{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BGA3Y67PJILNYPJKRNF3N5VOUR","short_pith_number":"pith:BGA3Y67P","canonical_record":{"source":{"id":"1304.8025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-30T15:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"399f54917a767df18d3fcaa97a0a5f5a4f8b7b2069b0f3960a0784bdb5ea1bc9","abstract_canon_sha256":"9b6fe05c8f718a565e40d451fdc86309a00268039e7d39d31c557ddbd2510632"},"schema_version":"1.0"},"canonical_sha256":"0981bc7bef4a16dc3d2a8b4bb6f6aea4471749129df312de2edae12683ad1bcb","source":{"kind":"arxiv","id":"1304.8025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8025","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8025v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8025","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"BGA3Y67PJILN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BGA3Y67PJILNYPJK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BGA3Y67P","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BGA3Y67PJILNYPJKRNF3N5VOUR","target":"record","payload":{"canonical_record":{"source":{"id":"1304.8025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-30T15:14:47Z","cross_cats_sorted":[],"title_canon_sha256":"399f54917a767df18d3fcaa97a0a5f5a4f8b7b2069b0f3960a0784bdb5ea1bc9","abstract_canon_sha256":"9b6fe05c8f718a565e40d451fdc86309a00268039e7d39d31c557ddbd2510632"},"schema_version":"1.0"},"canonical_sha256":"0981bc7bef4a16dc3d2a8b4bb6f6aea4471749129df312de2edae12683ad1bcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:51.112991Z","signature_b64":"mCAd9aBQpKGcI2XgTY8zEQGyquxdnVfwi5TP0dT71qF8UuKAAVFy7cwgi1V0RkaDsTnmsyA1Y0grLSSbdZZtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0981bc7bef4a16dc3d2a8b4bb6f6aea4471749129df312de2edae12683ad1bcb","last_reissued_at":"2026-05-18T03:26:51.112462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:51.112462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.8025","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZfz3oPE+7uYk9pf23CjaCqt7iiu/tDgloJ5OD2S7J+bAPKaFqX6Gv/lYp3JNCFdO5s7AbTbSnXvKJMQzKDlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:02:50.429383Z"},"content_sha256":"8bf90ba23e800bb893c6a4b4f92739cce0b16de3048ca1fb1de885baddca1d50","schema_version":"1.0","event_id":"sha256:8bf90ba23e800bb893c6a4b4f92739cce0b16de3048ca1fb1de885baddca1d50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BGA3Y67PJILNYPJKRNF3N5VOUR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness and scattering for the defocusing, mass - critical generalized KdV equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2013-04-30T15:14:47Z","abstract_excerpt":"In this paper we prove that the defocusing, mass - critical generalized KdV initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R})$. We prove this via a concentration compactness argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8025","kind":"arxiv","version":1},"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":"2026-05-18T03:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvPHrAIBYFVWSqLQXMTdW6PtOGqh/oFBP92kzilYj83fh2AGDbHrgR/fYJ5joDUTCh0JmvRkWOPvTotfRXo6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:02:50.429733Z"},"content_sha256":"7a5dfc04cfbca527bab891dbed0b4e63bd16b32159356254f703f638129a5bdc","schema_version":"1.0","event_id":"sha256:7a5dfc04cfbca527bab891dbed0b4e63bd16b32159356254f703f638129a5bdc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGA3Y67PJILNYPJKRNF3N5VOUR/bundle.json","state_url":"https://pith.science/pith/BGA3Y67PJILNYPJKRNF3N5VOUR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGA3Y67PJILNYPJKRNF3N5VOUR/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":"2026-06-01T13:02:50Z","links":{"resolver":"https://pith.science/pith/BGA3Y67PJILNYPJKRNF3N5VOUR","bundle":"https://pith.science/pith/BGA3Y67PJILNYPJKRNF3N5VOUR/bundle.json","state":"https://pith.science/pith/BGA3Y67PJILNYPJKRNF3N5VOUR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGA3Y67PJILNYPJKRNF3N5VOUR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BGA3Y67PJILNYPJKRNF3N5VOUR","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":"9b6fe05c8f718a565e40d451fdc86309a00268039e7d39d31c557ddbd2510632","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-30T15:14:47Z","title_canon_sha256":"399f54917a767df18d3fcaa97a0a5f5a4f8b7b2069b0f3960a0784bdb5ea1bc9"},"schema_version":"1.0","source":{"id":"1304.8025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.8025","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.8025v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.8025","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"BGA3Y67PJILN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BGA3Y67PJILNYPJK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BGA3Y67P","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:7a5dfc04cfbca527bab891dbed0b4e63bd16b32159356254f703f638129a5bdc","target":"graph","created_at":"2026-05-18T03:26:51Z","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, mass - critical generalized KdV initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R})$. We prove this via a concentration compactness argument.","authors_text":"Benjamin Dodson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-30T15:14:47Z","title":"Global well-posedness and scattering for the defocusing, mass - critical generalized KdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8025","kind":"arxiv","version":1},"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":"sha256:8bf90ba23e800bb893c6a4b4f92739cce0b16de3048ca1fb1de885baddca1d50","target":"record","created_at":"2026-05-18T03:26:51Z","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":"9b6fe05c8f718a565e40d451fdc86309a00268039e7d39d31c557ddbd2510632","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-30T15:14:47Z","title_canon_sha256":"399f54917a767df18d3fcaa97a0a5f5a4f8b7b2069b0f3960a0784bdb5ea1bc9"},"schema_version":"1.0","source":{"id":"1304.8025","kind":"arxiv","version":1}},"canonical_sha256":"0981bc7bef4a16dc3d2a8b4bb6f6aea4471749129df312de2edae12683ad1bcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0981bc7bef4a16dc3d2a8b4bb6f6aea4471749129df312de2edae12683ad1bcb","first_computed_at":"2026-05-18T03:26:51.112462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:51.112462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCAd9aBQpKGcI2XgTY8zEQGyquxdnVfwi5TP0dT71qF8UuKAAVFy7cwgi1V0RkaDsTnmsyA1Y0grLSSbdZZtDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:51.112991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.8025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bf90ba23e800bb893c6a4b4f92739cce0b16de3048ca1fb1de885baddca1d50","sha256:7a5dfc04cfbca527bab891dbed0b4e63bd16b32159356254f703f638129a5bdc"],"state_sha256":"4eddbdd0d83c90f32c1e364177828a8dfcc4c0074e232ef2ef749cf0d2e53e68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4I/EH8TlFGpl8Cd1B5p2yJhYz/aTN4IOnzkug5BhX5zPbrBJif37EudqKtAnhyZncrqckQBpJDZmJPngvitBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:02:50.431718Z","bundle_sha256":"eded96973675b70e5837e951aa4f67003ffb1439bd1e2dce31528708cef9cd2e"}}