{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:BBLGEIQPMAFQYHUYMEAELA4OXA","short_pith_number":"pith:BBLGEIQP","schema_version":"1.0","canonical_sha256":"085662220f600b0c1e98610045838eb80585a209e1e71bbd771b3bdec2317fde","source":{"kind":"arxiv","id":"0706.1818","version":1},"attestation_state":"computed","paper":{"title":"Ultra-relativistic geometrical shock dynamics and vorticity","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Andrew I. MacFadyen, Jeremy Goodman","submitted_at":"2007-06-13T03:28:55Z","abstract_excerpt":"Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly via a Riemann invariant. The nonrelativistic theory, formulated by G. B. Whitham and others, matches many experimental results surprisingly well. Motivated by astrophysical applications, we adapt the theory to ultra-relativistic shocks advancing into an ideal fluid whose pressure is negligible ahead of the shock, but one third of its proper energy density be"},"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":"0706.1818","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2007-06-13T03:28:55Z","cross_cats_sorted":[],"title_canon_sha256":"960e6e8bfb855af547cf106b31d1d04985c3b1e8a4f9da4e9da79bfea884f12d","abstract_canon_sha256":"6d8b4f934d49bb732acfaf1f27068a01958a3de4ff7029cae99e94433eddd2d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:30.183906Z","signature_b64":"ph2QxhRK3SWLA3lr6HUu8iTPuD1FK4pFzBLTQXCa3Sz6PXQCItXvdk1FPKIwUW0C/7SOM3vodArGK//nKs7rCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"085662220f600b0c1e98610045838eb80585a209e1e71bbd771b3bdec2317fde","last_reissued_at":"2026-05-18T02:16:30.183217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:30.183217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ultra-relativistic geometrical shock dynamics and vorticity","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Andrew I. MacFadyen, Jeremy Goodman","submitted_at":"2007-06-13T03:28:55Z","abstract_excerpt":"Geometrical shock dynamics, also called CCW theory, yields approximate equations for shock propagation in which only the conditions at the shock appear explicitly; the post-shock flow is presumed approximately uniform and enters implicitly via a Riemann invariant. The nonrelativistic theory, formulated by G. B. Whitham and others, matches many experimental results surprisingly well. Motivated by astrophysical applications, we adapt the theory to ultra-relativistic shocks advancing into an ideal fluid whose pressure is negligible ahead of the shock, but one third of its proper energy density be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1818","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":"0706.1818","created_at":"2026-05-18T02:16:30.183339+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.1818v1","created_at":"2026-05-18T02:16:30.183339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1818","created_at":"2026-05-18T02:16:30.183339+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBLGEIQPMAFQ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBLGEIQPMAFQYHUY","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBLGEIQP","created_at":"2026-05-18T12:25:55.427421+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/BBLGEIQPMAFQYHUYMEAELA4OXA","json":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA.json","graph_json":"https://pith.science/api/pith-number/BBLGEIQPMAFQYHUYMEAELA4OXA/graph.json","events_json":"https://pith.science/api/pith-number/BBLGEIQPMAFQYHUYMEAELA4OXA/events.json","paper":"https://pith.science/paper/BBLGEIQP"},"agent_actions":{"view_html":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA","download_json":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA.json","view_paper":"https://pith.science/paper/BBLGEIQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.1818&json=true","fetch_graph":"https://pith.science/api/pith-number/BBLGEIQPMAFQYHUYMEAELA4OXA/graph.json","fetch_events":"https://pith.science/api/pith-number/BBLGEIQPMAFQYHUYMEAELA4OXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA/action/storage_attestation","attest_author":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA/action/author_attestation","sign_citation":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA/action/citation_signature","submit_replication":"https://pith.science/pith/BBLGEIQPMAFQYHUYMEAELA4OXA/action/replication_record"}},"created_at":"2026-05-18T02:16:30.183339+00:00","updated_at":"2026-05-18T02:16:30.183339+00:00"}