{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5NK32V7UWBAVXWYI3SM4KFABA5","short_pith_number":"pith:5NK32V7U","schema_version":"1.0","canonical_sha256":"eb55bd57f4b0415bdb08dc99c5140107454bb1bbbe86554c5e6a2e83d40af5a9","source":{"kind":"arxiv","id":"1112.1153","version":3},"attestation_state":"computed","paper":{"title":"Evolution of Weak Shocks in One Dimensional Planar and Non-planar Gasdynamic Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Raghavendra Venkatraman, Vishnu D. Sharma","submitted_at":"2011-12-06T04:07:36Z","abstract_excerpt":"Asymptotic decay laws for planar and nonplanar shock waves and the first order associated discontinuities that catch up with the shock from behind are obtained using four different approximation methods. The singular surface theory is used to derive a pair of transport equations for the shock strength and the associated first order discontinuity, which represents the effect of precursor disturbances that overtake the shock from behind. The asymptotic behaviour of both the discontinuities is completely analysed. It is noticed that the decay of a first order discontinuity is much faster than the"},"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":"1112.1153","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-06T04:07:36Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"5fa73b9bbaab80a0bcd94cd10913de7229f88db75a3cbaedcca672b24e66de9f","abstract_canon_sha256":"2ce0da357bc00ca6414f33572f0517dffe1170f6770940cd9dd39c608fb6dfd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:28.171024Z","signature_b64":"l3ZWm7msxxlOypS67gx+QM4tfq97ZwUEajhQzM1nw7nu0FwuWcdAAzNVoGHLjU1/tunK+1xve6ul38qf1LPmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb55bd57f4b0415bdb08dc99c5140107454bb1bbbe86554c5e6a2e83d40af5a9","last_reissued_at":"2026-05-18T02:54:28.170526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:28.170526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Evolution of Weak Shocks in One Dimensional Planar and Non-planar Gasdynamic Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Raghavendra Venkatraman, Vishnu D. Sharma","submitted_at":"2011-12-06T04:07:36Z","abstract_excerpt":"Asymptotic decay laws for planar and nonplanar shock waves and the first order associated discontinuities that catch up with the shock from behind are obtained using four different approximation methods. The singular surface theory is used to derive a pair of transport equations for the shock strength and the associated first order discontinuity, which represents the effect of precursor disturbances that overtake the shock from behind. The asymptotic behaviour of both the discontinuities is completely analysed. It is noticed that the decay of a first order discontinuity is much faster than the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1153","kind":"arxiv","version":3},"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":"1112.1153","created_at":"2026-05-18T02:54:28.170610+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1153v3","created_at":"2026-05-18T02:54:28.170610+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1153","created_at":"2026-05-18T02:54:28.170610+00:00"},{"alias_kind":"pith_short_12","alias_value":"5NK32V7UWBAV","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5NK32V7UWBAVXWYI","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5NK32V7U","created_at":"2026-05-18T12:26:20.644004+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/5NK32V7UWBAVXWYI3SM4KFABA5","json":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5.json","graph_json":"https://pith.science/api/pith-number/5NK32V7UWBAVXWYI3SM4KFABA5/graph.json","events_json":"https://pith.science/api/pith-number/5NK32V7UWBAVXWYI3SM4KFABA5/events.json","paper":"https://pith.science/paper/5NK32V7U"},"agent_actions":{"view_html":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5","download_json":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5.json","view_paper":"https://pith.science/paper/5NK32V7U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1153&json=true","fetch_graph":"https://pith.science/api/pith-number/5NK32V7UWBAVXWYI3SM4KFABA5/graph.json","fetch_events":"https://pith.science/api/pith-number/5NK32V7UWBAVXWYI3SM4KFABA5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5/action/storage_attestation","attest_author":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5/action/author_attestation","sign_citation":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5/action/citation_signature","submit_replication":"https://pith.science/pith/5NK32V7UWBAVXWYI3SM4KFABA5/action/replication_record"}},"created_at":"2026-05-18T02:54:28.170610+00:00","updated_at":"2026-05-18T02:54:28.170610+00:00"}