{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2JPT3MC2ONLKB5INWRSW3KPEYK","short_pith_number":"pith:2JPT3MC2","canonical_record":{"source":{"id":"1612.02450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-07T21:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"782d09e851416de18bab1d3a99230c5db9f33dbd8a0624cae86076118add9fe2","abstract_canon_sha256":"73d42e02ad07b8e6195414c26a88fc076eef9382829871fab5ae3fa813be4d1e"},"schema_version":"1.0"},"canonical_sha256":"d25f3db05a7356a0f50db4656da9e4c29c4e5f769826de0188b4d0082cef10e3","source":{"kind":"arxiv","id":"1612.02450","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02450","created_at":"2026-05-18T00:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02450v1","created_at":"2026-05-18T00:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02450","created_at":"2026-05-18T00:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"2JPT3MC2ONLK","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2JPT3MC2ONLKB5IN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2JPT3MC2","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2JPT3MC2ONLKB5INWRSW3KPEYK","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-07T21:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"782d09e851416de18bab1d3a99230c5db9f33dbd8a0624cae86076118add9fe2","abstract_canon_sha256":"73d42e02ad07b8e6195414c26a88fc076eef9382829871fab5ae3fa813be4d1e"},"schema_version":"1.0"},"canonical_sha256":"d25f3db05a7356a0f50db4656da9e4c29c4e5f769826de0188b4d0082cef10e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:33.713022Z","signature_b64":"I3hWcwuPBJiwq83RVEdCU2DH3Togx/ABIryq28FIvOJqTmrTX7Azkio2APpbS/rNDhwrCg4puVb55MiZh1p2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d25f3db05a7356a0f50db4656da9e4c29c4e5f769826de0188b4d0082cef10e3","last_reissued_at":"2026-05-18T00:55:33.712388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:33.712388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02450","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":"2026-05-18T00:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTbIhhHX+3HTSrLHTyS8bZ7i22JH/d8SnGAmL8+zN6ER1VxT17qGhWDJwQw2XgjUZpFx0mMcC6cjhqeO/lxXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:43:12.669345Z"},"content_sha256":"1605699b85fed4a6d32f2f3bc7d80bad3e4e5dfb7ef1f3c3dd2f1ebbb60d0a5e","schema_version":"1.0","event_id":"sha256:1605699b85fed4a6d32f2f3bc7d80bad3e4e5dfb7ef1f3c3dd2f1ebbb60d0a5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2JPT3MC2ONLKB5INWRSW3KPEYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wellposedness of Neumann boundary-value problems of space-fractional differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Danping Yang, Hong Wang","submitted_at":"2016-12-07T21:13:28Z","abstract_excerpt":"Fractional differential equation (FDE) provides an accurate description of transport processes that exhibit anomalous diffusion but introduces new mathematical difficulties that have not been encountered in the context of integer-order differential equation. For example, the wellposedness of the Dirichlet boundary-value problem of one-dimensional variable-coefficient FDE is not fully resolved yet. In addition, Neumann boundary-value problem of FDE poses significant challenges, partly due to the fact that different forms of FDE and different types of Neumann boundary condition have been propose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02450","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":"2026-05-18T00:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v98zsNNfm22ipW3z3dLocB2VPmSbOYnKEcpObVeFkCYTaqniVdN4sttDvVsLTwgAPrC6YY9xE90LTb+Xz+g+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:43:12.670002Z"},"content_sha256":"97d303230cba5f9f274c0b84b0385f203d4b745042e50c38005e792f94d8ca0f","schema_version":"1.0","event_id":"sha256:97d303230cba5f9f274c0b84b0385f203d4b745042e50c38005e792f94d8ca0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JPT3MC2ONLKB5INWRSW3KPEYK/bundle.json","state_url":"https://pith.science/pith/2JPT3MC2ONLKB5INWRSW3KPEYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JPT3MC2ONLKB5INWRSW3KPEYK/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":"2026-06-07T16:43:12Z","links":{"resolver":"https://pith.science/pith/2JPT3MC2ONLKB5INWRSW3KPEYK","bundle":"https://pith.science/pith/2JPT3MC2ONLKB5INWRSW3KPEYK/bundle.json","state":"https://pith.science/pith/2JPT3MC2ONLKB5INWRSW3KPEYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JPT3MC2ONLKB5INWRSW3KPEYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2JPT3MC2ONLKB5INWRSW3KPEYK","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":"73d42e02ad07b8e6195414c26a88fc076eef9382829871fab5ae3fa813be4d1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-07T21:13:28Z","title_canon_sha256":"782d09e851416de18bab1d3a99230c5db9f33dbd8a0624cae86076118add9fe2"},"schema_version":"1.0","source":{"id":"1612.02450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02450","created_at":"2026-05-18T00:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02450v1","created_at":"2026-05-18T00:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02450","created_at":"2026-05-18T00:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"2JPT3MC2ONLK","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2JPT3MC2ONLKB5IN","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2JPT3MC2","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:97d303230cba5f9f274c0b84b0385f203d4b745042e50c38005e792f94d8ca0f","target":"graph","created_at":"2026-05-18T00:55:33Z","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":"Fractional differential equation (FDE) provides an accurate description of transport processes that exhibit anomalous diffusion but introduces new mathematical difficulties that have not been encountered in the context of integer-order differential equation. For example, the wellposedness of the Dirichlet boundary-value problem of one-dimensional variable-coefficient FDE is not fully resolved yet. In addition, Neumann boundary-value problem of FDE poses significant challenges, partly due to the fact that different forms of FDE and different types of Neumann boundary condition have been propose","authors_text":"Danping Yang, Hong Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-07T21:13:28Z","title":"Wellposedness of Neumann boundary-value problems of space-fractional differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02450","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":"sha256:1605699b85fed4a6d32f2f3bc7d80bad3e4e5dfb7ef1f3c3dd2f1ebbb60d0a5e","target":"record","created_at":"2026-05-18T00:55:33Z","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":"73d42e02ad07b8e6195414c26a88fc076eef9382829871fab5ae3fa813be4d1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-07T21:13:28Z","title_canon_sha256":"782d09e851416de18bab1d3a99230c5db9f33dbd8a0624cae86076118add9fe2"},"schema_version":"1.0","source":{"id":"1612.02450","kind":"arxiv","version":1}},"canonical_sha256":"d25f3db05a7356a0f50db4656da9e4c29c4e5f769826de0188b4d0082cef10e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d25f3db05a7356a0f50db4656da9e4c29c4e5f769826de0188b4d0082cef10e3","first_computed_at":"2026-05-18T00:55:33.712388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:33.712388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3hWcwuPBJiwq83RVEdCU2DH3Togx/ABIryq28FIvOJqTmrTX7Azkio2APpbS/rNDhwrCg4puVb55MiZh1p2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:33.713022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1605699b85fed4a6d32f2f3bc7d80bad3e4e5dfb7ef1f3c3dd2f1ebbb60d0a5e","sha256:97d303230cba5f9f274c0b84b0385f203d4b745042e50c38005e792f94d8ca0f"],"state_sha256":"00e44769f5d4b1aefd3214ed7a07aad2140a44c25ac235b2fcb38836217a716e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F7OjKJi8gjvzwYdeHpk/7REVOm3xVYvovRjUm2r2R3D5BCPHARWbxmyrpm2jEvjLIiwNFbop57IORwIuFbrqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:43:12.674184Z","bundle_sha256":"d40cf8afd328350f0f3f378f57b8c33a4e121c6a085a39e29e89baf9ea3db2f1"}}