{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2X7TIILD2X3DPGH4IMWRFKTYWX","short_pith_number":"pith:2X7TIILD","schema_version":"1.0","canonical_sha256":"d5ff342163d5f63798fc432d12aa78b5f96977affe9874d0679d6dc911c8f0b8","source":{"kind":"arxiv","id":"1207.2804","version":1},"attestation_state":"computed","paper":{"title":"Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"astro-ph.SR","authors_text":"(2) Canadian Institute for Theoretical Astrophysics, Astrophysical Plasmas, Benjamin P Brown (1), Canada), Center for Magnetic Self-Organization in Laboratory, Ellen G Zweibel (1) ((1) Department of Astronomy, Geoffrey M Vasil (2), University of Toronto, University of Wisconsin-Madison","submitted_at":"2012-07-11T22:19:49Z","abstract_excerpt":"Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial i"},"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":"1207.2804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2012-07-11T22:19:49Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"fbcb1e0b96ddb909c629a8aea96f6ea2a044620a58eb3fa518a2e68bed5ff831","abstract_canon_sha256":"bc5dde6f8e06fb67ac07816f784e6ee54bcf5f7d49d8c459895139ab06577ece"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:52.511212Z","signature_b64":"ayWx95BlUCz3pi6GvryNS1//EgDfxBXIiDSFu4M2bt63DHCmV1DenerR8ZyIfmEAjhkwyDbfIUvokaDPj1ItBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5ff342163d5f63798fc432d12aa78b5f96977affe9874d0679d6dc911c8f0b8","last_reissued_at":"2026-05-18T03:47:52.510776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:52.510776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"astro-ph.SR","authors_text":"(2) Canadian Institute for Theoretical Astrophysics, Astrophysical Plasmas, Benjamin P Brown (1), Canada), Center for Magnetic Self-Organization in Laboratory, Ellen G Zweibel (1) ((1) Department of Astronomy, Geoffrey M Vasil (2), University of Toronto, University of Wisconsin-Madison","submitted_at":"2012-07-11T22:19:49Z","abstract_excerpt":"Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2804","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":"1207.2804","created_at":"2026-05-18T03:47:52.510836+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.2804v1","created_at":"2026-05-18T03:47:52.510836+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2804","created_at":"2026-05-18T03:47:52.510836+00:00"},{"alias_kind":"pith_short_12","alias_value":"2X7TIILD2X3D","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2X7TIILD2X3DPGH4","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2X7TIILD","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/2X7TIILD2X3DPGH4IMWRFKTYWX","json":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX.json","graph_json":"https://pith.science/api/pith-number/2X7TIILD2X3DPGH4IMWRFKTYWX/graph.json","events_json":"https://pith.science/api/pith-number/2X7TIILD2X3DPGH4IMWRFKTYWX/events.json","paper":"https://pith.science/paper/2X7TIILD"},"agent_actions":{"view_html":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX","download_json":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX.json","view_paper":"https://pith.science/paper/2X7TIILD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.2804&json=true","fetch_graph":"https://pith.science/api/pith-number/2X7TIILD2X3DPGH4IMWRFKTYWX/graph.json","fetch_events":"https://pith.science/api/pith-number/2X7TIILD2X3DPGH4IMWRFKTYWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX/action/storage_attestation","attest_author":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX/action/author_attestation","sign_citation":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX/action/citation_signature","submit_replication":"https://pith.science/pith/2X7TIILD2X3DPGH4IMWRFKTYWX/action/replication_record"}},"created_at":"2026-05-18T03:47:52.510836+00:00","updated_at":"2026-05-18T03:47:52.510836+00:00"}