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Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vecto"},"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":"gr-qc/9810090","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1998-10-30T13:48:28Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"9af49d1d9aec50cad16a5af90fccd13e1f2dee4d66c22820b9b4e40835cc017f","abstract_canon_sha256":"ee3f6c91e87fd5d2eefd3309b05caeeaca373054bda592c54e4f3bf372585960"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:11.882371Z","signature_b64":"wjRYXWfGuOhvhqXmBReYe5/EQnAHhGd6jyArsFTs0BNzR/DFI5L/XBGbtBZVqT/A/C5AJYSBW0j4JV980vC7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a98e7ad47a0215d5583c648fb5bce117c075ab8606de8c27b6da315077d7d15","last_reissued_at":"2026-05-18T04:25:11.881818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:11.881818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Expansion Term In Hamilton's Equations","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"gr-qc","authors_text":"Mark D. Roberts","submitted_at":"1998-10-30T13:48:28Z","abstract_excerpt":"For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are\n  $- (\\delta H_{c})/(\\delta q)=\\dot{\\pi}+\\Theta\\pi,\n  $+ (\\delta H_{c})/(\\delta \\pi)=\\dot{q}$,\n  where $\\Theta = V^{a}_{.;a}$ is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. 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