{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HNW64PEHQBGU3W2VMX2MGWMORD","short_pith_number":"pith:HNW64PEH","canonical_record":{"source":{"id":"1405.6675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-26T18:43:18Z","cross_cats_sorted":[],"title_canon_sha256":"6d3f877a34b468e15da55066cda0ffa3975c959c1e15a8801f85dfde067d7222","abstract_canon_sha256":"3a3f4a9f482fb217bb66167ae19f34a1d6f063e2c9b4d907b0a63729bf71248a"},"schema_version":"1.0"},"canonical_sha256":"3b6dee3c87804d4ddb5565f4c3598e88c77641f5fcb8520dbcd9cad9d222c4b5","source":{"kind":"arxiv","id":"1405.6675","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6675","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6675v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6675","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"HNW64PEHQBGU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNW64PEHQBGU3W2V","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNW64PEH","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HNW64PEHQBGU3W2VMX2MGWMORD","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-26T18:43:18Z","cross_cats_sorted":[],"title_canon_sha256":"6d3f877a34b468e15da55066cda0ffa3975c959c1e15a8801f85dfde067d7222","abstract_canon_sha256":"3a3f4a9f482fb217bb66167ae19f34a1d6f063e2c9b4d907b0a63729bf71248a"},"schema_version":"1.0"},"canonical_sha256":"3b6dee3c87804d4ddb5565f4c3598e88c77641f5fcb8520dbcd9cad9d222c4b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:04.289574Z","signature_b64":"cO5BF4asBD59A9YeC6TuLnQx9cwxKs/DMycU3XNzTwlWF/BiR0eg4BNspEQjo7y8r33txzwPd8ksIG7DWI2MCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b6dee3c87804d4ddb5565f4c3598e88c77641f5fcb8520dbcd9cad9d222c4b5","last_reissued_at":"2026-05-18T02:18:04.288900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:04.288900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6675","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FVQrd1jzRo60KSILC1tUsA/uA4pWDMFLg8PmqDwuZj7HDrMiq4NBf3yo56jzQCldLn9eIfjSwwtwp9+j9RcDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:50:47.341888Z"},"content_sha256":"33d59f29c54185bd11570bbe3619dd1bd633383df5f640d0b4a4b760e1fe35d3","schema_version":"1.0","event_id":"sha256:33d59f29c54185bd11570bbe3619dd1bd633383df5f640d0b4a4b760e1fe35d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HNW64PEHQBGU3W2VMX2MGWMORD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Liouville theorem for the Degasperis-Procesi equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Brandolese (ICJ)","submitted_at":"2014-05-26T18:43:18Z","abstract_excerpt":"We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution. We also establish the analogue of such Liouville-type theorem for the Degasperis-Procesi equation with an additional dispersive term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6675","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":"2026-05-18T02:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TnQa1UJIiT71oMVy0UPItR1a6/5ueyaRCk8nNsPFsUdQCAuYqfW7Knj4P5m+fSVUj7i6HIePtgpBEshqERkqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:50:47.342548Z"},"content_sha256":"310fef4c6ca544e83abb657f991e1f8c7575a305a58350df9ed9536424b75a5e","schema_version":"1.0","event_id":"sha256:310fef4c6ca544e83abb657f991e1f8c7575a305a58350df9ed9536424b75a5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNW64PEHQBGU3W2VMX2MGWMORD/bundle.json","state_url":"https://pith.science/pith/HNW64PEHQBGU3W2VMX2MGWMORD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNW64PEHQBGU3W2VMX2MGWMORD/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":"2026-06-07T02:50:47Z","links":{"resolver":"https://pith.science/pith/HNW64PEHQBGU3W2VMX2MGWMORD","bundle":"https://pith.science/pith/HNW64PEHQBGU3W2VMX2MGWMORD/bundle.json","state":"https://pith.science/pith/HNW64PEHQBGU3W2VMX2MGWMORD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNW64PEHQBGU3W2VMX2MGWMORD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HNW64PEHQBGU3W2VMX2MGWMORD","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":"3a3f4a9f482fb217bb66167ae19f34a1d6f063e2c9b4d907b0a63729bf71248a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-26T18:43:18Z","title_canon_sha256":"6d3f877a34b468e15da55066cda0ffa3975c959c1e15a8801f85dfde067d7222"},"schema_version":"1.0","source":{"id":"1405.6675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6675","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6675v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6675","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"HNW64PEHQBGU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNW64PEHQBGU3W2V","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNW64PEH","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:310fef4c6ca544e83abb657f991e1f8c7575a305a58350df9ed9536424b75a5e","target":"graph","created_at":"2026-05-18T02:18:04Z","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 prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution. We also establish the analogue of such Liouville-type theorem for the Degasperis-Procesi equation with an additional dispersive term.","authors_text":"Lorenzo Brandolese (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-26T18:43:18Z","title":"A Liouville theorem for the Degasperis-Procesi equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6675","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":"sha256:33d59f29c54185bd11570bbe3619dd1bd633383df5f640d0b4a4b760e1fe35d3","target":"record","created_at":"2026-05-18T02:18:04Z","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":"3a3f4a9f482fb217bb66167ae19f34a1d6f063e2c9b4d907b0a63729bf71248a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-26T18:43:18Z","title_canon_sha256":"6d3f877a34b468e15da55066cda0ffa3975c959c1e15a8801f85dfde067d7222"},"schema_version":"1.0","source":{"id":"1405.6675","kind":"arxiv","version":2}},"canonical_sha256":"3b6dee3c87804d4ddb5565f4c3598e88c77641f5fcb8520dbcd9cad9d222c4b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b6dee3c87804d4ddb5565f4c3598e88c77641f5fcb8520dbcd9cad9d222c4b5","first_computed_at":"2026-05-18T02:18:04.288900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:04.288900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cO5BF4asBD59A9YeC6TuLnQx9cwxKs/DMycU3XNzTwlWF/BiR0eg4BNspEQjo7y8r33txzwPd8ksIG7DWI2MCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:04.289574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33d59f29c54185bd11570bbe3619dd1bd633383df5f640d0b4a4b760e1fe35d3","sha256:310fef4c6ca544e83abb657f991e1f8c7575a305a58350df9ed9536424b75a5e"],"state_sha256":"013bb6e558ff201c1a10a3eec85717c4d668b37d8d7ce72555ddd7fde9f5f7cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01I38/6UdkW2K+/MvYy6BJ8lMM+j2L6ujXdbkF1/UBqRCPpHihdHYfKwvKkDMaA/eqW9keYtx34o3Q721pGvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:50:47.346045Z","bundle_sha256":"cb05d5039159f26126fe9483d153d37aa5d6fa423715b00874c3c62c89a7f89d"}}