{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:545P642TJPN7MFEVFT4D573G7K","short_pith_number":"pith:545P642T","canonical_record":{"source":{"id":"1012.4778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-21T20:01:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"91f9c80596c8b4641214eaa78c64261cd80d3e5dfda7f1da3b665501477c4361","abstract_canon_sha256":"90a905170f88bf8030bc7b2081335da6b08899952f7183090ff0cc2c5aa615cf"},"schema_version":"1.0"},"canonical_sha256":"ef3aff73534bdbf614952cf83eff66fa9d18738a3bdc95f81cd8a8a5352c2eaa","source":{"kind":"arxiv","id":"1012.4778","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4778","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4778v1","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4778","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"545P642TJPN7","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"545P642TJPN7MFEV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"545P642T","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:545P642TJPN7MFEVFT4D573G7K","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-21T20:01:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"91f9c80596c8b4641214eaa78c64261cd80d3e5dfda7f1da3b665501477c4361","abstract_canon_sha256":"90a905170f88bf8030bc7b2081335da6b08899952f7183090ff0cc2c5aa615cf"},"schema_version":"1.0"},"canonical_sha256":"ef3aff73534bdbf614952cf83eff66fa9d18738a3bdc95f81cd8a8a5352c2eaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:19.076805Z","signature_b64":"gjps/PEw2fiRImnjoZaBKUg4F2m0q5pwWnwcgi/uzHWBAPA3Vpt7heDBK1qCc16z5jGaG2E20cewfMMZyxMAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef3aff73534bdbf614952cf83eff66fa9d18738a3bdc95f81cd8a8a5352c2eaa","last_reissued_at":"2026-05-18T02:04:19.076128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:19.076128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4778","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":"2026-05-18T02:04:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neiYAM2tjyvQIlO//f5rXpsDT4e2FE2llCoclhFPl6aZoK17KYonhTh2CB7qDRlqdFPNVswcd+bfQx006KN3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:46:17.393293Z"},"content_sha256":"6e7f31a65f338ad6a40925cab99dce650fa50b9dd09b6d87bf5a6286695e078a","schema_version":"1.0","event_id":"sha256:6e7f31a65f338ad6a40925cab99dce650fa50b9dd09b6d87bf5a6286695e078a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:545P642TJPN7MFEVFT4D573G7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Properties of Linearized Equations of Low Compressible Fluid Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Nikolay Gusev","submitted_at":"2010-12-21T20:01:23Z","abstract_excerpt":"Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions towards the incompressible limit when compressibility tends to zero is studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4778","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":"2026-05-18T02:04:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XsiOCfaQ6nDUUoed5oHBrVLvTM8c/HNGRxehd07kYSwtKTXj9rP51tYRvUHtFHJr5aYjURGTtIl6O5HQ4W0mCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:46:17.393656Z"},"content_sha256":"4c5918085005c9d48435c9ee8bbce8e6a404324b82811408fc46079e77e43ae7","schema_version":"1.0","event_id":"sha256:4c5918085005c9d48435c9ee8bbce8e6a404324b82811408fc46079e77e43ae7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/545P642TJPN7MFEVFT4D573G7K/bundle.json","state_url":"https://pith.science/pith/545P642TJPN7MFEVFT4D573G7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/545P642TJPN7MFEVFT4D573G7K/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":"2026-06-24T07:46:17Z","links":{"resolver":"https://pith.science/pith/545P642TJPN7MFEVFT4D573G7K","bundle":"https://pith.science/pith/545P642TJPN7MFEVFT4D573G7K/bundle.json","state":"https://pith.science/pith/545P642TJPN7MFEVFT4D573G7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/545P642TJPN7MFEVFT4D573G7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:545P642TJPN7MFEVFT4D573G7K","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":"90a905170f88bf8030bc7b2081335da6b08899952f7183090ff0cc2c5aa615cf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-21T20:01:23Z","title_canon_sha256":"91f9c80596c8b4641214eaa78c64261cd80d3e5dfda7f1da3b665501477c4361"},"schema_version":"1.0","source":{"id":"1012.4778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4778","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4778v1","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4778","created_at":"2026-05-18T02:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"545P642TJPN7","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"545P642TJPN7MFEV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"545P642T","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:4c5918085005c9d48435c9ee8bbce8e6a404324b82811408fc46079e77e43ae7","target":"graph","created_at":"2026-05-18T02:04:19Z","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":"Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions towards the incompressible limit when compressibility tends to zero is studied.","authors_text":"Nikolay Gusev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-21T20:01:23Z","title":"Asymptotic Properties of Linearized Equations of Low Compressible Fluid Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4778","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":"sha256:6e7f31a65f338ad6a40925cab99dce650fa50b9dd09b6d87bf5a6286695e078a","target":"record","created_at":"2026-05-18T02:04:19Z","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":"90a905170f88bf8030bc7b2081335da6b08899952f7183090ff0cc2c5aa615cf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-21T20:01:23Z","title_canon_sha256":"91f9c80596c8b4641214eaa78c64261cd80d3e5dfda7f1da3b665501477c4361"},"schema_version":"1.0","source":{"id":"1012.4778","kind":"arxiv","version":1}},"canonical_sha256":"ef3aff73534bdbf614952cf83eff66fa9d18738a3bdc95f81cd8a8a5352c2eaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef3aff73534bdbf614952cf83eff66fa9d18738a3bdc95f81cd8a8a5352c2eaa","first_computed_at":"2026-05-18T02:04:19.076128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:19.076128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gjps/PEw2fiRImnjoZaBKUg4F2m0q5pwWnwcgi/uzHWBAPA3Vpt7heDBK1qCc16z5jGaG2E20cewfMMZyxMAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:19.076805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e7f31a65f338ad6a40925cab99dce650fa50b9dd09b6d87bf5a6286695e078a","sha256:4c5918085005c9d48435c9ee8bbce8e6a404324b82811408fc46079e77e43ae7"],"state_sha256":"464ce406c53752bd2a7122ff921624a05a7c337cced5c86eb79b667596ec8552"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKm4nX+axaipxbT9ElLETgwYU0nUjgsTYvFiHFDuvvQ8EIoFq7zUZ3Xyz6zxDDqL6I2ZORLw+B9oiKvKl/uvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:46:17.395578Z","bundle_sha256":"1820276653c5b5f5dfdf2b20688047f11626419a37b77db473aacb992b7f12bd"}}