{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:FUKFP5OVSAI4J4EOHU66VEX6JI","short_pith_number":"pith:FUKFP5OV","canonical_record":{"source":{"id":"2506.18029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2025-06-22T13:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"2eb58b4acf6e87c9caf7fe7156838d06df08872280ccaea7c58f376b7f4af97d","abstract_canon_sha256":"0ecc189df93e8de82d82fe0a1f7dc5302a7cfc9cf3c2835bf40e702c5f55a2da"},"schema_version":"1.0"},"canonical_sha256":"2d1457f5d59011c4f08e3d3dea92fe4a2b1cab2105d588513904184f2ba1454f","source":{"kind":"arxiv","id":"2506.18029","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18029","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18029v2","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18029","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"FUKFP5OVSAI4","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_16","alias_value":"FUKFP5OVSAI4J4EO","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_8","alias_value":"FUKFP5OV","created_at":"2026-06-19T16:12:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:FUKFP5OVSAI4J4EOHU66VEX6JI","target":"record","payload":{"canonical_record":{"source":{"id":"2506.18029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2025-06-22T13:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"2eb58b4acf6e87c9caf7fe7156838d06df08872280ccaea7c58f376b7f4af97d","abstract_canon_sha256":"0ecc189df93e8de82d82fe0a1f7dc5302a7cfc9cf3c2835bf40e702c5f55a2da"},"schema_version":"1.0"},"canonical_sha256":"2d1457f5d59011c4f08e3d3dea92fe4a2b1cab2105d588513904184f2ba1454f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:14.041721Z","signature_b64":"uirEKeBSz949JRBAPEdQylfnVHW5Bdjyc4flp9+2u15L1lI4LMqFUhN0zBx5w3K0WL6dicU5UQolQvqrCTZ5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d1457f5d59011c4f08e3d3dea92fe4a2b1cab2105d588513904184f2ba1454f","last_reissued_at":"2026-06-19T16:12:14.041179Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:14.041179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.18029","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:12:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5BtPr2VyXdXVFdMGDLVT7fF97jT0l+r2FmPgz7YwTC6lxDUv8PHr3IRIQWZFikLraof+9elMqsCAJZ/ebBpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:51:15.322370Z"},"content_sha256":"f83e863b7456a433569a542867139e33dabe67a4c23b81c12f139d8f4a5e70c1","schema_version":"1.0","event_id":"sha256:f83e863b7456a433569a542867139e33dabe67a4c23b81c12f139d8f4a5e70c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:FUKFP5OVSAI4J4EOHU66VEX6JI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Hans-Peter Schr\\\"ocker, Z\\\"ulal Derin Yaqub","submitted_at":"2025-06-22T13:15:22Z","abstract_excerpt":"In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories are well known, the case of line trajectories is more complicated and has not been studied. We explain when such motions exist and how to compute them. Our method gives explicit formulas for constructing these motions and shows that, in many cases, the solution is unique. We also show examples and explain how to use these results to design simple mechanisms th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18029","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.18029/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:12:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgqI8pM0lfwlhaX/Rszpxv+BhH38ybeuq8sEo2RY6eBXduU0vgAhimMlesZK6/aZkbuZjVEseOKO7v4l2QOfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:51:15.322744Z"},"content_sha256":"6219f1c299c8121b97a395389274cdace7358a01a4ba2aaed6fea76f68565871","schema_version":"1.0","event_id":"sha256:6219f1c299c8121b97a395389274cdace7358a01a4ba2aaed6fea76f68565871"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUKFP5OVSAI4J4EOHU66VEX6JI/bundle.json","state_url":"https://pith.science/pith/FUKFP5OVSAI4J4EOHU66VEX6JI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUKFP5OVSAI4J4EOHU66VEX6JI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T10:51:15Z","links":{"resolver":"https://pith.science/pith/FUKFP5OVSAI4J4EOHU66VEX6JI","bundle":"https://pith.science/pith/FUKFP5OVSAI4J4EOHU66VEX6JI/bundle.json","state":"https://pith.science/pith/FUKFP5OVSAI4J4EOHU66VEX6JI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUKFP5OVSAI4J4EOHU66VEX6JI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FUKFP5OVSAI4J4EOHU66VEX6JI","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":"0ecc189df93e8de82d82fe0a1f7dc5302a7cfc9cf3c2835bf40e702c5f55a2da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2025-06-22T13:15:22Z","title_canon_sha256":"2eb58b4acf6e87c9caf7fe7156838d06df08872280ccaea7c58f376b7f4af97d"},"schema_version":"1.0","source":{"id":"2506.18029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18029","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18029v2","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18029","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"FUKFP5OVSAI4","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_16","alias_value":"FUKFP5OVSAI4J4EO","created_at":"2026-06-19T16:12:14Z"},{"alias_kind":"pith_short_8","alias_value":"FUKFP5OV","created_at":"2026-06-19T16:12:14Z"}],"graph_snapshots":[{"event_id":"sha256:6219f1c299c8121b97a395389274cdace7358a01a4ba2aaed6fea76f68565871","target":"graph","created_at":"2026-06-19T16:12:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.18029/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories are well known, the case of line trajectories is more complicated and has not been studied. We explain when such motions exist and how to compute them. Our method gives explicit formulas for constructing these motions and shows that, in many cases, the solution is unique. We also show examples and explain how to use these results to design simple mechanisms th","authors_text":"Hans-Peter Schr\\\"ocker, Z\\\"ulal Derin Yaqub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2025-06-22T13:15:22Z","title":"Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18029","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:f83e863b7456a433569a542867139e33dabe67a4c23b81c12f139d8f4a5e70c1","target":"record","created_at":"2026-06-19T16:12:14Z","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":"0ecc189df93e8de82d82fe0a1f7dc5302a7cfc9cf3c2835bf40e702c5f55a2da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2025-06-22T13:15:22Z","title_canon_sha256":"2eb58b4acf6e87c9caf7fe7156838d06df08872280ccaea7c58f376b7f4af97d"},"schema_version":"1.0","source":{"id":"2506.18029","kind":"arxiv","version":2}},"canonical_sha256":"2d1457f5d59011c4f08e3d3dea92fe4a2b1cab2105d588513904184f2ba1454f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d1457f5d59011c4f08e3d3dea92fe4a2b1cab2105d588513904184f2ba1454f","first_computed_at":"2026-06-19T16:12:14.041179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:14.041179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uirEKeBSz949JRBAPEdQylfnVHW5Bdjyc4flp9+2u15L1lI4LMqFUhN0zBx5w3K0WL6dicU5UQolQvqrCTZ5Dg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:14.041721Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.18029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f83e863b7456a433569a542867139e33dabe67a4c23b81c12f139d8f4a5e70c1","sha256:6219f1c299c8121b97a395389274cdace7358a01a4ba2aaed6fea76f68565871"],"state_sha256":"4b9882c3b2815140fe8ff64e318562636011411715d1302601cc0625b98e3c66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auJWpKXY0FnWbjt9Avqkg74JUC9lTAkF80gPwPnGGYXxTYa2Eakr7zM5jHS1V7FFB/IUl0ZWdTi8EF9fmLJ1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:51:15.324814Z","bundle_sha256":"9d1ff69d746144e8d3da2e1c2eda30764d263cf371df0e1acec17999ff6a93e2"}}