{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ONRVBIOTHT4JFDOW4EJTET5OBZ","short_pith_number":"pith:ONRVBIOT","canonical_record":{"source":{"id":"1812.00223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-01T16:28:18Z","cross_cats_sorted":[],"title_canon_sha256":"a0b204473a6797e0e139e93468ce385b12b8a4135912a02d10306dbc999015b8","abstract_canon_sha256":"fe385066472ae2e30c0a4996a187907c11a0b610a7fd4c8ad15acf077cdf0092"},"schema_version":"1.0"},"canonical_sha256":"736350a1d33cf8928dd6e113324fae0e71764372e66798ea72d811c120862d89","source":{"kind":"arxiv","id":"1812.00223","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00223","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00223v2","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00223","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"ONRVBIOTHT4J","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ONRVBIOTHT4JFDOW","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ONRVBIOT","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ONRVBIOTHT4JFDOW4EJTET5OBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.00223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-01T16:28:18Z","cross_cats_sorted":[],"title_canon_sha256":"a0b204473a6797e0e139e93468ce385b12b8a4135912a02d10306dbc999015b8","abstract_canon_sha256":"fe385066472ae2e30c0a4996a187907c11a0b610a7fd4c8ad15acf077cdf0092"},"schema_version":"1.0"},"canonical_sha256":"736350a1d33cf8928dd6e113324fae0e71764372e66798ea72d811c120862d89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:59.460041Z","signature_b64":"2+ZjWPK+9/mU7zOV65vcP9Dg2UF+doplreS9Wqus7ilD6qoOmhB69eltLxS/hLkRIqiDu6fLqWbJkPgv1fUcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"736350a1d33cf8928dd6e113324fae0e71764372e66798ea72d811c120862d89","last_reissued_at":"2026-05-17T23:49:59.459529Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:59.459529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.00223","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYVfurZQ6UHP2KFZB9ac2pUOQhjEJF0i2sZU9zYb9H9DHfHZx5DxD6PIS6C8aPsMerX4j6FoMkPJa7cbfBj4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:13:23.279677Z"},"content_sha256":"e1ece4b959af2963566727172a95d915f4670788504a9f74f296ee471da47f5b","schema_version":"1.0","event_id":"sha256:e1ece4b959af2963566727172a95d915f4670788504a9f74f296ee471da47f5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ONRVBIOTHT4JFDOW4EJTET5OBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time Asymptotic expansions of solution for fourth-order Schr\\\"odinger equation with zero resonance or eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongliang Feng, Xiaohua Yao, Zhao Wu","submitted_at":"2018-12-01T16:28:18Z","abstract_excerpt":"In this paper, we first deduce the asymptotic expansions of resolvent of $H=(-\\Delta)^2+V$ with the presence of resonance or eigenvalue at the degenerate zero threshold for $d\\geq5$. In particular, we identify these resonance spaces for full kinds of zero resonances. As a consequence, we then establish the {\\it time asymptotic expansions} and {\\it Kato-Jensen estimates} for the solution of fourth-order Schr\\\"odinger equation under the presence of zero resonance or eigenvalue."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00223","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":"2026-05-17T23:49:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RDvwyaVYP42AGxOz29L5ujRB6TmHfhY5Ljn77iyzgWrbhdKt8onrC//HyOiYNkhMEy6Zq1uVjgcBlP8oEb4qBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:13:23.280366Z"},"content_sha256":"49f4c05c4bef340cf68c468737e5965015a912021be471cfa630f520dfb1eeb1","schema_version":"1.0","event_id":"sha256:49f4c05c4bef340cf68c468737e5965015a912021be471cfa630f520dfb1eeb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ/bundle.json","state_url":"https://pith.science/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ/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":"2026-05-25T19:13:23Z","links":{"resolver":"https://pith.science/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ","bundle":"https://pith.science/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ/bundle.json","state":"https://pith.science/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ONRVBIOTHT4JFDOW4EJTET5OBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ONRVBIOTHT4JFDOW4EJTET5OBZ","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":"fe385066472ae2e30c0a4996a187907c11a0b610a7fd4c8ad15acf077cdf0092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-01T16:28:18Z","title_canon_sha256":"a0b204473a6797e0e139e93468ce385b12b8a4135912a02d10306dbc999015b8"},"schema_version":"1.0","source":{"id":"1812.00223","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00223","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00223v2","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00223","created_at":"2026-05-17T23:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"ONRVBIOTHT4J","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ONRVBIOTHT4JFDOW","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ONRVBIOT","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:49f4c05c4bef340cf68c468737e5965015a912021be471cfa630f520dfb1eeb1","target":"graph","created_at":"2026-05-17T23:49:59Z","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 first deduce the asymptotic expansions of resolvent of $H=(-\\Delta)^2+V$ with the presence of resonance or eigenvalue at the degenerate zero threshold for $d\\geq5$. In particular, we identify these resonance spaces for full kinds of zero resonances. As a consequence, we then establish the {\\it time asymptotic expansions} and {\\it Kato-Jensen estimates} for the solution of fourth-order Schr\\\"odinger equation under the presence of zero resonance or eigenvalue.","authors_text":"Hongliang Feng, Xiaohua Yao, Zhao Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-01T16:28:18Z","title":"Time Asymptotic expansions of solution for fourth-order Schr\\\"odinger equation with zero resonance or eigenvalue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00223","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:e1ece4b959af2963566727172a95d915f4670788504a9f74f296ee471da47f5b","target":"record","created_at":"2026-05-17T23:49:59Z","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":"fe385066472ae2e30c0a4996a187907c11a0b610a7fd4c8ad15acf077cdf0092","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-01T16:28:18Z","title_canon_sha256":"a0b204473a6797e0e139e93468ce385b12b8a4135912a02d10306dbc999015b8"},"schema_version":"1.0","source":{"id":"1812.00223","kind":"arxiv","version":2}},"canonical_sha256":"736350a1d33cf8928dd6e113324fae0e71764372e66798ea72d811c120862d89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"736350a1d33cf8928dd6e113324fae0e71764372e66798ea72d811c120862d89","first_computed_at":"2026-05-17T23:49:59.459529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:59.459529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2+ZjWPK+9/mU7zOV65vcP9Dg2UF+doplreS9Wqus7ilD6qoOmhB69eltLxS/hLkRIqiDu6fLqWbJkPgv1fUcAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:59.460041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00223","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1ece4b959af2963566727172a95d915f4670788504a9f74f296ee471da47f5b","sha256:49f4c05c4bef340cf68c468737e5965015a912021be471cfa630f520dfb1eeb1"],"state_sha256":"195ce856a34506d37868c217a6db4a2fd17291049915deb73087c5db8acaae20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iy/b+rqNk6gwpJRkbUwkhRLVXQ7HLydBVc69Z/d2amq5jGwkF72YuSza/V0tXTx2+U7BScQxhNGA2V9/EWdKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:13:23.284160Z","bundle_sha256":"69b47b0e38d02b0920f3c23f41bf505c6be8cb7b11b760129b43e661dea386a2"}}