"2026-05-30T00:07:45Z","links":{"resolver":"https://pith.science/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7","bundle":"https://pith.science/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7/bundle.json","state":"https://pith.science/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GP7TSUAVNBTKB7PNW5HHFY4Q7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5GP7TSUAVNBTKB7PNW5HHFY4Q7","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":"6734f887ea0b4846165f5648eb3da7f5a1bcfc726fd75261868267acd69efc27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-01T00:20:53Z","title_canon_sha256":"1b9d1be54008e16c2a8d1d349885d9a7ec29faa82e5c367c9e2a25e7d1e951ba"},"schema_version":"1.0","source":{"id":"1010.0040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0040","created_at":"2026-05-18T04:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0040v2","created_at":"2026-05-18T04:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0040","created_at":"2026-05-18T04:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"5GP7TSUAVNBT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5GP7TSUAVNBTKB7P","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5GP7TSUA","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:d322cf9428adefb4e4980acd87c2249b87fcf9acb8988c51b54fddeac53d1e67","target":"graph","created_at":"2026-05-18T04:26:23Z","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":"In this paper we prove that the defocusing, quintic nonlinear Schr\\\"odinger initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R})$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in [11]. Since we are considering an $L^{2}$ - critical initial value problem we will localize to low frequencies.","authors_text":"Benjamin Dodson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-01T00:20:53Z","title":"Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr\\\"odinger equation when $d = 1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0040","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:bec80ddaf151b4d1d173b18fd37c481549795dde4db2768c0b7e16913c738bdf","target":"record","created_at":"2026-05-18T04:26:23Z","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":"6734f887ea0b4846165f5648eb3da7f5a1bcfc726fd75261868267acd69efc27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-10-01T00:20:53Z","title_canon_sha256":"1b9d1be54008e16c2a8d1d349885d9a7ec29faa82e5c367c9e2a25e7d1e951ba"},"schema_version":"1.0","source":{"id":"1010.0040","kind":"arxiv","version":2}},"canonical_sha256":"e99ff9ca80ab433507ef6dba73971c87ea02b989c543e5cba0c1eccdfc89127a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e99ff9ca80ab433507ef6dba73971c87ea02b989c543e5cba0c1eccdfc89127a","first_computed_at":"2026-05-18T04:26:23.126394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:23.126394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kuch30JItp2U0ahcucb7zlCDXIH0NrrcXkFxKlBWyjZFVvLjv7nbZ0EF6zyCDMV7/jnc8jzEdXgm3erkEHogDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:23.126870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bec80ddaf151b4d1d173b18fd37c481549795dde4db2768c0b7e16913c738bdf","sha256:d322cf9428adefb4e4980acd87c2249b87fcf9acb8988c51b54fddeac53d1e67"],"state_sha256":"f0e24238a69fab920165db78705024512262d126d5a9c96d1630684325b0f01b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkCVERngJ8gbsf0hK0K9wBadaVqnsI3q23q98VZhHNYY8BzmRrMUFfIdMXetjP7novKe86NYzM+NADRE34LeAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:07:45.270111Z","bundle_sha256":"2a0dc8391edfb10290317879b0b39646dd53f8759ca2ef262c3efab962b104f5"}}