{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TAKPTODKKA7QZC6H2ZTQB3TIWH","short_pith_number":"pith:TAKPTODK","schema_version":"1.0","canonical_sha256":"9814f9b86a503f0c8bc7d66700ee68b1e5bb73c269632610c4b6e64033bf666d","source":{"kind":"arxiv","id":"1408.3885","version":3},"attestation_state":"computed","paper":{"title":"Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Akio Sugamoto, Kazuharu Bamba, Mayumi Saitou","submitted_at":"2014-08-18T02:00:19Z","abstract_excerpt":"Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\\theta$, a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by $\\theta$. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.3885","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-08-18T02:00:19Z","cross_cats_sorted":[],"title_canon_sha256":"fe430ed24541ac42d4078e14e3739c7c21fb633da4473fbe7681ec92ccad0b45","abstract_canon_sha256":"247c20678ff62b41b1fa694ce0727f402dc224099e7c6ab754ed48061fc66172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:40.166033Z","signature_b64":"4zFdpTr+JmUaiIG+vTXBB36YMcuwbncpTLJDSAGaN38Nl7ex2Ox3uOhh1/ZmN3B2yjppB7j2oSpOxUFNiqx6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9814f9b86a503f0c8bc7d66700ee68b1e5bb73c269632610c4b6e64033bf666d","last_reissued_at":"2026-05-18T02:39:40.165420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:40.165420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hydrodynamics on non-commutative space --A step toward hydrodynamics of granular materials--","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Akio Sugamoto, Kazuharu Bamba, Mayumi Saitou","submitted_at":"2014-08-18T02:00:19Z","abstract_excerpt":"Hydrodynamics on non-commutative space is studied based on a formulation of hydrodynamics by Y. Nambu in terms of Poisson and Nambu brackets. Replacing these brackets by Moyal brackets with a parameter $\\theta$, a new hydrodynamics on non-commutative space is derived. It may be a step toward to find the hydrodynamics of granular materials whose minimum volume is given by $\\theta$. To clarify this minimum volume, path integral quantization and uncertainty relation of Nambu dynamics are examined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3885","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.3885","created_at":"2026-05-18T02:39:40.165524+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3885v3","created_at":"2026-05-18T02:39:40.165524+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3885","created_at":"2026-05-18T02:39:40.165524+00:00"},{"alias_kind":"pith_short_12","alias_value":"TAKPTODKKA7Q","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TAKPTODKKA7QZC6H","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TAKPTODK","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH","json":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH.json","graph_json":"https://pith.science/api/pith-number/TAKPTODKKA7QZC6H2ZTQB3TIWH/graph.json","events_json":"https://pith.science/api/pith-number/TAKPTODKKA7QZC6H2ZTQB3TIWH/events.json","paper":"https://pith.science/paper/TAKPTODK"},"agent_actions":{"view_html":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH","download_json":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH.json","view_paper":"https://pith.science/paper/TAKPTODK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3885&json=true","fetch_graph":"https://pith.science/api/pith-number/TAKPTODKKA7QZC6H2ZTQB3TIWH/graph.json","fetch_events":"https://pith.science/api/pith-number/TAKPTODKKA7QZC6H2ZTQB3TIWH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH/action/storage_attestation","attest_author":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH/action/author_attestation","sign_citation":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH/action/citation_signature","submit_replication":"https://pith.science/pith/TAKPTODKKA7QZC6H2ZTQB3TIWH/action/replication_record"}},"created_at":"2026-05-18T02:39:40.165524+00:00","updated_at":"2026-05-18T02:39:40.165524+00:00"}