{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7PJUVLXDMQKSKOZGKBYZXQERVL","short_pith_number":"pith:7PJUVLXD","canonical_record":{"source":{"id":"1101.4527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-24T13:43:01Z","cross_cats_sorted":[],"title_canon_sha256":"a59fc91959f74d6cf1928c86e77fecedbc94ededc3e2a6206d87ce112e22b2d5","abstract_canon_sha256":"32ef3a794da59a58fab67bed44a20f175c921080133d9d016d98f1ac7615f7cb"},"schema_version":"1.0"},"canonical_sha256":"fbd34aaee36415253b2650719bc091aafb58e350538f12a773edf74542b93b7e","source":{"kind":"arxiv","id":"1101.4527","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4527","created_at":"2026-05-18T02:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4527v2","created_at":"2026-05-18T02:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4527","created_at":"2026-05-18T02:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"7PJUVLXDMQKS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7PJUVLXDMQKSKOZG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7PJUVLXD","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7PJUVLXDMQKSKOZGKBYZXQERVL","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-24T13:43:01Z","cross_cats_sorted":[],"title_canon_sha256":"a59fc91959f74d6cf1928c86e77fecedbc94ededc3e2a6206d87ce112e22b2d5","abstract_canon_sha256":"32ef3a794da59a58fab67bed44a20f175c921080133d9d016d98f1ac7615f7cb"},"schema_version":"1.0"},"canonical_sha256":"fbd34aaee36415253b2650719bc091aafb58e350538f12a773edf74542b93b7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:24.835492Z","signature_b64":"5sjRpfYO17wWUHaFbGeH0MSu9xgOe/G4H4xxtPbhQpON73PXPgfY5C2WVM0fYC8XKR15hVpU+h4GRbfRb0mdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbd34aaee36415253b2650719bc091aafb58e350538f12a773edf74542b93b7e","last_reissued_at":"2026-05-18T02:03:24.834714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:24.834714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4527","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":"2026-05-18T02:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZt5CbtSUs+BhtnqeKC2v1ikXrC4GUQHa4Lgevrei5OZOMU5UCqakIT9F4EXkYsdxDjyxMI05hkuA44WnhlaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:19:32.970393Z"},"content_sha256":"f6efa1022df32791f80424bddbd99c31cae141b580b7f6751cf638f8228748ef","schema_version":"1.0","event_id":"sha256:f6efa1022df32791f80424bddbd99c31cae141b580b7f6751cf638f8228748ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7PJUVLXDMQKSKOZGKBYZXQERVL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness of the energy-critical defocusing NLS on $\\mathbb{R}\\times\\mathbb{T}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru D. Ionescu, Benoit Pausader","submitted_at":"2011-01-24T13:43:01Z","abstract_excerpt":"In this paper we prove global well-posedness in $H^1$ for the energy-critical defocusing initial-value problem \\begin{equation*} (i\\partial_t+\\Delta_x)u=u|u|^2,\\qquad u(0)=\\phi, \\end{equation*} in the semiperiodic setting $x\\in\\R\\times\\T^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4527","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":"2026-05-18T02:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKocyNQSQ5SDBvL36rs4Fji3EJo4vghui3U77qx4W9gbSrO+HSwts6xnyzNIkM9/YJkgSlQyQCRX6Nxv+CS2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:19:32.971113Z"},"content_sha256":"860e5f1cd81e168e5ebf589b5e781d169b4245a3714cba5a9991dfcc178fa696","schema_version":"1.0","event_id":"sha256:860e5f1cd81e168e5ebf589b5e781d169b4245a3714cba5a9991dfcc178fa696"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7PJUVLXDMQKSKOZGKBYZXQERVL/bundle.json","state_url":"https://pith.science/pith/7PJUVLXDMQKSKOZGKBYZXQERVL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7PJUVLXDMQKSKOZGKBYZXQERVL/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":"2026-05-29T20:19:32Z","links":{"resolver":"https://pith.science/pith/7PJUVLXDMQKSKOZGKBYZXQERVL","bundle":"https://pith.science/pith/7PJUVLXDMQKSKOZGKBYZXQERVL/bundle.json","state":"https://pith.science/pith/7PJUVLXDMQKSKOZGKBYZXQERVL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7PJUVLXDMQKSKOZGKBYZXQERVL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7PJUVLXDMQKSKOZGKBYZXQERVL","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":"32ef3a794da59a58fab67bed44a20f175c921080133d9d016d98f1ac7615f7cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-24T13:43:01Z","title_canon_sha256":"a59fc91959f74d6cf1928c86e77fecedbc94ededc3e2a6206d87ce112e22b2d5"},"schema_version":"1.0","source":{"id":"1101.4527","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4527","created_at":"2026-05-18T02:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4527v2","created_at":"2026-05-18T02:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4527","created_at":"2026-05-18T02:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"7PJUVLXDMQKS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7PJUVLXDMQKSKOZG","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7PJUVLXD","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:860e5f1cd81e168e5ebf589b5e781d169b4245a3714cba5a9991dfcc178fa696","target":"graph","created_at":"2026-05-18T02:03:24Z","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 global well-posedness in $H^1$ for the energy-critical defocusing initial-value problem \\begin{equation*} (i\\partial_t+\\Delta_x)u=u|u|^2,\\qquad u(0)=\\phi, \\end{equation*} in the semiperiodic setting $x\\in\\R\\times\\T^3$.","authors_text":"Alexandru D. Ionescu, Benoit Pausader","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-24T13:43:01Z","title":"Global well-posedness of the energy-critical defocusing NLS on $\\mathbb{R}\\times\\mathbb{T}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4527","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:f6efa1022df32791f80424bddbd99c31cae141b580b7f6751cf638f8228748ef","target":"record","created_at":"2026-05-18T02:03:24Z","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":"32ef3a794da59a58fab67bed44a20f175c921080133d9d016d98f1ac7615f7cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-24T13:43:01Z","title_canon_sha256":"a59fc91959f74d6cf1928c86e77fecedbc94ededc3e2a6206d87ce112e22b2d5"},"schema_version":"1.0","source":{"id":"1101.4527","kind":"arxiv","version":2}},"canonical_sha256":"fbd34aaee36415253b2650719bc091aafb58e350538f12a773edf74542b93b7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbd34aaee36415253b2650719bc091aafb58e350538f12a773edf74542b93b7e","first_computed_at":"2026-05-18T02:03:24.834714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:24.834714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5sjRpfYO17wWUHaFbGeH0MSu9xgOe/G4H4xxtPbhQpON73PXPgfY5C2WVM0fYC8XKR15hVpU+h4GRbfRb0mdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:24.835492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4527","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6efa1022df32791f80424bddbd99c31cae141b580b7f6751cf638f8228748ef","sha256:860e5f1cd81e168e5ebf589b5e781d169b4245a3714cba5a9991dfcc178fa696"],"state_sha256":"7bfe61e593bc7b76050f4469fba30a0b3cdf0b9e4bd63609755d7ba659fed8e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VfwZDdh2ud4FdMwNzlXGohFItXlIkqQB8pAmTWPw1XNB0nB0LzSFVJaq2Vpfg5aktrODkCn7hHzrhxtOsi8hCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:19:32.975063Z","bundle_sha256":"19a603036576998628c8cec9c1953dce2008c30c6f773bdc7c1a0db898c0b499"}}