{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AY7EKAL2IUH4BXBSKLAYOMULRO","short_pith_number":"pith:AY7EKAL2","schema_version":"1.0","canonical_sha256":"063e45017a450fc0dc3252c187328b8b9a500c94ee79feed7afcaac3cdec9adc","source":{"kind":"arxiv","id":"1802.09097","version":1},"attestation_state":"computed","paper":{"title":"Rotation Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Donald Silberger, Sylvia Silberger","submitted_at":"2018-02-25T22:16:30Z","abstract_excerpt":"A query, about the orbit $P{\\cal W}$ in real 3-space of a point $P$ under an isometry group ${\\cal W}$ generated by edge rotations of a tetrahedron, leads to contrasting notions, ${\\cal W}$ versus ${\\cal S}$, of \"rotation group\". The set R $=\\{r_{{\\sf A}_1},r_{{\\sf A}_2}\\}$ of rotations $r_{{\\sf A} _i}$ about axes ${\\sf A}_i$ generates two manifestations of an isometry group on $\\Re^3$:\n  (1). In the {\\em stationary} group ${\\cal S:=S}$(R), all axes {\\sf B} are fixed under a rotation $r_{\\sf A}$ about {\\sf A}.\n  (2). In the {\\em peripatetic} group ${\\cal W:=W}$(R), each $r_{\\sf A}$ transforms "},"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":"1802.09097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-02-25T22:16:30Z","cross_cats_sorted":[],"title_canon_sha256":"841ac7034e5e7f8f59264a3f519b6f779fc155c0ca156c3a525fe07dc3635f67","abstract_canon_sha256":"392eaf49a3cf001c8a668b0b053565919bf58105d86130b98d2e22f3b2e5dc14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:35.536398Z","signature_b64":"wrKc4NRvEEQLM7txUP92tE8gGfIOSMTbqhL3d2sdQPdhQZ+muOHl4wGNBr6O5zGxKSIvHcyzrhMO/STyXksQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"063e45017a450fc0dc3252c187328b8b9a500c94ee79feed7afcaac3cdec9adc","last_reissued_at":"2026-05-18T00:22:35.535696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:35.535696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rotation Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Donald Silberger, Sylvia Silberger","submitted_at":"2018-02-25T22:16:30Z","abstract_excerpt":"A query, about the orbit $P{\\cal W}$ in real 3-space of a point $P$ under an isometry group ${\\cal W}$ generated by edge rotations of a tetrahedron, leads to contrasting notions, ${\\cal W}$ versus ${\\cal S}$, of \"rotation group\". The set R $=\\{r_{{\\sf A}_1},r_{{\\sf A}_2}\\}$ of rotations $r_{{\\sf A} _i}$ about axes ${\\sf A}_i$ generates two manifestations of an isometry group on $\\Re^3$:\n  (1). In the {\\em stationary} group ${\\cal S:=S}$(R), all axes {\\sf B} are fixed under a rotation $r_{\\sf A}$ about {\\sf A}.\n  (2). In the {\\em peripatetic} group ${\\cal W:=W}$(R), each $r_{\\sf A}$ transforms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09097","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":""},"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":"1802.09097","created_at":"2026-05-18T00:22:35.535800+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.09097v1","created_at":"2026-05-18T00:22:35.535800+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09097","created_at":"2026-05-18T00:22:35.535800+00:00"},{"alias_kind":"pith_short_12","alias_value":"AY7EKAL2IUH4","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AY7EKAL2IUH4BXBS","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AY7EKAL2","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO","json":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO.json","graph_json":"https://pith.science/api/pith-number/AY7EKAL2IUH4BXBSKLAYOMULRO/graph.json","events_json":"https://pith.science/api/pith-number/AY7EKAL2IUH4BXBSKLAYOMULRO/events.json","paper":"https://pith.science/paper/AY7EKAL2"},"agent_actions":{"view_html":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO","download_json":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO.json","view_paper":"https://pith.science/paper/AY7EKAL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.09097&json=true","fetch_graph":"https://pith.science/api/pith-number/AY7EKAL2IUH4BXBSKLAYOMULRO/graph.json","fetch_events":"https://pith.science/api/pith-number/AY7EKAL2IUH4BXBSKLAYOMULRO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO/action/storage_attestation","attest_author":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO/action/author_attestation","sign_citation":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO/action/citation_signature","submit_replication":"https://pith.science/pith/AY7EKAL2IUH4BXBSKLAYOMULRO/action/replication_record"}},"created_at":"2026-05-18T00:22:35.535800+00:00","updated_at":"2026-05-18T00:22:35.535800+00:00"}