{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PTGSV6IHNUESHJQAVLXSBTVMJJ","short_pith_number":"pith:PTGSV6IH","canonical_record":{"source":{"id":"1908.00798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-02T10:55:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2b70835081bfa48e1f7db3a01d441b48b738bdbd0a6137550e51ce302a776a66","abstract_canon_sha256":"a8f2c1346aaa0f6241ebe06dc25b46d75d9bb8ea29c8733c7ebe09da809cb366"},"schema_version":"1.0"},"canonical_sha256":"7ccd2af9076d0923a600aaef20ceac4a5aeee1a670bdc8face174ed09d7e2bc8","source":{"kind":"arxiv","id":"1908.00798","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00798","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00798v2","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00798","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"PTGSV6IHNUES","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"pith_short_16","alias_value":"PTGSV6IHNUESHJQA","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"pith_short_8","alias_value":"PTGSV6IH","created_at":"2026-07-05T02:49:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PTGSV6IHNUESHJQAVLXSBTVMJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.00798","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-02T10:55:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2b70835081bfa48e1f7db3a01d441b48b738bdbd0a6137550e51ce302a776a66","abstract_canon_sha256":"a8f2c1346aaa0f6241ebe06dc25b46d75d9bb8ea29c8733c7ebe09da809cb366"},"schema_version":"1.0"},"canonical_sha256":"7ccd2af9076d0923a600aaef20ceac4a5aeee1a670bdc8face174ed09d7e2bc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:49:49.411713Z","signature_b64":"L7dvYwF8IIBdyyXD7BkmS+tUOnt3uYIc7mZLSBtS7q485LxUg19Msq4lSDlr9FNDXyLfSv56keLFwXxTf8Y0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ccd2af9076d0923a600aaef20ceac4a5aeee1a670bdc8face174ed09d7e2bc8","last_reissued_at":"2026-07-05T02:49:49.411251Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:49:49.411251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.00798","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":"2026-07-05T02:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cWAa4ugv0Fxhxof2vtYWXabMmyCt08cqbr+oKdvB93bMOVdsWxqE5CJvVOjvcNyvAXRPPRSKJtqSPEv7KNbYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:18:04.511134Z"},"content_sha256":"1e9fb291eee3b42aedbd14d22cddff45a1019c2e674b9eff4aa9b8901c80c769","schema_version":"1.0","event_id":"sha256:1e9fb291eee3b42aedbd14d22cddff45a1019c2e674b9eff4aa9b8901c80c769"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PTGSV6IHNUESHJQAVLXSBTVMJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double bracket formulation for the distribution function approach to multibead-chain suspensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.flu-dyn","authors_text":"Ching Lok Chong","submitted_at":"2019-08-02T10:55:02Z","abstract_excerpt":"A suspension of elastic chains of small beads in a Newtonian fluid is a common model for a viscoelastic polymer solution. The configuration of these multibead chains can be described by a distribution function that evolves according to a Liouville or Fokker--Planck equation. For example, when we consider a suspension of Hookean bead-spring pairs, this approach leads to the well-known upper-convected Maxwell model. This is done by taking the second moment of the Fokker--Planck equation that governs the distribution function, which describes the stress of the bead-spring pairs on the fluid. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00798","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00798/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9XkqGC2ZOTlrmw5Z/rZTLXglzU88sin3kq8MEeP00S97XZ30mnGbIKjcqwZVe2yBNMMWJeWCt+pl3p5wpd5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:18:04.512166Z"},"content_sha256":"ccda83866de0d91d7e416b17d4a89cc4ad9b71c890fc8efdf569ee569c82a18c","schema_version":"1.0","event_id":"sha256:ccda83866de0d91d7e416b17d4a89cc4ad9b71c890fc8efdf569ee569c82a18c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ/bundle.json","state_url":"https://pith.science/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ/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":"2026-08-17T00:18:04Z","links":{"resolver":"https://pith.science/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ","bundle":"https://pith.science/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ/bundle.json","state":"https://pith.science/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTGSV6IHNUESHJQAVLXSBTVMJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PTGSV6IHNUESHJQAVLXSBTVMJJ","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":"a8f2c1346aaa0f6241ebe06dc25b46d75d9bb8ea29c8733c7ebe09da809cb366","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-02T10:55:02Z","title_canon_sha256":"2b70835081bfa48e1f7db3a01d441b48b738bdbd0a6137550e51ce302a776a66"},"schema_version":"1.0","source":{"id":"1908.00798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00798","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00798v2","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00798","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"PTGSV6IHNUES","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"pith_short_16","alias_value":"PTGSV6IHNUESHJQA","created_at":"2026-07-05T02:49:49Z"},{"alias_kind":"pith_short_8","alias_value":"PTGSV6IH","created_at":"2026-07-05T02:49:49Z"}],"graph_snapshots":[{"event_id":"sha256:ccda83866de0d91d7e416b17d4a89cc4ad9b71c890fc8efdf569ee569c82a18c","target":"graph","created_at":"2026-07-05T02:49:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.00798/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A suspension of elastic chains of small beads in a Newtonian fluid is a common model for a viscoelastic polymer solution. The configuration of these multibead chains can be described by a distribution function that evolves according to a Liouville or Fokker--Planck equation. For example, when we consider a suspension of Hookean bead-spring pairs, this approach leads to the well-known upper-convected Maxwell model. This is done by taking the second moment of the Fokker--Planck equation that governs the distribution function, which describes the stress of the bead-spring pairs on the fluid. The ","authors_text":"Ching Lok Chong","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-02T10:55:02Z","title":"Double bracket formulation for the distribution function approach to multibead-chain suspensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00798","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":"sha256:1e9fb291eee3b42aedbd14d22cddff45a1019c2e674b9eff4aa9b8901c80c769","target":"record","created_at":"2026-07-05T02:49:49Z","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":"a8f2c1346aaa0f6241ebe06dc25b46d75d9bb8ea29c8733c7ebe09da809cb366","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2019-08-02T10:55:02Z","title_canon_sha256":"2b70835081bfa48e1f7db3a01d441b48b738bdbd0a6137550e51ce302a776a66"},"schema_version":"1.0","source":{"id":"1908.00798","kind":"arxiv","version":2}},"canonical_sha256":"7ccd2af9076d0923a600aaef20ceac4a5aeee1a670bdc8face174ed09d7e2bc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ccd2af9076d0923a600aaef20ceac4a5aeee1a670bdc8face174ed09d7e2bc8","first_computed_at":"2026-07-05T02:49:49.411251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:49:49.411251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L7dvYwF8IIBdyyXD7BkmS+tUOnt3uYIc7mZLSBtS7q485LxUg19Msq4lSDlr9FNDXyLfSv56keLFwXxTf8Y0Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:49:49.411713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e9fb291eee3b42aedbd14d22cddff45a1019c2e674b9eff4aa9b8901c80c769","sha256:ccda83866de0d91d7e416b17d4a89cc4ad9b71c890fc8efdf569ee569c82a18c"],"state_sha256":"49128ef51a64518b237f862e2f198e21eeda03a73259df2aed9cd2038becefaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAdyRUTxsCJFJ/GpG8sYR/fwgGe6iX/5ZIzxDQcBKekF+Qb7O0mytv67OdSDJPON2gTJqglzBCor9TG0cRW+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T00:18:04.520215Z","bundle_sha256":"0e942bbcd9098f62e6f56f77285d0d695cbcd9eb17bf37338f9d654732bd2fc8"}}