{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7RIGF7NH5CYOIJNRA3JIYFNV2B","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":"2a2e7fcfc1419f9076e0c7c223edb43bf264a3eb7b409fdf545deb603c9745e3","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-25T18:56:58Z","title_canon_sha256":"c1cec9c7c5526636309419e6fd241929596388c29652d7d262d13125a1028fcc"},"schema_version":"1.0","source":{"id":"1406.6664","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6664","created_at":"2026-05-18T02:45:13Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6664v3","created_at":"2026-05-18T02:45:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6664","created_at":"2026-05-18T02:45:13Z"},{"alias_kind":"pith_short_12","alias_value":"7RIGF7NH5CYO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7RIGF7NH5CYOIJNR","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7RIGF7NH","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:e32e350e37068de155737b711273b6655f8ce801eaffcdb6bc19bea12c2b7410","target":"graph","created_at":"2026-05-18T02:45:13Z","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 show that any matrix-polynomial combination of free noncommutative random variables each having an algebraic law has again an algebraic law. Our result answers a question raised by a recent paper of Shlyakhtenko and Skoufranis. The result belongs to a family of results with origins outside free probability theory, including a result of Aomoto asserting algebraicity of the Green function of random walk of quite general type on a free group.","authors_text":"Greg W. Anderson","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-25T18:56:58Z","title":"Preservation of algebraicity in free probability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6664","kind":"arxiv","version":3},"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:e4a38f271dd58c9a06e8bdfbf48ad270dd142550cdb7d3fabb26e9af79b34653","target":"record","created_at":"2026-05-18T02:45:13Z","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":"2a2e7fcfc1419f9076e0c7c223edb43bf264a3eb7b409fdf545deb603c9745e3","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-25T18:56:58Z","title_canon_sha256":"c1cec9c7c5526636309419e6fd241929596388c29652d7d262d13125a1028fcc"},"schema_version":"1.0","source":{"id":"1406.6664","kind":"arxiv","version":3}},"canonical_sha256":"fc5062fda7e8b0e425b106d28c15b5d0423cbb406826084cefbf26b9190c7d59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc5062fda7e8b0e425b106d28c15b5d0423cbb406826084cefbf26b9190c7d59","first_computed_at":"2026-05-18T02:45:13.964246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:13.964246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+LIShrxMnsIagANJtiaoE+9r3WezUx8lQi7aQQHoenZP8H9sc4wQ+I8p9QLCghxJR0T2CYZhOg3NONqtrgsZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:13.964871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6664","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4a38f271dd58c9a06e8bdfbf48ad270dd142550cdb7d3fabb26e9af79b34653","sha256:e32e350e37068de155737b711273b6655f8ce801eaffcdb6bc19bea12c2b7410"],"state_sha256":"0f0749ceb09ed87a87ab32ec584f6a2adde8376e01d69d1526d1e7121b90c3c2"}