{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IMG3RZFN3FFH3V775KBYJPRQZ2","short_pith_number":"pith:IMG3RZFN","canonical_record":{"source":{"id":"1611.03980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-11-12T10:19:27Z","cross_cats_sorted":[],"title_canon_sha256":"424fc5bfefa5994f23de144c40ec7114d306630e6a0fa5caf66a2ec96b1a77e5","abstract_canon_sha256":"327d59a77bcda95a04b8fd436f517455c131784921a91eb363b5595d5523d16b"},"schema_version":"1.0"},"canonical_sha256":"430db8e4add94a7dd7ffea8384be30ce80e703b8ef92190646e9db3b6c4ffe35","source":{"kind":"arxiv","id":"1611.03980","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03980","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03980v1","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03980","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"IMG3RZFN3FFH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IMG3RZFN3FFH3V77","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IMG3RZFN","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IMG3RZFN3FFH3V775KBYJPRQZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-11-12T10:19:27Z","cross_cats_sorted":[],"title_canon_sha256":"424fc5bfefa5994f23de144c40ec7114d306630e6a0fa5caf66a2ec96b1a77e5","abstract_canon_sha256":"327d59a77bcda95a04b8fd436f517455c131784921a91eb363b5595d5523d16b"},"schema_version":"1.0"},"canonical_sha256":"430db8e4add94a7dd7ffea8384be30ce80e703b8ef92190646e9db3b6c4ffe35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:17.939415Z","signature_b64":"ihreKIgGEkSA+x0XT+wyH0EUtUvLtinISXm9gQkmUP86yptdIpXAQJTEN0Ph4Dxw2rYiSndScMSj85PvXbJmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"430db8e4add94a7dd7ffea8384be30ce80e703b8ef92190646e9db3b6c4ffe35","last_reissued_at":"2026-05-18T00:59:17.938707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:17.938707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03980","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L69N0uqPr55Pw0fhXkSstHe2a/2kwiUgwpfbz+pGWHXzYRUx5OWtMWlvVseX2rp5n21H+wfENFHTcrq0H8NiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:18:22.094821Z"},"content_sha256":"f3ecc74176e6193d45d1bdac1d34403c7da1e8965715cc91dfc4e6523c1bc72c","schema_version":"1.0","event_id":"sha256:f3ecc74176e6193d45d1bdac1d34403c7da1e8965715cc91dfc4e6523c1bc72c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IMG3RZFN3FFH3V775KBYJPRQZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Many Faces of Boussinesq Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Nasser Al-Salti, Vladimir A. Vladimirov","submitted_at":"2016-11-12T10:19:27Z","abstract_excerpt":"The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of veloc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03980","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgFgmwW5qYAzPwVLgKBnq+/mJr5mGRBTXG7chaSu/P5B9Dlp3F0h4+gBwulP9YMjyuhzuVcFsFlz36nTUaCFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:18:22.095503Z"},"content_sha256":"6561a2b005558ffe351acaec5185a0a51f25222f9d4f0970512f7a5494b02a65","schema_version":"1.0","event_id":"sha256:6561a2b005558ffe351acaec5185a0a51f25222f9d4f0970512f7a5494b02a65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IMG3RZFN3FFH3V775KBYJPRQZ2/bundle.json","state_url":"https://pith.science/pith/IMG3RZFN3FFH3V775KBYJPRQZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IMG3RZFN3FFH3V775KBYJPRQZ2/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":"2026-05-31T10:18:22Z","links":{"resolver":"https://pith.science/pith/IMG3RZFN3FFH3V775KBYJPRQZ2","bundle":"https://pith.science/pith/IMG3RZFN3FFH3V775KBYJPRQZ2/bundle.json","state":"https://pith.science/pith/IMG3RZFN3FFH3V775KBYJPRQZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IMG3RZFN3FFH3V775KBYJPRQZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IMG3RZFN3FFH3V775KBYJPRQZ2","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":"327d59a77bcda95a04b8fd436f517455c131784921a91eb363b5595d5523d16b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-11-12T10:19:27Z","title_canon_sha256":"424fc5bfefa5994f23de144c40ec7114d306630e6a0fa5caf66a2ec96b1a77e5"},"schema_version":"1.0","source":{"id":"1611.03980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03980","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03980v1","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03980","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"IMG3RZFN3FFH","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IMG3RZFN3FFH3V77","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IMG3RZFN","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:6561a2b005558ffe351acaec5185a0a51f25222f9d4f0970512f7a5494b02a65","target":"graph","created_at":"2026-05-18T00:59:17Z","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":"The \\emph{equations of Boussinesq approximation} (EBA) for an incompressible and inhomogeneous in density fluid are analyzed from a viewpoint of the asymptotic theory. A systematic scaling shows that there is an infinite number of related asymptotic models. We have divided them into three classes: `poor', `reasonable' and `good' Boussinesq approximations. Each model can be characterized by two parameters $q$ and $k$, where $q =1, 2, 3, \\dots$ and $k=0, \\pm 1, \\pm 2,\\dots$. Parameter $q$ is related to the `quality' of approximation, while $k$ gives us an infinite set of possible scales of veloc","authors_text":"Nasser Al-Salti, Vladimir A. Vladimirov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-11-12T10:19:27Z","title":"Many Faces of Boussinesq Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03980","kind":"arxiv","version":1},"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:f3ecc74176e6193d45d1bdac1d34403c7da1e8965715cc91dfc4e6523c1bc72c","target":"record","created_at":"2026-05-18T00:59:17Z","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":"327d59a77bcda95a04b8fd436f517455c131784921a91eb363b5595d5523d16b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2016-11-12T10:19:27Z","title_canon_sha256":"424fc5bfefa5994f23de144c40ec7114d306630e6a0fa5caf66a2ec96b1a77e5"},"schema_version":"1.0","source":{"id":"1611.03980","kind":"arxiv","version":1}},"canonical_sha256":"430db8e4add94a7dd7ffea8384be30ce80e703b8ef92190646e9db3b6c4ffe35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"430db8e4add94a7dd7ffea8384be30ce80e703b8ef92190646e9db3b6c4ffe35","first_computed_at":"2026-05-18T00:59:17.938707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:17.938707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihreKIgGEkSA+x0XT+wyH0EUtUvLtinISXm9gQkmUP86yptdIpXAQJTEN0Ph4Dxw2rYiSndScMSj85PvXbJmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:17.939415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3ecc74176e6193d45d1bdac1d34403c7da1e8965715cc91dfc4e6523c1bc72c","sha256:6561a2b005558ffe351acaec5185a0a51f25222f9d4f0970512f7a5494b02a65"],"state_sha256":"1a69e9d61380539b58ca637c8baacdb204ad976a85a9bc42a9569c64ddc13a28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TNoh3QkvgbLhjmqhbkOivuUgoE6A04lMio/8GZMU7pEEewWctfvKOSlngpWfZyk1IQcpsm0usLyhy/Xq4RM+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:18:22.099204Z","bundle_sha256":"61290831c6dbada4d877a77ff19606b7b70832b6b6bc02804485a075010ff551"}}