{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KCYBHFGUOPLTGCL2UTBUZN57FY","short_pith_number":"pith:KCYBHFGU","canonical_record":{"source":{"id":"1801.09966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-30T12:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"0c8dffc8a2386cec1886a48367545f062df76b7b6a1fd99314833f60cb255bf2","abstract_canon_sha256":"28c59aaa1c645f5a83fc55f382c67e4ac617c1f69807f969510a67687dd03de3"},"schema_version":"1.0"},"canonical_sha256":"50b01394d473d733097aa4c34cb7bf2e26ca5e5e58b6b32cad6689c13852c509","source":{"kind":"arxiv","id":"1801.09966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09966","created_at":"2026-05-18T00:08:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09966v1","created_at":"2026-05-18T00:08:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09966","created_at":"2026-05-18T00:08:10Z"},{"alias_kind":"pith_short_12","alias_value":"KCYBHFGUOPLT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KCYBHFGUOPLTGCL2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KCYBHFGU","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KCYBHFGUOPLTGCL2UTBUZN57FY","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-30T12:48:03Z","cross_cats_sorted":[],"title_canon_sha256":"0c8dffc8a2386cec1886a48367545f062df76b7b6a1fd99314833f60cb255bf2","abstract_canon_sha256":"28c59aaa1c645f5a83fc55f382c67e4ac617c1f69807f969510a67687dd03de3"},"schema_version":"1.0"},"canonical_sha256":"50b01394d473d733097aa4c34cb7bf2e26ca5e5e58b6b32cad6689c13852c509","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:10.459827Z","signature_b64":"HrAiZrmdj7t2iJA7WBbYYXdpXH6trRnO/uunyjntCf8fgAJt4B5OmyV77Oy3WdnM2y0CEjvoAmN4+c7959EQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50b01394d473d733097aa4c34cb7bf2e26ca5e5e58b6b32cad6689c13852c509","last_reissued_at":"2026-05-18T00:08:10.459397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:10.459397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09966","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":"2026-05-18T00:08:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qjs7k/mcQoh3htna17IA/mfTY6dS/DOcHHlHa87Y8wuadJuK4Cx3jjbI58c9Vbm+cQ0NWd+09cy4LqNc9J2bDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:11:37.438419Z"},"content_sha256":"04c323162fb8c000dd9c179854317826ab0a5cbf500d1939fd8f2713201483ab","schema_version":"1.0","event_id":"sha256:04c323162fb8c000dd9c179854317826ab0a5cbf500d1939fd8f2713201483ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KCYBHFGUOPLTGCL2UTBUZN57FY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the propagation of regularity and decay of solutions to the Benjamin equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boling Guo, Guoquan Qin","submitted_at":"2018-01-30T12:48:03Z","abstract_excerpt":"In this paper, we investigate some special regularities and decay properties of solutions to the initial value problem(IVP) of the Benjamin equation. The main result shows that: for initial datum $u_{0}\\in H^{s}(\\mathbb{R})$ with $s>3/4,$ if the restriction of $u_{0}$ belongs to $H^{l}((x_{0}, \\infty))$ for some $l\\in \\mathbb{Z}^{+}$ and $x_{0}\\in \\mathbb{R},$ then the restriction of the corresponding solution $u(\\cdot, t)$ belongs to $H^{l}((\\alpha, \\infty))$ for any $\\alpha\\in \\mathbb{R}$ and any $t\\in(0, T)$. Consequently, this type of regularity travels with infinite speed to its left as t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09966","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":"2026-05-18T00:08:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fnMp49HOmKZryghuq2/XA9J9YMHse8Yb3A4dZF8ZvnHT9xSG/sd4hYBQ2R/A+2kYmiKAZsKNz+ZejJlGkTTYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:11:37.438852Z"},"content_sha256":"6288a5319e1cb6b16f9872d48eacfde966d08c92d41d9558503e52b0c806df39","schema_version":"1.0","event_id":"sha256:6288a5319e1cb6b16f9872d48eacfde966d08c92d41d9558503e52b0c806df39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCYBHFGUOPLTGCL2UTBUZN57FY/bundle.json","state_url":"https://pith.science/