{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SLR6X37DR3GLZYMEYOEAIFTXG7","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":"fb8e072fbac4fc2922137edcff05477866e7820dfcb0a6faa808a437d993014f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-05T11:50:22Z","title_canon_sha256":"b0acb1f0f3d1f9ad0489974054934b7062ec76d33aff6c8d04b21437bf4356c1"},"schema_version":"1.0","source":{"id":"1612.01319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01319","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01319v1","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01319","created_at":"2026-05-18T00:55:52Z"},{"alias_kind":"pith_short_12","alias_value":"SLR6X37DR3GL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SLR6X37DR3GLZYME","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SLR6X37D","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:8d0cd2a7fdacd08923444bddf551cafcdb2aa822b73eb29bbb4bc6b9940a50aa","target":"graph","created_at":"2026-05-18T00:55:52Z","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 introduce a one-parameter family of transforms, $U^t_{(m)}$, $t>0$, from the Hilbert space of Clifford algebra valued square integrable functions on the $m$--dimensional sphere, $L^2(S^{m},d\\sigma_{m})\\otimes \\mathbb{C}_{m+1}$, to the Hilbert spaces, ${\\mathcal M}L^2(\\mathbb{R}^{m+1} \\setminus \\{0\\},d\\mu_t)$, of monogenic functions on $\\mathbb{R}^{m+1}\\setminus \\{0\\}$ which are square integrable with respect to appropriate measures, $d\\mu_t$. We prove that these transforms are unitary isomorphisms of the Hilbert spaces and are extensions of the Segal-Bargman coherent state transform, $U_{(1","authors_text":"Jo\\~ao P. Nunes, Jos\\'e Mour\\~ao, Pei Dang, Tao Qian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-05T11:50:22Z","title":"Clifford Coherent State Transforms on Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01319","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":"sha256:2a0a4857dc5303a1e0fe22ae27fcfc52cda8963f61282f6744be94fc80d332f5","target":"record","created_at":"2026-05-18T00:55:52Z","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":"fb8e072fbac4fc2922137edcff05477866e7820dfcb0a6faa808a437d993014f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-05T11:50:22Z","title_canon_sha256":"b0acb1f0f3d1f9ad0489974054934b7062ec76d33aff6c8d04b21437bf4356c1"},"schema_version":"1.0","source":{"id":"1612.01319","kind":"arxiv","version":1}},"canonical_sha256":"92e3ebefe38eccbce184c38804167737e7cc7a47e6ee53f5d908171b5707f22a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92e3ebefe38eccbce184c38804167737e7cc7a47e6ee53f5d908171b5707f22a","first_computed_at":"2026-05-18T00:55:52.939536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:52.939536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2f5Rf2KgsKopy9K3YOter4G28GrdLwSajo0sz0Kr45V36xbIgS54KxvMk3yzA1+ahcSPnCyue9bIsXVxXj2NDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:52.940009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a0a4857dc5303a1e0fe22ae27fcfc52cda8963f61282f6744be94fc80d332f5","sha256:8d0cd2a7fdacd08923444bddf551cafcdb2aa822b73eb29bbb4bc6b9940a50aa"],"state_sha256":"434788d10d0878d0bb3bf919e557680f3e475cf136766e790d639dde3459b4ce"}