{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HR2OTBVPDSJPWLI3IL7YWXJAJB","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":"2c53655d79c9826a4ff8049544377507e4edf5df34f93fa72b8efb3713823a76","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T13:26:11Z","title_canon_sha256":"34be894c0797127f0468ceb39d5b1136de8ae672e7da368f6d6df905c6bde5a1"},"schema_version":"1.0","source":{"id":"1310.0701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0701","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0701v1","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0701","created_at":"2026-05-18T02:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"HR2OTBVPDSJP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HR2OTBVPDSJPWLI3","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HR2OTBVP","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:1990fc95f2505abe08fd7138fc9c83253783605104d42e3c8fcf0ea840f8852e","target":"graph","created_at":"2026-05-18T02:28:31Z","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 investigate positive definiteness of the Brownian kernel K(x,y)=1/2(d(x,x_0) + d(y,x_0) - d(x,y)) on a compact group G and in particular for G=SO(n).","authors_text":"Maurizia Rossi, Paolo Baldi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T13:26:11Z","title":"On L\\'evy's Brownian motion indexed by the elements of compact groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0701","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":"sha256:588f6cdd99cb6dd7ceca826649636298f061993d70c0536eac2b0f7613c95973","target":"record","created_at":"2026-05-18T02:28:31Z","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":"2c53655d79c9826a4ff8049544377507e4edf5df34f93fa72b8efb3713823a76","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-02T13:26:11Z","title_canon_sha256":"34be894c0797127f0468ceb39d5b1136de8ae672e7da368f6d6df905c6bde5a1"},"schema_version":"1.0","source":{"id":"1310.0701","kind":"arxiv","version":1}},"canonical_sha256":"3c74e986af1c92fb2d1b42ff8b5d2048745a9db7a396abfbe0336b54bc9c94cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c74e986af1c92fb2d1b42ff8b5d2048745a9db7a396abfbe0336b54bc9c94cb","first_computed_at":"2026-05-18T02:28:31.986953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:31.986953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZLzHXY2O1U32ubzB4elQQfNHO6WLaiv6hTEgd72KlSqh/7FEBHwQnsIiNGdQEYoXnDeIP02FwQjSRFyd6dAGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:31.987605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:588f6cdd99cb6dd7ceca826649636298f061993d70c0536eac2b0f7613c95973","sha256:1990fc95f2505abe08fd7138fc9c83253783605104d42e3c8fcf0ea840f8852e"],"state_sha256":"86928cecd27e50066ab19f957274d4896301bd9497ec128d0e1fe25dc37cfd28"}