{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3FGKDWA5NHQFTUCBLNRCS44BO7","short_pith_number":"pith:3FGKDWA5","schema_version":"1.0","canonical_sha256":"d94ca1d81d69e059d0415b6229738177c2172223cf1b074fdec5a0a40e596aa5","source":{"kind":"arxiv","id":"1210.0487","version":1},"attestation_state":"computed","paper":{"title":"The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Michael I. Weinstein, Ovidiu Costin, Saleh Tanveer","submitted_at":"2012-10-01T17:58:38Z","abstract_excerpt":"General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\\sim e^{-\\Gamma t}, \\Gamma>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $\\Gamma \\approx \\frac{A}{\\epsilon} \\frac{We}{\\epsilon^{2}} \\exp(-B \\frac{We}{\\epsilon^2})$, where $0<\\epsilon\\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants.\n  In this paper, we prove this conjecture and calculate $A$ and $B$ to lead"},"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":"1210.0487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-01T17:58:38Z","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"title_canon_sha256":"c154cf33facacf17ccb5ffd579529ef460d174bb32c27601f7e8fcb5de6d0c23","abstract_canon_sha256":"9eadbcf3e2d41424156948c9581b334e8720b9a908b278683e258ebd8f8c7bac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:22.342822Z","signature_b64":"aJFXXXzcyQXNRtSlnZnUyp0d3B5CYLI1/oiJ2QaIicztLVBDCZvXHMxyEJiORPvlWeQ+MGUTJZdElwpR3u3kDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d94ca1d81d69e059d0415b6229738177c2172223cf1b074fdec5a0a40e596aa5","last_reissued_at":"2026-05-18T03:44:22.342296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:22.342296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Michael I. Weinstein, Ovidiu Costin, Saleh Tanveer","submitted_at":"2012-10-01T17:58:38Z","abstract_excerpt":"General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\\sim e^{-\\Gamma t}, \\Gamma>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $\\Gamma \\approx \\frac{A}{\\epsilon} \\frac{We}{\\epsilon^{2}} \\exp(-B \\frac{We}{\\epsilon^2})$, where $0<\\epsilon\\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants.\n  In this paper, we prove this conjecture and calculate $A$ and $B$ to lead"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0487","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.0487","created_at":"2026-05-18T03:44:22.342396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.0487v1","created_at":"2026-05-18T03:44:22.342396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0487","created_at":"2026-05-18T03:44:22.342396+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FGKDWA5NHQF","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FGKDWA5NHQFTUCB","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FGKDWA5","created_at":"2026-05-18T12:26:50.516681+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/3FGKDWA5NHQFTUCBLNRCS44BO7","json":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7.json","graph_json":"https://pith.science/api/pith-number/3FGKDWA5NHQFTUCBLNRCS44BO7/graph.json","events_json":"https://pith.science/api/pith-number/3FGKDWA5NHQFTUCBLNRCS44BO7/events.json","paper":"https://pith.science/paper/3FGKDWA5"},"agent_actions":{"view_html":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7","download_json":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7.json","view_paper":"https://pith.science/paper/3FGKDWA5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.0487&json=true","fetch_graph":"https://pith.science/api/pith-number/3FGKDWA5NHQFTUCBLNRCS44BO7/graph.json","fetch_events":"https://pith.science/api/pith-number/3FGKDWA5NHQFTUCBLNRCS44BO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7/action/storage_attestation","attest_author":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7/action/author_attestation","sign_citation":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7/action/citation_signature","submit_replication":"https://pith.science/pith/3FGKDWA5NHQFTUCBLNRCS44BO7/action/replication_record"}},"created_at":"2026-05-18T03:44:22.342396+00:00","updated_at":"2026-05-18T03:44:22.342396+00:00"}