{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:GK35J2UOV6CVH2BCQXYD43JSBI","short_pith_number":"pith:GK35J2UO","schema_version":"1.0","canonical_sha256":"32b7d4ea8eaf8553e82285f03e6d320a05329cf41301a6c0bf15a4f57bcea9d1","source":{"kind":"arxiv","id":"2107.04149","version":1},"attestation_state":"computed","paper":{"title":"Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Flank D. M. Bezerra, Lucas A. Santos","submitted_at":"2021-07-08T23:50:47Z","abstract_excerpt":"In this short paper, we review the Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices. We derive the rotations by any angle through the spectral behavior of the fractional powers of the rotation matrix by $\\frac{\\pi}{2}$ in $\\mathbb{R}^3$ about some axis."},"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":"2107.04149","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2021-07-08T23:50:47Z","cross_cats_sorted":[],"title_canon_sha256":"fb2bc1109681fac6b805dfb083178e5a6f60ce16513851a2ccb1055ac67029c0","abstract_canon_sha256":"01960f4d15f297100497724f2a8bdd1c1ff6c42ff1917f470d886e6fff8d32f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:30.139031Z","signature_b64":"V03ZJvqt2ZjH+7qqta+Pfopklex+MJ77j4Kg73EGNBOp+UY8joRNnWpeMhqFzEHuNUKZ3XzbDzD8QuNpYNVtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32b7d4ea8eaf8553e82285f03e6d320a05329cf41301a6c0bf15a4f57bcea9d1","last_reissued_at":"2026-07-05T02:56:30.138632Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:30.138632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Flank D. M. Bezerra, Lucas A. Santos","submitted_at":"2021-07-08T23:50:47Z","abstract_excerpt":"In this short paper, we review the Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices. We derive the rotations by any angle through the spectral behavior of the fractional powers of the rotation matrix by $\\frac{\\pi}{2}$ in $\\mathbb{R}^3$ about some axis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.04149","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.04149/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2107.04149","created_at":"2026-07-05T02:56:30.138693+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.04149v1","created_at":"2026-07-05T02:56:30.138693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.04149","created_at":"2026-07-05T02:56:30.138693+00:00"},{"alias_kind":"pith_short_12","alias_value":"GK35J2UOV6CV","created_at":"2026-07-05T02:56:30.138693+00:00"},{"alias_kind":"pith_short_16","alias_value":"GK35J2UOV6CVH2BC","created_at":"2026-07-05T02:56:30.138693+00:00"},{"alias_kind":"pith_short_8","alias_value":"GK35J2UO","created_at":"2026-07-05T02:56:30.138693+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.00302","citing_title":"Beyond Atomic Geometry Representations in Materials Science: A Human-in-the-Loop Multimodal Framework","ref_index":1993,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI","json":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI.json","graph_json":"https://pith.science/api/pith-number/GK35J2UOV6CVH2BCQXYD43JSBI/graph.json","events_json":"https://pith.science/api/pith-number/GK35J2UOV6CVH2BCQXYD43JSBI/events.json","paper":"https://pith.science/paper/GK35J2UO"},"agent_actions":{"view_html":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI","download_json":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI.json","view_paper":"https://pith.science/paper/GK35J2UO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.04149&json=true","fetch_graph":"https://pith.science/api/pith-number/GK35J2UOV6CVH2BCQXYD43JSBI/graph.json","fetch_events":"https://pith.science/api/pith-number/GK35J2UOV6CVH2BCQXYD43JSBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI/action/storage_attestation","attest_author":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI/action/author_attestation","sign_citation":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI/action/citation_signature","submit_replication":"https://pith.science/pith/GK35J2UOV6CVH2BCQXYD43JSBI/action/replication_record"}},"created_at":"2026-07-05T02:56:30.138693+00:00","updated_at":"2026-07-05T02:56:30.138693+00:00"}