{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4YPQGSMWVY4JZQNQRGGNVRPZBM","short_pith_number":"pith:4YPQGSMW","schema_version":"1.0","canonical_sha256":"e61f034996ae389cc1b0898cdac5f90b1d00730659b224e96ce9d6dfdbfe8b67","source":{"kind":"arxiv","id":"1307.4903","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of causal maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Michael G. Cowling, Nils Byrial Andersen","submitted_at":"2013-07-18T10:55:14Z","abstract_excerpt":"We show that order-invariant injective maps on the noncompactly causal symmetric space $SO_0 (1,n)/SO_0 (1,n-1)$ belong to $O(1,n)^+$."},"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":"1307.4903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-18T10:55:14Z","cross_cats_sorted":[],"title_canon_sha256":"89866f2fab278763ebb508e46d0ff2c530e70b32a88616fdce1830aaf57cb153","abstract_canon_sha256":"2d506f60653f43e6225f77c288857cd29e9c0d50d581c83817eb88b1eb24083a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:07.272151Z","signature_b64":"ZXWjf5vdZvJLWnXa0S9Jm+DG2onN3nsQtt9+OPJLt1g4KOQqzgvNpXBiqyRQOHy5rXmOPHyhPF1vuOhZVx6KBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e61f034996ae389cc1b0898cdac5f90b1d00730659b224e96ce9d6dfdbfe8b67","last_reissued_at":"2026-05-18T03:18:07.271460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:07.271460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of causal maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Michael G. Cowling, Nils Byrial Andersen","submitted_at":"2013-07-18T10:55:14Z","abstract_excerpt":"We show that order-invariant injective maps on the noncompactly causal symmetric space $SO_0 (1,n)/SO_0 (1,n-1)$ belong to $O(1,n)^+$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4903","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":"1307.4903","created_at":"2026-05-18T03:18:07.271576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.4903v1","created_at":"2026-05-18T03:18:07.271576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4903","created_at":"2026-05-18T03:18:07.271576+00:00"},{"alias_kind":"pith_short_12","alias_value":"4YPQGSMWVY4J","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4YPQGSMWVY4JZQNQ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4YPQGSMW","created_at":"2026-05-18T12:27:34.582898+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/4YPQGSMWVY4JZQNQRGGNVRPZBM","json":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM.json","graph_json":"https://pith.science/api/pith-number/4YPQGSMWVY4JZQNQRGGNVRPZBM/graph.json","events_json":"https://pith.science/api/pith-number/4YPQGSMWVY4JZQNQRGGNVRPZBM/events.json","paper":"https://pith.science/paper/4YPQGSMW"},"agent_actions":{"view_html":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM","download_json":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM.json","view_paper":"https://pith.science/paper/4YPQGSMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.4903&json=true","fetch_graph":"https://pith.science/api/pith-number/4YPQGSMWVY4JZQNQRGGNVRPZBM/graph.json","fetch_events":"https://pith.science/api/pith-number/4YPQGSMWVY4JZQNQRGGNVRPZBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM/action/storage_attestation","attest_author":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM/action/author_attestation","sign_citation":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM/action/citation_signature","submit_replication":"https://pith.science/pith/4YPQGSMWVY4JZQNQRGGNVRPZBM/action/replication_record"}},"created_at":"2026-05-18T03:18:07.271576+00:00","updated_at":"2026-05-18T03:18:07.271576+00:00"}