pith/KCYBHFGUOPLTGCL2UTBUZN57FY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCYBHFGUOPLTGCL2UTBUZN57FY/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":"2026-05-31T00:11:37Z","links":{"resolver":"https://pith.science/pith/KCYBHFGUOPLTGCL2UTBUZN57FY","bundle":"https://pith.science/pith/KCYBHFGUOPLTGCL2UTBUZN57FY/bundle.json","state":"https://pith.science/pith/KCYBHFGUOPLTGCL2UTBUZN57FY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCYBHFGUOPLTGCL2UTBUZN57FY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KCYBHFGUOPLTGCL2UTBUZN57FY","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":"28c59aaa1c645f5a83fc55f382c67e4ac617c1f69807f969510a67687dd03de3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-30T12:48:03Z","title_canon_sha256":"0c8dffc8a2386cec1886a48367545f062df76b7b6a1fd99314833f60cb255bf2"},"schema_version":"1.0","source":{"id":"1801.09966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09966","created_at":"2026-05-18T00:08:10Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09966v1","created_at":"2026-05-18T00:08:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09966","created_at":"2026-05-18T00:08:10Z"},{"alias_kind":"pith_short_12","alias_value":"KCYBHFGUOPLT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KCYBHFGUOPLTGCL2","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KCYBHFGU","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:6288a5319e1cb6b16f9872d48eacfde966d08c92d41d9558503e52b0c806df39","target":"graph","created_at":"2026-05-18T00:08:10Z","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 investigate some special regularities and decay properties of solutions to the initial value problem(IVP) of the Benjamin equation. The main result shows that: for initial datum $u_{0}\\in H^{s}(\\mathbb{R})$ with $s>3/4,$ if the restriction of $u_{0}$ belongs to $H^{l}((x_{0}, \\infty))$ for some $l\\in \\mathbb{Z}^{+}$ and $x_{0}\\in \\mathbb{R},$ then the restriction of the corresponding solution $u(\\cdot, t)$ belongs to $H^{l}((\\alpha, \\infty))$ for any $\\alpha\\in \\mathbb{R}$ and any $t\\in(0, T)$. Consequently, this type of regularity travels with infinite speed to its left as t","authors_text":"Boling Guo, Guoquan Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-30T12:48:03Z","title":"On the propagation of regularity and decay of solutions to the Benjamin equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09966","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":"sha256:04c323162fb8c000dd9c179854317826ab0a5cbf500d1939fd8f2713201483ab","target":"record","created_at":"2026-05-18T00:08:10Z","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":"28c59aaa1c645f5a83fc55f382c67e4ac617c1f69807f969510a67687dd03de3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-30T12:48:03Z","title_canon_sha256":"0c8dffc8a2386cec1886a48367545f062df76b7b6a1fd99314833f60cb255bf2"},"schema_version":"1.0","source":{"id":"1801.09966","kind":"arxiv","version":1}},"canonical_sha256":"50b01394d473d733097aa4c34cb7bf2e26ca5e5e58b6b32cad6689c13852c509","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50b01394d473d733097aa4c34cb7bf2e26ca5e5e58b6b32cad6689c13852c509","first_computed_at":"2026-05-18T00:08:10.459397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:10.459397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HrAiZrmdj7t2iJA7WBbYYXdpXH6trRnO/uunyjntCf8fgAJt4B5OmyV77Oy3WdnM2y0CEjvoAmN4+c7959EQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:10.459827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04c323162fb8c000dd9c179854317826ab0a5cbf500d1939fd8f2713201483ab","sha256:6288a5319e1cb6b16f9872d48eacfde966d08c92d41d9558503e52b0c806df39"],"state_sha256":"adf74ec64cd509eec1ed985beb8bd9b5b24b6a11db6955e55d0b5eb1f9b54b54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GdN73yCNWXBb1QcY3q9PTMA9/PaIkmpf07WvNePWCrIjbAm8I9ncnq2+P83GcunezUwH6Pjw+9zAdMGaDQ0qAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:11:37.443212Z","bundle_sha256":"da758f1ea45131e94586192b1a409c9311b83f1a281dd13fab8c0955e6c1b7fd"}}