{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZVYFSI6RH6LU7TJ5DXCLLFY222","short_pith_number":"pith:ZVYFSI6R","canonical_record":{"source":{"id":"1406.2024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-06-08T20:52:15Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"d226bcbb373c2684bfca1e70ad76996bdaec2d06501572f2e8d29f2522b3655e","abstract_canon_sha256":"e6857c2f99b85b67ef17eac7c595c91536ba456101bb9fc9cca49cae0824c598"},"schema_version":"1.0"},"canonical_sha256":"cd705923d13f974fcd3d1dc4b5971ad6b33c96b65f153f593ffcd1379af23862","source":{"kind":"arxiv","id":"1406.2024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2024","created_at":"2026-05-18T02:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2024v1","created_at":"2026-05-18T02:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2024","created_at":"2026-05-18T02:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZVYFSI6RH6LU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZVYFSI6RH6LU7TJ5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZVYFSI6R","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZVYFSI6RH6LU7TJ5DXCLLFY222","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-06-08T20:52:15Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"d226bcbb373c2684bfca1e70ad76996bdaec2d06501572f2e8d29f2522b3655e","abstract_canon_sha256":"e6857c2f99b85b67ef17eac7c595c91536ba456101bb9fc9cca49cae0824c598"},"schema_version":"1.0"},"canonical_sha256":"cd705923d13f974fcd3d1dc4b5971ad6b33c96b65f153f593ffcd1379af23862","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:11.906521Z","signature_b64":"PWNmvNvBDqxGxqVxyXwyL/0kfwAkYYiaBURpcd4kLPhQfsYtzHnbuQZcX6vOfniBtS1J42z3tazcLU6MvPAZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd705923d13f974fcd3d1dc4b5971ad6b33c96b65f153f593ffcd1379af23862","last_reissued_at":"2026-05-18T02:50:11.905818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:11.905818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2024","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":"2026-05-18T02:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZVHH3K0l7PC5TpS3ll8aV6h/glYyN0jbYdkbDvO/aVa/zy0IvDr4J/AxSkab6FNYwFqFqKrFS+Ww3epqwpDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T10:05:43.294531Z"},"content_sha256":"4bbd534c2c4dcbed103756d76f37b68a482d7927344b83f85965be24f8ef5986","schema_version":"1.0","event_id":"sha256:4bbd534c2c4dcbed103756d76f37b68a482d7927344b83f85965be24f8ef5986"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZVYFSI6RH6LU7TJ5DXCLLFY222","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilfer fractional advection-diffusion equations with power-law initial condition; a Numerical study using variational iteration method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Iftikhar Ali, Nadeem Malik","submitted_at":"2014-06-08T20:52:15Z","abstract_excerpt":"We propose a Hilfer advection-diffusion equation of order $0<\\alpha<1$ and type $0\\leq\\beta\\leq1$, and find the power series solution by using variational iteration method. Power series solutions are expressed in a form that is easy to implement numerically and in some particular cases, solutions are expressed in terms of Mittag-Leffler function. Absolute convergence of power series solutions is proved and the sensitivity of the solutions is discussed with respect to changes in the values of different parameters. For power law initial conditions it is shown that the Hilfer advection-diffusion "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2024","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":"2026-05-18T02:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17vKZ3Zxb5rrgLfHCKy5piE4TaD8W3nFu6IzpEL+WXw0bEEhrqD7u0xbnV7/d9pHO539vj2cUppmLzo62BCoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T10:05:43.294871Z"},"content_sha256":"bb798d8e07e6551c194547e67296ec9c3111862f60d18728804c06c39a09ce11","schema_version":"1.0","event_id":"sha256:bb798d8e07e6551c194547e67296ec9c3111862f60d18728804c06c39a09ce11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222/bundle.json","state_url":"https://pith.science/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222/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":"2026-07-10T10:05:43Z","links":{"resolver":"https://pith.science/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222","bundle":"https://pith.science/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222/bundle.json","state":"https://pith.science/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZVYFSI6RH6LU7TJ5DXCLLFY222/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZVYFSI6RH6LU7TJ5DXCLLFY222","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":"e6857c2f99b85b67ef17eac7c595c91536ba456101bb9fc9cca49cae0824c598","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-06-08T20:52:15Z","title_canon_sha256":"d226bcbb373c2684bfca1e70ad76996bdaec2d06501572f2e8d29f2522b3655e"},"schema_version":"1.0","source":{"id":"1406.2024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2024","created_at":"2026-05-18T02:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2024v1","created_at":"2026-05-18T02:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2024","created_at":"2026-05-18T02:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZVYFSI6RH6LU","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZVYFSI6RH6LU7TJ5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZVYFSI6R","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:bb798d8e07e6551c194547e67296ec9c3111862f60d18728804c06c39a09ce11","target":"graph","created_at":"2026-05-18T02:50:11Z","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 propose a Hilfer advection-diffusion equation of order $0<\\alpha<1$ and type $0\\leq\\beta\\leq1$, and find the power series solution by using variational iteration method. Power series solutions are expressed in a form that is easy to implement numerically and in some particular cases, solutions are expressed in terms of Mittag-Leffler function. Absolute convergence of power series solutions is proved and the sensitivity of the solutions is discussed with respect to changes in the values of different parameters. For power law initial conditions it is shown that the Hilfer advection-diffusion ","authors_text":"Iftikhar Ali, Nadeem Malik","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-06-08T20:52:15Z","title":"Hilfer fractional advection-diffusion equations with power-law initial condition; a Numerical study using variational iteration method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2024","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":"sha256:4bbd534c2c4dcbed103756d76f37b68a482d7927344b83f85965be24f8ef5986","target":"record","created_at":"2026-05-18T02:50:11Z","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":"e6857c2f99b85b67ef17eac7c595c91536ba456101bb9fc9cca49cae0824c598","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-06-08T20:52:15Z","title_canon_sha256":"d226bcbb373c2684bfca1e70ad76996bdaec2d06501572f2e8d29f2522b3655e"},"schema_version":"1.0","source":{"id":"1406.2024","kind":"arxiv","version":1}},"canonical_sha256":"cd705923d13f974fcd3d1dc4b5971ad6b33c96b65f153f593ffcd1379af23862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd705923d13f974fcd3d1dc4b5971ad6b33c96b65f153f593ffcd1379af23862","first_computed_at":"2026-05-18T02:50:11.905818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:11.905818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PWNmvNvBDqxGxqVxyXwyL/0kfwAkYYiaBURpcd4kLPhQfsYtzHnbuQZcX6vOfniBtS1J42z3tazcLU6MvPAZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:11.906521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bbd534c2c4dcbed103756d76f37b68a482d7927344b83f85965be24f8ef5986","sha256:bb798d8e07e6551c194547e67296ec9c3111862f60d18728804c06c39a09ce11"],"state_sha256":"99d87e7d5716c9b98c80b2ded24930c02484396805fb742fc28faf78a9b8e532"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"luCgeKfYN0YcE4awBr1AQZ/AkbwNNNFU+QnzNb1jsYGTpM8kmWP6CgZMvGbovUtgIkwddGCVag4eCmO+lAQCCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T10:05:43.296633Z","bundle_sha256":"698f0a3d25f4f061228c7be1117c91926305d9c4b833481bafefee9a9cf840ad"}}