{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:FSZRRC6PBK7XJEQW6VY4VNLGA3","short_pith_number":"pith:FSZRRC6P","canonical_record":{"source":{"id":"0905.3093","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-05-19T13:07:51Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"c458626938ef6ac7a75cac336fa917747c8318bc84ed5022c2a8e37c6948fd50","abstract_canon_sha256":"e2e37fca410805ae36f083e79cfba23bebd2b858843a91416ffb5524517e1fd6"},"schema_version":"1.0"},"canonical_sha256":"2cb3188bcf0abf749216f571cab56606ded366dbbefc401ab34e9bcb712fd73f","source":{"kind":"arxiv","id":"0905.3093","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3093","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3093v2","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3093","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"FSZRRC6PBK7X","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FSZRRC6PBK7XJEQW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FSZRRC6P","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:FSZRRC6PBK7XJEQW6VY4VNLGA3","target":"record","payload":{"canonical_record":{"source":{"id":"0905.3093","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-05-19T13:07:51Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"c458626938ef6ac7a75cac336fa917747c8318bc84ed5022c2a8e37c6948fd50","abstract_canon_sha256":"e2e37fca410805ae36f083e79cfba23bebd2b858843a91416ffb5524517e1fd6"},"schema_version":"1.0"},"canonical_sha256":"2cb3188bcf0abf749216f571cab56606ded366dbbefc401ab34e9bcb712fd73f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:38.647920Z","signature_b64":"VwOaVH6a7B0SLLsXTZijguRAQfV8U7bONAZlyWj9qhT/n2Gz2Rg10THhTHy71/zcAGb840WGnBbN8BSmmlcFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cb3188bcf0abf749216f571cab56606ded366dbbefc401ab34e9bcb712fd73f","last_reissued_at":"2026-05-18T02:13:38.647517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:38.647517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.3093","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":"2026-05-18T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OXREqpJALLKocJ6nuJkHrMP6NxpuKIHGMe7sI5ic402lwU6VeRnSJ0NfK6mgh8eMV2sVGlo1ZKCi7F8fTohyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:35:59.101373Z"},"content_sha256":"86a979917db2a2456a9a5ef775e8ab79ac366acf9b8bc254f94b2fa960d8f0b3","schema_version":"1.0","event_id":"sha256:86a979917db2a2456a9a5ef775e8ab79ac366acf9b8bc254f94b2fa960d8f0b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:FSZRRC6PBK7XJEQW6VY4VNLGA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice-Boltzmann model for axisymmetric thermal flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"physics.comp-ph","authors_text":"G. H. Tang, Q. Li, W. Q. Tao, Y. L. He","submitted_at":"2009-05-19T13:07:51Z","abstract_excerpt":"In this brief report, a thermal lattice-Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3093","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":"2026-05-18T02:13:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XzXIxBNqnC+9FHjOjS7WxAfYb80yRNXw5ofix0rk04y2ZqSV6bAZGCVRALFIRZEzW3iBTOmIXyjcoNZu4uHZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:35:59.101728Z"},"content_sha256":"47f9609e896acdbe67bb9273d2f5fe74082c25640e38588a9223d132b47558d0","schema_version":"1.0","event_id":"sha256:47f9609e896acdbe67bb9273d2f5fe74082c25640e38588a9223d132b47558d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3/bundle.json","state_url":"https://pith.science/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3/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":"2026-06-24T06:35:59Z","links":{"resolver":"https://pith.science/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3","bundle":"https://pith.science/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3/bundle.json","state":"https://pith.science/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSZRRC6PBK7XJEQW6VY4VNLGA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FSZRRC6PBK7XJEQW6VY4VNLGA3","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":"e2e37fca410805ae36f083e79cfba23bebd2b858843a91416ffb5524517e1fd6","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-05-19T13:07:51Z","title_canon_sha256":"c458626938ef6ac7a75cac336fa917747c8318bc84ed5022c2a8e37c6948fd50"},"schema_version":"1.0","source":{"id":"0905.3093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3093","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3093v2","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3093","created_at":"2026-05-18T02:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"FSZRRC6PBK7X","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FSZRRC6PBK7XJEQW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FSZRRC6P","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:47f9609e896acdbe67bb9273d2f5fe74082c25640e38588a9223d132b47558d0","target":"graph","created_at":"2026-05-18T02:13:38Z","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":"In this brief report, a thermal lattice-Boltzmann (LB) model is presented for axisymmetric thermal flows in the incompressible limit. The model is based on the double-distribution-function LB method, which has attracted much attention since its emergence for its excellent numerical stability. Compared with the existing axisymmetric thermal LB models, the present model is simpler and retains the inherent features of the standard LB method. Numerical simulations are carried out for the thermally developing laminar flows in circular ducts and the natural convection in an annulus between two coaxi","authors_text":"G. H. Tang, Q. Li, W. Q. Tao, Y. L. He","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-05-19T13:07:51Z","title":"Lattice-Boltzmann model for axisymmetric thermal flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3093","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":"sha256:86a979917db2a2456a9a5ef775e8ab79ac366acf9b8bc254f94b2fa960d8f0b3","target":"record","created_at":"2026-05-18T02:13:38Z","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":"e2e37fca410805ae36f083e79cfba23bebd2b858843a91416ffb5524517e1fd6","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2009-05-19T13:07:51Z","title_canon_sha256":"c458626938ef6ac7a75cac336fa917747c8318bc84ed5022c2a8e37c6948fd50"},"schema_version":"1.0","source":{"id":"0905.3093","kind":"arxiv","version":2}},"canonical_sha256":"2cb3188bcf0abf749216f571cab56606ded366dbbefc401ab34e9bcb712fd73f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cb3188bcf0abf749216f571cab56606ded366dbbefc401ab34e9bcb712fd73f","first_computed_at":"2026-05-18T02:13:38.647517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:38.647517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VwOaVH6a7B0SLLsXTZijguRAQfV8U7bONAZlyWj9qhT/n2Gz2Rg10THhTHy71/zcAGb840WGnBbN8BSmmlcFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:38.647920Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86a979917db2a2456a9a5ef775e8ab79ac366acf9b8bc254f94b2fa960d8f0b3","sha256:47f9609e896acdbe67bb9273d2f5fe74082c25640e38588a9223d132b47558d0"],"state_sha256":"c756db42f75c4c4df85f0489b1fa5ba52ce07bd053c2c53d69f2ee60b7a9683b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rny7JNLPr+cBeDYWGkZCr6n03FHUfrfx24+KhQO5oOxkvp1GSrgwDE5+fBLqF6a7pB/T474Zj0mwL+jP1xmyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:35:59.103644Z","bundle_sha256":"45c14e5381569ee4738431b5183b6bd9b3888124074ab5286ebaf24c308cdbeb"}}