{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JMQIZKNG23O5IYCZX7NNIJU7FO","short_pith_number":"pith:JMQIZKNG","canonical_record":{"source":{"id":"1801.09352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T03:06:56Z","cross_cats_sorted":[],"title_canon_sha256":"e36a90d240f23e1d3a3d46f7322c1901eccb033e04967304f2ea2ac71614a6ec","abstract_canon_sha256":"38175c88531c0cb9b8113ba2bb937900a36afb1c41592c6802f70e95c5e0992b"},"schema_version":"1.0"},"canonical_sha256":"4b208ca9a6d6ddd46059bfdad4269f2b95ab982189311f04e9ea058bf109662c","source":{"kind":"arxiv","id":"1801.09352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09352","created_at":"2026-05-17T23:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09352v1","created_at":"2026-05-17T23:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09352","created_at":"2026-05-17T23:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"JMQIZKNG23O5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JMQIZKNG23O5IYCZ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JMQIZKNG","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JMQIZKNG23O5IYCZX7NNIJU7FO","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T03:06:56Z","cross_cats_sorted":[],"title_canon_sha256":"e36a90d240f23e1d3a3d46f7322c1901eccb033e04967304f2ea2ac71614a6ec","abstract_canon_sha256":"38175c88531c0cb9b8113ba2bb937900a36afb1c41592c6802f70e95c5e0992b"},"schema_version":"1.0"},"canonical_sha256":"4b208ca9a6d6ddd46059bfdad4269f2b95ab982189311f04e9ea058bf109662c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:17.700716Z","signature_b64":"kVzFC4LLzR0TGJ9/T+chuK4QYZ6pJk3IJl7BH8m0oid7CqK6ZY57Bzbzysve9wFD+Z5b89p52pqZqI0XwuiXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b208ca9a6d6ddd46059bfdad4269f2b95ab982189311f04e9ea058bf109662c","last_reissued_at":"2026-05-17T23:59:17.700266Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:17.700266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09352","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":"2026-05-17T23:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UGWD8+pHCZSlt7wZwBu2XX141hMcL2RUPwZ3RjQEI483aK7ME2BAaKD83cUDPzasqIa+gEfZjMpEehCW0H1wAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:51:16.746300Z"},"content_sha256":"0ab0087422d30d062d7a1a23a430b83657b290d5c5785a76cec4fdd3595d0f48","schema_version":"1.0","event_id":"sha256:0ab0087422d30d062d7a1a23a430b83657b290d5c5785a76cec4fdd3595d0f48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JMQIZKNG23O5IYCZX7NNIJU7FO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"HongGuang Sun, Wei Xu, Wen Chen, Yingjie Liang","submitted_at":"2018-01-29T03:06:56Z","abstract_excerpt":"Many theoretical and experimental results show that solute transport in heterogeneous porous media exhibits multi-scaling behaviors. To describe such non-Fickian diffusions, this work provides a distributed order Hausdorff diffusion model to describe the tracer transport in porous media. This model is proved to be equivalent with the diffusion equation model with a nonlinear time dependent diffusion coefficient. In conjunction with the structural derivative, its mean squared displacement (MSD) of the tracer particles is explicitly derived as a dilogarithm function when the weight function of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09352","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":"2026-05-17T23:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWwSbKls4ZGPxrb/FiWpe7l27h7Hmu56skCzEGv0su57V7tBomSXZGHdL5+dUwbxrgSX8QCym6xzTV48tIzXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:51:16.746666Z"},"content_sha256":"4c0190e96a873f4c44073336844cb65a0b57576574bf0b07dfeba19979a3aaa3","schema_version":"1.0","event_id":"sha256:4c0190e96a873f4c44073336844cb65a0b57576574bf0b07dfeba19979a3aaa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMQIZKNG23O5IYCZX7NNIJU7FO/bundle.json","state_url":"https://pith.science/pith/JMQIZKNG23O5IYCZX7NNIJU7FO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMQIZKNG23O5IYCZX7NNIJU7FO/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":"2026-06-02T23:51:16Z","links":{"resolver":"https://pith.science/pith/JMQIZKNG23O5IYCZX7NNIJU7FO","bundle":"https://pith.science/pith/JMQIZKNG23O5IYCZX7NNIJU7FO/bundle.json","state":"https://pith.science/pith/JMQIZKNG23O5IYCZX7NNIJU7FO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMQIZKNG23O5IYCZX7NNIJU7FO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JMQIZKNG23O5IYCZX7NNIJU7FO","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":"38175c88531c0cb9b8113ba2bb937900a36afb1c41592c6802f70e95c5e0992b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T03:06:56Z","title_canon_sha256":"e36a90d240f23e1d3a3d46f7322c1901eccb033e04967304f2ea2ac71614a6ec"},"schema_version":"1.0","source":{"id":"1801.09352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09352","created_at":"2026-05-17T23:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09352v1","created_at":"2026-05-17T23:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09352","created_at":"2026-05-17T23:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"JMQIZKNG23O5","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JMQIZKNG23O5IYCZ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JMQIZKNG","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:4c0190e96a873f4c44073336844cb65a0b57576574bf0b07dfeba19979a3aaa3","target":"graph","created_at":"2026-05-17T23:59:17Z","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":"Many theoretical and experimental results show that solute transport in heterogeneous porous media exhibits multi-scaling behaviors. To describe such non-Fickian diffusions, this work provides a distributed order Hausdorff diffusion model to describe the tracer transport in porous media. This model is proved to be equivalent with the diffusion equation model with a nonlinear time dependent diffusion coefficient. In conjunction with the structural derivative, its mean squared displacement (MSD) of the tracer particles is explicitly derived as a dilogarithm function when the weight function of t","authors_text":"HongGuang Sun, Wei Xu, Wen Chen, Yingjie Liang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T03:06:56Z","title":"Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09352","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":"sha256:0ab0087422d30d062d7a1a23a430b83657b290d5c5785a76cec4fdd3595d0f48","target":"record","created_at":"2026-05-17T23:59:17Z","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":"38175c88531c0cb9b8113ba2bb937900a36afb1c41592c6802f70e95c5e0992b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T03:06:56Z","title_canon_sha256":"e36a90d240f23e1d3a3d46f7322c1901eccb033e04967304f2ea2ac71614a6ec"},"schema_version":"1.0","source":{"id":"1801.09352","kind":"arxiv","version":1}},"canonical_sha256":"4b208ca9a6d6ddd46059bfdad4269f2b95ab982189311f04e9ea058bf109662c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b208ca9a6d6ddd46059bfdad4269f2b95ab982189311f04e9ea058bf109662c","first_computed_at":"2026-05-17T23:59:17.700266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:17.700266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kVzFC4LLzR0TGJ9/T+chuK4QYZ6pJk3IJl7BH8m0oid7CqK6ZY57Bzbzysve9wFD+Z5b89p52pqZqI0XwuiXBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:17.700716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ab0087422d30d062d7a1a23a430b83657b290d5c5785a76cec4fdd3595d0f48","sha256:4c0190e96a873f4c44073336844cb65a0b57576574bf0b07dfeba19979a3aaa3"],"state_sha256":"d94afc664993644227739cafbed9ce0c4fa6074ce609be783ed6ba0120caf103"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4XqjDmHClz95UIBuQHK1SQrfCk9kSgx1SV4EIXUHQbqEVYlcRrN3vR5VXeew6h4Ik4WeRZ1rdeYry92kPq9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:51:16.748566Z","bundle_sha256":"2ea4255381bf1c63983ec20b010ad25a8454c3f8987af457a5f6656c76907377"}}