{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KOW6BFYNZTKXORMMOXLO7JTNRO","short_pith_number":"pith:KOW6BFYN","canonical_record":{"source":{"id":"1004.0721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-05T21:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"67684e8b938eb48e3b7b0135840ed0c9a1db328c2ee23918e82d659c7f1bc675","abstract_canon_sha256":"b5a709179776cc3d41ec84b93ce80ba619023d351ab3617a67bb09095aa140f8"},"schema_version":"1.0"},"canonical_sha256":"53ade0970dccd577458c75d6efa66d8b8ad730eed24afd89f965f8b02205e1ef","source":{"kind":"arxiv","id":"1004.0721","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0721","created_at":"2026-05-18T04:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0721v2","created_at":"2026-05-18T04:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0721","created_at":"2026-05-18T04:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"KOW6BFYNZTKX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KOW6BFYNZTKXORMM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KOW6BFYN","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KOW6BFYNZTKXORMMOXLO7JTNRO","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-05T21:21:28Z","cross_cats_sorted":[],"title_canon_sha256":"67684e8b938eb48e3b7b0135840ed0c9a1db328c2ee23918e82d659c7f1bc675","abstract_canon_sha256":"b5a709179776cc3d41ec84b93ce80ba619023d351ab3617a67bb09095aa140f8"},"schema_version":"1.0"},"canonical_sha256":"53ade0970dccd577458c75d6efa66d8b8ad730eed24afd89f965f8b02205e1ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:16.607780Z","signature_b64":"ZPOCG0DvlrDoU3gCG8e3Hj2XvQaegqAq82V2MvsvX8aCLd+PGgJBwm9mc4LF+sYsJ+AI/3z5YBIyd0P9vBdsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53ade0970dccd577458c75d6efa66d8b8ad730eed24afd89f965f8b02205e1ef","last_reissued_at":"2026-05-18T04:39:16.607218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:16.607218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0721","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":"2026-05-18T04:39:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4S7Gi5/99+tZnQ6D8jDaRrRBoI11+FgRvVXAInVwEljxE4x8rHDgirh7JPDpl9iZun++fTrZM8JQTiCsBvqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:12:28.946692Z"},"content_sha256":"1e255b41fb4dcf394ed5b8a4dfd5d7b2f8d206e8dcfc369710a591466af277cb","schema_version":"1.0","event_id":"sha256:1e255b41fb4dcf394ed5b8a4dfd5d7b2f8d206e8dcfc369710a591466af277cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KOW6BFYNZTKXORMMOXLO7JTNRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new proof of long range scattering for critical nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabio Pusateri, Jun Kato","submitted_at":"2010-04-05T21:21:28Z","abstract_excerpt":"We present a new proof of global existence and long range scattering, from small initial data, for the one-dimensional cubic gauge invariant nonlinear Schr\\\"odinger equation, and for Hartree equations in dimension $n \\geq 2$. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0721","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":"2026-05-18T04:39:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8PSJE88zlihgd68DThb7OhHHi1cyCCAHJUnuZIwaarP37HFlVhUSkN4gdFlzXZPG+DkCg5x/jKjwmWSfb30GCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:12:28.947333Z"},"content_sha256":"10136ade937e337aeb1a3eb8b0502bfe0d89a0f6c85d5956a7cd6b51d0599559","schema_version":"1.0","event_id":"sha256:10136ade937e337aeb1a3eb8b0502bfe0d89a0f6c85d5956a7cd6b51d0599559"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOW6BFYNZTKXORMMOXLO7JTNRO/bundle.json","state_url":"https://pith.science/pith/KOW6BFYNZTKXORMMOXLO7JTNRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOW6BFYNZTKXORMMOXLO7JTNRO/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":"2026-05-29T15:12:28Z","links":{"resolver":"https://pith.science/pith/KOW6BFYNZTKXORMMOXLO7JTNRO","bundle":"https://pith.science/pith/KOW6BFYNZTKXORMMOXLO7JTNRO/bundle.json","state":"https://pith.science/pith/KOW6BFYNZTKXORMMOXLO7JTNRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOW6BFYNZTKXORMMOXLO7JTNRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KOW6BFYNZTKXORMMOXLO7JTNRO","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":"b5a709179776cc3d41ec84b93ce80ba619023d351ab3617a67bb09095aa140f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-05T21:21:28Z","title_canon_sha256":"67684e8b938eb48e3b7b0135840ed0c9a1db328c2ee23918e82d659c7f1bc675"},"schema_version":"1.0","source":{"id":"1004.0721","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0721","created_at":"2026-05-18T04:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0721v2","created_at":"2026-05-18T04:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0721","created_at":"2026-05-18T04:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"KOW6BFYNZTKX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KOW6BFYNZTKXORMM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KOW6BFYN","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:10136ade937e337aeb1a3eb8b0502bfe0d89a0f6c85d5956a7cd6b51d0599559","target":"graph","created_at":"2026-05-18T04:39:16Z","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":"We present a new proof of global existence and long range scattering, from small initial data, for the one-dimensional cubic gauge invariant nonlinear Schr\\\"odinger equation, and for Hartree equations in dimension $n \\geq 2$. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument.","authors_text":"Fabio Pusateri, Jun Kato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-05T21:21:28Z","title":"A new proof of long range scattering for critical nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0721","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":"sha256:1e255b41fb4dcf394ed5b8a4dfd5d7b2f8d206e8dcfc369710a591466af277cb","target":"record","created_at":"2026-05-18T04:39:16Z","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":"b5a709179776cc3d41ec84b93ce80ba619023d351ab3617a67bb09095aa140f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-05T21:21:28Z","title_canon_sha256":"67684e8b938eb48e3b7b0135840ed0c9a1db328c2ee23918e82d659c7f1bc675"},"schema_version":"1.0","source":{"id":"1004.0721","kind":"arxiv","version":2}},"canonical_sha256":"53ade0970dccd577458c75d6efa66d8b8ad730eed24afd89f965f8b02205e1ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53ade0970dccd577458c75d6efa66d8b8ad730eed24afd89f965f8b02205e1ef","first_computed_at":"2026-05-18T04:39:16.607218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:16.607218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZPOCG0DvlrDoU3gCG8e3Hj2XvQaegqAq82V2MvsvX8aCLd+PGgJBwm9mc4LF+sYsJ+AI/3z5YBIyd0P9vBdsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:16.607780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0721","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e255b41fb4dcf394ed5b8a4dfd5d7b2f8d206e8dcfc369710a591466af277cb","sha256:10136ade937e337aeb1a3eb8b0502bfe0d89a0f6c85d5956a7cd6b51d0599559"],"state_sha256":"58be6acb9c502ca8c70e2f3aaf1be7ee3f99b14c8acec40dcfcbe31b1c0b620d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5pPrv4GGhvnkV2pgV1ZcfmZoA+v1OBS/3fueZDT4tpHZ7+wT3TlpO2+WWKXtSx37X0/qjMyoOit5Kr5ehGaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:12:28.950999Z","bundle_sha256":"3375217979277784a9419d05f7678158da5dc7f9c9136eb265412f9976abf6f4"}}