{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UF46HZTLJLBUM253KMQEYTSHQM","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":"f3c47345339be82d9306d791ddb87753d7033c42255ad382f6c86f909589eac8","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-11-20T00:24:32Z","title_canon_sha256":"e4e8e207a6ade4384ce13be41fd80d9cddcae3f536ef345513ed08ef76cfd372"},"schema_version":"1.0","source":{"id":"1811.08030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08030","created_at":"2026-05-18T00:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08030v1","created_at":"2026-05-18T00:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08030","created_at":"2026-05-18T00:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"UF46HZTLJLBU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UF46HZTLJLBUM253","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UF46HZTL","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:7bf67614a0f1eeb1f15cab38b5b603c46c4468976e3816b0bf23d272cd65e6df","target":"graph","created_at":"2026-05-18T00:00:17Z","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":"A Steiner chain of length k consists of k circles, tangent to two given non-intersecting circles (the parent circles) and tangent to each other in a cyclic pattern. The Steiner porism states that once a chain of k circles exists, there exists a 1-parameter family of such chains with the same parent circles that can be constructed starting with any initial circle, tangent to the parent circles. What do the circles in these 1-parameter family of Steiner chains of length k have in common? We prove that the first k-1 moments of their curvatures remain constant within a 1-parameter family. For k=3,","authors_text":"Richard Evan Schwartz, Serge Tabachnikov","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-11-20T00:24:32Z","title":"Descartes Circle Theorem, Steiner Porism, and Spherical Designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08030","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:b660e2e541a897ff4c8f6c0f9b54b4f5a0e88d37a9e2329b9c535ad635c361f8","target":"record","created_at":"2026-05-18T00:00:17Z","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":"f3c47345339be82d9306d791ddb87753d7033c42255ad382f6c86f909589eac8","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-11-20T00:24:32Z","title_canon_sha256":"e4e8e207a6ade4384ce13be41fd80d9cddcae3f536ef345513ed08ef76cfd372"},"schema_version":"1.0","source":{"id":"1811.08030","kind":"arxiv","version":1}},"canonical_sha256":"a179e3e66b4ac3466bbb53204c4e47831beccdd1c78fe82e1a47fe7ebcdc83f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a179e3e66b4ac3466bbb53204c4e47831beccdd1c78fe82e1a47fe7ebcdc83f4","first_computed_at":"2026-05-18T00:00:17.067935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:17.067935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v1l0850la+T+rmZ67v3MS8D2UYE9rgI7oWKpAQDCbKB8Bdd6Igfm+0ZIXcZH+FBlV4ZhLyJFpFxWObVxqnwODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:17.068554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b660e2e541a897ff4c8f6c0f9b54b4f5a0e88d37a9e2329b9c535ad635c361f8","sha256:7bf67614a0f1eeb1f15cab38b5b603c46c4468976e3816b0bf23d272cd65e6df"],"state_sha256":"85ce4b7a61c6e415b1636cdc7a71d91c81cf181780faaf7494dfaa831f3b7962"}