{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:B4MW4MDDVZMHV6LLFZFNKKQOJX","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":"0652929581dc20c944ada0e6ef33e425e2c3edb7b139a3d7cf8d0f41775329c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2019-04-23T11:10:26Z","title_canon_sha256":"06820e03167e0d9d8cd96ce6609d07683e0253aaf2195dbcbd7b1368f92f2253"},"schema_version":"1.0","source":{"id":"1904.09973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09973","created_at":"2026-05-17T23:47:55Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09973v1","created_at":"2026-05-17T23:47:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09973","created_at":"2026-05-17T23:47:55Z"},{"alias_kind":"pith_short_12","alias_value":"B4MW4MDDVZMH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B4MW4MDDVZMHV6LL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B4MW4MDD","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:619cbe617726b70e4ae45b57fa055cd52f40d63f6bc617b7b35e389b2befa68f","target":"graph","created_at":"2026-05-17T23:47:55Z","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":"This is a direct computation of the spectral representation of homogeneous spin-weighted spherical random fields with arbitrary integer spin. It generalises known results from Cosmology for the spin-2 Cosmic Microwave Background polarisation and Cosmic Shear fields, without decomposition into $E$- and $B$-modes. The derivation uses an instructive representation of spin-weighted spherical functions over the Spin(3) group, where the transformation behaviour of spin-weighted fields can be treated more naturally than over the sphere, and where the group nature of Spin(3) greatly simplifies calcula","authors_text":"Nicolas Tessore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2019-04-23T11:10:26Z","title":"The Spectral Representation of Homogeneous Spin-Weighted Random Fields on the Sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09973","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:f28b675a0311d3d8591a6081906da1ab784dd975d27432d7c244e12c958edd95","target":"record","created_at":"2026-05-17T23:47:55Z","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":"0652929581dc20c944ada0e6ef33e425e2c3edb7b139a3d7cf8d0f41775329c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2019-04-23T11:10:26Z","title_canon_sha256":"06820e03167e0d9d8cd96ce6609d07683e0253aaf2195dbcbd7b1368f92f2253"},"schema_version":"1.0","source":{"id":"1904.09973","kind":"arxiv","version":1}},"canonical_sha256":"0f196e3063ae587af96b2e4ad52a0e4dd1a44f938e8ecc6245ae41d5e0b1fe71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f196e3063ae587af96b2e4ad52a0e4dd1a44f938e8ecc6245ae41d5e0b1fe71","first_computed_at":"2026-05-17T23:47:55.337441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:55.337441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RMKLUULJiqzf5d4nLtfuwuGc6LWrTsthaJ33Oi1Lq2om2d1Cwi88kc2zQcguMG+M+A2AlpkAGZkKOefA0cJLAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:55.338011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f28b675a0311d3d8591a6081906da1ab784dd975d27432d7c244e12c958edd95","sha256:619cbe617726b70e4ae45b57fa055cd52f40d63f6bc617b7b35e389b2befa68f"],"state_sha256":"cc3846e9601cc90f604e5109b7846d6b647be56a9ca0a87303f0555f5f284159"}