{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:B6N3QMATP3BD4V4ASXHSHCBGIF","short_pith_number":"pith:B6N3QMAT","canonical_record":{"source":{"id":"1804.07075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-19T10:44:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d31764e2189fc81133c875702b9536ba9c256c39386f10e049bf5bc49387102f","abstract_canon_sha256":"7446ba6eda5b4b37add79f16e712635bb2d509eef7c2391cb8871b295f66b396"},"schema_version":"1.0"},"canonical_sha256":"0f9bb830137ec23e578095cf23882641742dcf3a040d5c63d66c63e1da4a14fa","source":{"kind":"arxiv","id":"1804.07075","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07075","created_at":"2026-05-18T00:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07075v1","created_at":"2026-05-18T00:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07075","created_at":"2026-05-18T00:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"B6N3QMATP3BD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B6N3QMATP3BD4V4A","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B6N3QMAT","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:B6N3QMATP3BD4V4ASXHSHCBGIF","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-19T10:44:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d31764e2189fc81133c875702b9536ba9c256c39386f10e049bf5bc49387102f","abstract_canon_sha256":"7446ba6eda5b4b37add79f16e712635bb2d509eef7c2391cb8871b295f66b396"},"schema_version":"1.0"},"canonical_sha256":"0f9bb830137ec23e578095cf23882641742dcf3a040d5c63d66c63e1da4a14fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:01.559546Z","signature_b64":"Pffx4gKB9mg0RtVZ+XOfPGMSX66fngxsm6ZlW9WYQISENHMkgR/QZVJCfPRQ9g9iZE++p1uVWswzLw1/ErAqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f9bb830137ec23e578095cf23882641742dcf3a040d5c63d66c63e1da4a14fa","last_reissued_at":"2026-05-18T00:18:01.558882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:01.558882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07075","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":"2026-05-18T00:18:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3tpS5xJsvQ2Nw+zGJ0udwnxSAZnWXoDO1ZkJR0+IcxxcX2Cu3cihNbWY1ra2sCNez2Y8WdNNNAdjPbDoeheDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:21:54.255055Z"},"content_sha256":"34ff0deaaa7e8045743ad142040c1ee1a2121064862ee72e4ad1bd1647039bc1","schema_version":"1.0","event_id":"sha256:34ff0deaaa7e8045743ad142040c1ee1a2121064862ee72e4ad1bd1647039bc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:B6N3QMATP3BD4V4ASXHSHCBGIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Traveling waves for the quartic focusing Half Wave equation in one space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Jacopo Bellazzini, Nicola Visciglia, Vladimir Georgiev","submitted_at":"2018-04-19T10:44:04Z","abstract_excerpt":"We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\\frac 12}(\\R)$ norm. This fact shows that small data scattering is not possible for (HW) equation and that below the ground state energy there are solutions whose energy travels as a localised packet and which preserve this localisation in time. This behaviour for (HW) is in sharp contrast with classical NLS in any dimension and with fractional NLS with radial data. The second result addressed is the non existence of traveling wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07075","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":"2026-05-18T00:18:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vzEimNjmMbawSpGHLtME4sVmBVHwNhChutT9uM0bsdJSCHBg/LfOGsTaPsXowZcK+w01xkSvZ8hqVrEq/AJ9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:21:54.255801Z"},"content_sha256":"8114a774eb890dd1c9fdb6bd815dd1f7404103f0df5e65f40b04b529951ce6a6","schema_version":"1.0","event_id":"sha256:8114a774eb890dd1c9fdb6bd815dd1f7404103f0df5e65f40b04b529951ce6a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6N3QMATP3BD4V4ASXHSHCBGIF/bundle.json","state_url":"https://pith.science/pith/B6N3QMATP3BD4V4ASXHSHCBGIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6N3QMATP3BD4V4ASXHSHCBGIF/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":"2026-05-27T18:21:54Z","links":{"resolver":"https://pith.science/pith/B6N3QMATP3BD4V4ASXHSHCBGIF","bundle":"https://pith.science/pith/B6N3QMATP3BD4V4ASXHSHCBGIF/bundle.json","state":"https://pith.science/pith/B6N3QMATP3BD4V4ASXHSHCBGIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6N3QMATP3BD4V4ASXHSHCBGIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:B6N3QMATP3BD4V4ASXHSHCBGIF","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":"7446ba6eda5b4b37add79f16e712635bb2d509eef7c2391cb8871b295f66b396","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-19T10:44:04Z","title_canon_sha256":"d31764e2189fc81133c875702b9536ba9c256c39386f10e049bf5bc49387102f"},"schema_version":"1.0","source":{"id":"1804.07075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07075","created_at":"2026-05-18T00:18:01Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07075v1","created_at":"2026-05-18T00:18:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07075","created_at":"2026-05-18T00:18:01Z"},{"alias_kind":"pith_short_12","alias_value":"B6N3QMATP3BD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"B6N3QMATP3BD4V4A","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"B6N3QMAT","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:8114a774eb890dd1c9fdb6bd815dd1f7404103f0df5e65f40b04b529951ce6a6","target":"graph","created_at":"2026-05-18T00:18:01Z","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 consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\\frac 12}(\\R)$ norm. This fact shows that small data scattering is not possible for (HW) equation and that below the ground state energy there are solutions whose energy travels as a localised packet and which preserve this localisation in time. This behaviour for (HW) is in sharp contrast with classical NLS in any dimension and with fractional NLS with radial data. The second result addressed is the non existence of traveling wa","authors_text":"Jacopo Bellazzini, Nicola Visciglia, Vladimir Georgiev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-19T10:44:04Z","title":"Traveling waves for the quartic focusing Half Wave equation in one space dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07075","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":"sha256:34ff0deaaa7e8045743ad142040c1ee1a2121064862ee72e4ad1bd1647039bc1","target":"record","created_at":"2026-05-18T00:18:01Z","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":"7446ba6eda5b4b37add79f16e712635bb2d509eef7c2391cb8871b295f66b396","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-19T10:44:04Z","title_canon_sha256":"d31764e2189fc81133c875702b9536ba9c256c39386f10e049bf5bc49387102f"},"schema_version":"1.0","source":{"id":"1804.07075","kind":"arxiv","version":1}},"canonical_sha256":"0f9bb830137ec23e578095cf23882641742dcf3a040d5c63d66c63e1da4a14fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f9bb830137ec23e578095cf23882641742dcf3a040d5c63d66c63e1da4a14fa","first_computed_at":"2026-05-18T00:18:01.558882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:01.558882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pffx4gKB9mg0RtVZ+XOfPGMSX66fngxsm6ZlW9WYQISENHMkgR/QZVJCfPRQ9g9iZE++p1uVWswzLw1/ErAqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:01.559546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34ff0deaaa7e8045743ad142040c1ee1a2121064862ee72e4ad1bd1647039bc1","sha256:8114a774eb890dd1c9fdb6bd815dd1f7404103f0df5e65f40b04b529951ce6a6"],"state_sha256":"023fbcb8bf0f3aea075bfb6dde20ca0a725e434c49a9befc20638a39e6bd907c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgulQ3ANFXsaleSbM9C69w2+AVu30QtKTFHrn9rlqdAjMLDMZKNPt2XmkM2HjtIr0zMYtPZngEKJSG9BJ+4NCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:21:54.259793Z","bundle_sha256":"b4583dc1a9b7728301d6ab7980b960d6136737e7044cfb75d63ee73fb9dcea3a"}}