{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3VRCCJ4WU2QXRZMGNQC6CRYLWP","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":"1c77bf8079ea08355b8f2299bbb9cd015caba77963bf730fb072cde7cef6c87d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2015-01-29T07:49:50Z","title_canon_sha256":"15d749c1aba9abf0e7ac2d7843f88d3bfec388a38c52bbbfef86778a1f52437b"},"schema_version":"1.0","source":{"id":"1501.07365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07365","created_at":"2026-05-18T01:37:44Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07365v2","created_at":"2026-05-18T01:37:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07365","created_at":"2026-05-18T01:37:44Z"},{"alias_kind":"pith_short_12","alias_value":"3VRCCJ4WU2QX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3VRCCJ4WU2QXRZMG","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3VRCCJ4W","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:deaa027f7dbc71d510c337534a082c562157c607b14374c54ecd870e1f78ab9c","target":"graph","created_at":"2026-05-18T01:37:44Z","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":"In this paper, we construct two types of 7R closed single loop linkages by combining different factorizations of a general (non-vertical) Darboux motion. These factorizations are obtained by extensions of a factorization algorithm for a generic rational motion. The first type of 7R linkages has several one-dimensional configuration components and one of them corresponds to the Darboux motion. The other type is a 7R linkage with two degrees of freedom and without one-dimensional component. The Darboux motion is a curve in an irreducible two dimensional configuration component.","authors_text":"Hans-Peter Schr\\\"ocker, Josef Schicho, Zijia Li","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2015-01-29T07:49:50Z","title":"7R Darboux Linkages by Factorization of Motion Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07365","kind":"arxiv","version":2},"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:ff94f57bd92a104f92f8e7c3524cb6005f00f7faf4bb1e82f79925060ab7ed5f","target":"record","created_at":"2026-05-18T01:37:44Z","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":"1c77bf8079ea08355b8f2299bbb9cd015caba77963bf730fb072cde7cef6c87d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.RO","submitted_at":"2015-01-29T07:49:50Z","title_canon_sha256":"15d749c1aba9abf0e7ac2d7843f88d3bfec388a38c52bbbfef86778a1f52437b"},"schema_version":"1.0","source":{"id":"1501.07365","kind":"arxiv","version":2}},"canonical_sha256":"dd62212796a6a178e5866c05e1470bb3c4dfb77e58b9f635fafcae60f0672d83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd62212796a6a178e5866c05e1470bb3c4dfb77e58b9f635fafcae60f0672d83","first_computed_at":"2026-05-18T01:37:44.482877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:44.482877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CiVos8kVaYdIo6duMax/2FDvr/d8r9co+iinSny06MLAsxKK8wIHkk1Uo6OjVAjcI3QQa5bB+tDEveZ9JAAQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:44.483417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff94f57bd92a104f92f8e7c3524cb6005f00f7faf4bb1e82f79925060ab7ed5f","sha256:deaa027f7dbc71d510c337534a082c562157c607b14374c54ecd870e1f78ab9c"],"state_sha256":"59dfd44bc926777350ab62aa748f049fb45423b37c575e115f2019ec369617bb"}