{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:F733SU373V3BFYU7RWXE2NNPYQ","short_pith_number":"pith:F733SU37","canonical_record":{"source":{"id":"1711.10362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T14:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"ffd8d923e95df87cf6a3f52b14eca87476ef1fc83d4e5a3efc6efe019f8eed29","abstract_canon_sha256":"8e1604371e03c302030f9ebed62ea9c732f0586565253538e15c38a12d4ea4b8"},"schema_version":"1.0"},"canonical_sha256":"2ff7b9537fdd7612e29f8dae4d35afc431593e8317b92da72e4292ad0c2dcc2c","source":{"kind":"arxiv","id":"1711.10362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10362","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10362v1","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10362","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"F733SU373V3B","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F733SU373V3BFYU7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F733SU37","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:F733SU373V3BFYU7RWXE2NNPYQ","target":"record","payload":{"canonical_record":{"source":{"id":"1711.10362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T14:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"ffd8d923e95df87cf6a3f52b14eca87476ef1fc83d4e5a3efc6efe019f8eed29","abstract_canon_sha256":"8e1604371e03c302030f9ebed62ea9c732f0586565253538e15c38a12d4ea4b8"},"schema_version":"1.0"},"canonical_sha256":"2ff7b9537fdd7612e29f8dae4d35afc431593e8317b92da72e4292ad0c2dcc2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:43.482419Z","signature_b64":"OBZiqrPUGR5rLHetMnDeU38t7ausqWQiSXSf6yIgNPtZFTgtohbCZc5FPk3OTZ6uUzsvss4XhAJkmnZp0k7uDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff7b9537fdd7612e29f8dae4d35afc431593e8317b92da72e4292ad0c2dcc2c","last_reissued_at":"2026-05-17T23:42:43.481682Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:43.481682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.10362","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":"2026-05-17T23:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYlS4s9QRwma3VbUlQpi8hSIiBs5UNUislAWW/dqprfH8z9PCScv8ZzQIsIMtYHIpU019QR8KuxHUBd7i8C6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:32:04.351359Z"},"content_sha256":"916eb7bc4070f3442cfea3d7cd6947eceebf419c5b300fc717d591548df3de5f","schema_version":"1.0","event_id":"sha256:916eb7bc4070f3442cfea3d7cd6947eceebf419c5b300fc717d591548df3de5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:F733SU373V3BFYU7RWXE2NNPYQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the 4D Nonlinear Schr\\\"odinger equation with combined terms under the energy threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Jiqiang Zheng, Tengfei Zhang","submitted_at":"2017-11-13T14:50:29Z","abstract_excerpt":"In this paper, we consider the longtime dynamics of the solutions to focusing energy-critical Schr\\\"odinger equation with a defocusing energy-subcritical perturbation term under a ground state energy threshold in four spatial dimension. This extends the results in Miao et al. (Commun Math Phys 318(3):767-808, 2013, The dynamics of the NLS with the combined terms in five and higher dimensions. Some topics in harmonic analysis and applications, advanced lectures in mathematics, ALM34, Higher Education Press, Beijing, pp 265-298, 2015) to four dimension without radial assumption and the proof of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10362","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":"2026-05-17T23:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfGPGvvMQmu1yIusamoqJjfhgG9cFWayvJafXJXQyY9See3ilCwWmGyCEEAD12Poz1FTyN8JqlNgYESYDZQtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:32:04.352047Z"},"content_sha256":"ad9f928e6e77f1d885af3f7ea3c56c81d1889d0635888f292a21699919209ef9","schema_version":"1.0","event_id":"sha256:ad9f928e6e77f1d885af3f7ea3c56c81d1889d0635888f292a21699919209ef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F733SU373V3BFYU7RWXE2NNPYQ/bundle.json","state_url":"https://pith.science/pith/F733SU373V3BFYU7RWXE2NNPYQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F733SU373V3BFYU7RWXE2NNPYQ/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":"2026-05-27T11:32:04Z","links":{"resolver":"https://pith.science/pith/F733SU373V3BFYU7RWXE2NNPYQ","bundle":"https://pith.science/pith/F733SU373V3BFYU7RWXE2NNPYQ/bundle.json","state":"https://pith.science/pith/F733SU373V3BFYU7RWXE2NNPYQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F733SU373V3BFYU7RWXE2NNPYQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F733SU373V3BFYU7RWXE2NNPYQ","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":"8e1604371e03c302030f9ebed62ea9c732f0586565253538e15c38a12d4ea4b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T14:50:29Z","title_canon_sha256":"ffd8d923e95df87cf6a3f52b14eca87476ef1fc83d4e5a3efc6efe019f8eed29"},"schema_version":"1.0","source":{"id":"1711.10362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10362","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10362v1","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10362","created_at":"2026-05-17T23:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"F733SU373V3B","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F733SU373V3BFYU7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F733SU37","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ad9f928e6e77f1d885af3f7ea3c56c81d1889d0635888f292a21699919209ef9","target":"graph","created_at":"2026-05-17T23:42:43Z","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 consider the longtime dynamics of the solutions to focusing energy-critical Schr\\\"odinger equation with a defocusing energy-subcritical perturbation term under a ground state energy threshold in four spatial dimension. This extends the results in Miao et al. (Commun Math Phys 318(3):767-808, 2013, The dynamics of the NLS with the combined terms in five and higher dimensions. Some topics in harmonic analysis and applications, advanced lectures in mathematics, ALM34, Higher Education Press, Beijing, pp 265-298, 2015) to four dimension without radial assumption and the proof of ","authors_text":"Changxing Miao, Jiqiang Zheng, Tengfei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T14:50:29Z","title":"On the 4D Nonlinear Schr\\\"odinger equation with combined terms under the energy threshold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10362","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":"sha256:916eb7bc4070f3442cfea3d7cd6947eceebf419c5b300fc717d591548df3de5f","target":"record","created_at":"2026-05-17T23:42:43Z","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":"8e1604371e03c302030f9ebed62ea9c732f0586565253538e15c38a12d4ea4b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T14:50:29Z","title_canon_sha256":"ffd8d923e95df87cf6a3f52b14eca87476ef1fc83d4e5a3efc6efe019f8eed29"},"schema_version":"1.0","source":{"id":"1711.10362","kind":"arxiv","version":1}},"canonical_sha256":"2ff7b9537fdd7612e29f8dae4d35afc431593e8317b92da72e4292ad0c2dcc2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ff7b9537fdd7612e29f8dae4d35afc431593e8317b92da72e4292ad0c2dcc2c","first_computed_at":"2026-05-17T23:42:43.481682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:43.481682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OBZiqrPUGR5rLHetMnDeU38t7ausqWQiSXSf6yIgNPtZFTgtohbCZc5FPk3OTZ6uUzsvss4XhAJkmnZp0k7uDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:43.482419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:916eb7bc4070f3442cfea3d7cd6947eceebf419c5b300fc717d591548df3de5f","sha256:ad9f928e6e77f1d885af3f7ea3c56c81d1889d0635888f292a21699919209ef9"],"state_sha256":"fe416708989692ecd9c517b5944d1c932ebdd4a364e0cfd2ad1c387cf3992215"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jd8oygOwnz8YlqWAKriLhxPZ0kR79R8hC0ECDMWuBR8yz54vh4cU7ErGndz1L68cernPQ08LjOVAZ58hJvD8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:32:04.355591Z","bundle_sha256":"50b3cce5fb3c0bbf1df7a8e10f42ce82a11d4814dafa32ceea1145c24f93af38"}}