{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XEE7SWWEUT3ZKXXMKPBKYILOZJ","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":"12148e26991ca792a666ee0fa9dc616c9ae67e93880a4f73d993f2aa2e86c6c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-07T13:20:09Z","title_canon_sha256":"d8f69173788a275b4e0065673e38fef4a65a2c985b075ca31ed49c4057fb50e6"},"schema_version":"1.0","source":{"id":"1709.02224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02224","created_at":"2026-05-18T00:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02224v1","created_at":"2026-05-18T00:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02224","created_at":"2026-05-18T00:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"XEE7SWWEUT3Z","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XEE7SWWEUT3ZKXXM","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XEE7SWWE","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:493cd94f1f0ccd60f3e690e63e8bb9cac071e5d6ec36566856853f33630cf6e0","target":"graph","created_at":"2026-05-18T00:17:42Z","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":"We discuss channel surfaces in the context of Lie sphere geometry and characterise them as certain $\\Omega_{0}$-surfaces. Since $\\Omega_{0}$-surfaces possess a rich transformation theory, we study the behaviour of channel surfaces under these transformations. Furthermore, by using certain Dupin cyclide congruences, we characterise Ribaucour pairs of channel surfaces.","authors_text":"Gudrun Szewieczek, Mason Pember","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-07T13:20:09Z","title":"Channel surfaces in Lie sphere geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02224","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:bd2376f460eaf70372a8080ae7656c8f857ffff3d8ce047c53de7b37f397c2bf","target":"record","created_at":"2026-05-18T00:17:42Z","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":"12148e26991ca792a666ee0fa9dc616c9ae67e93880a4f73d993f2aa2e86c6c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-07T13:20:09Z","title_canon_sha256":"d8f69173788a275b4e0065673e38fef4a65a2c985b075ca31ed49c4057fb50e6"},"schema_version":"1.0","source":{"id":"1709.02224","kind":"arxiv","version":1}},"canonical_sha256":"b909f95ac4a4f7955eec53c2ac216eca4c89fa3e6c4dcc668b61ef6e80e557ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b909f95ac4a4f7955eec53c2ac216eca4c89fa3e6c4dcc668b61ef6e80e557ad","first_computed_at":"2026-05-18T00:17:42.966250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:42.966250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cbRLZO0uggup8aDlJ+KwSy39G+MqB2QNMTGtp4EQQcmO6AaVtZ8rt/kOgYRVJs/W1DW1NvYJYYrPejUToMCZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:42.967040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd2376f460eaf70372a8080ae7656c8f857ffff3d8ce047c53de7b37f397c2bf","sha256:493cd94f1f0ccd60f3e690e63e8bb9cac071e5d6ec36566856853f33630cf6e0"],"state_sha256":"8ea2a91f26e576218bcb3abe675bbe9c2ddc3a7746ebcad9ea19e9a98852b885"}