{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7HK5ZDH3HKAPVTWZMX6FS4RXVV","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":"5ea57f5f10e91e4213e8f56e28afb78f8203e7223a8970f80258051e066cda1a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-28T16:19:04Z","title_canon_sha256":"f6291c471763f436a5f14bbe21023f5ab70a72ab3d58639843c0d271813c8bae"},"schema_version":"1.0","source":{"id":"1806.11058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.11058","created_at":"2026-05-17T23:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.11058v2","created_at":"2026-05-17T23:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11058","created_at":"2026-05-17T23:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"7HK5ZDH3HKAP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7HK5ZDH3HKAPVTWZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7HK5ZDH3","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:eb6e99788f2b80ededd6e58e6705874072aec33b2b7b97074e6d3c049d29867f","target":"graph","created_at":"2026-05-17T23:56:09Z","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 associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.","authors_text":"Daniel Alpay, Daniele C. Struppa, Ismael L. Paiva","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-28T16:19:04Z","title":"Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11058","kind":"arxiv","version":2},"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:ec9cbbfb440112bda84cb8527cb76abef887e10ab47da5279f7c4228af7f2c11","target":"record","created_at":"2026-05-17T23:56:09Z","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":"5ea57f5f10e91e4213e8f56e28afb78f8203e7223a8970f80258051e066cda1a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-06-28T16:19:04Z","title_canon_sha256":"f6291c471763f436a5f14bbe21023f5ab70a72ab3d58639843c0d271813c8bae"},"schema_version":"1.0","source":{"id":"1806.11058","kind":"arxiv","version":2}},"canonical_sha256":"f9d5dc8cfb3a80faced965fc597237ad56c0c1a15785c72d43ed62a6ce519ad3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9d5dc8cfb3a80faced965fc597237ad56c0c1a15785c72d43ed62a6ce519ad3","first_computed_at":"2026-05-17T23:56:09.850221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:09.850221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rujO72O+4pNoMCiwyPz91fSMhmo+GfAmu9X2yH1yuEJSNmiGwoqhHqZfDZjPkH5Gv8iOkxW4spS4QbFrYOBbCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:09.850956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.11058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec9cbbfb440112bda84cb8527cb76abef887e10ab47da5279f7c4228af7f2c11","sha256:eb6e99788f2b80ededd6e58e6705874072aec33b2b7b97074e6d3c049d29867f"],"state_sha256":"a1b294ce5b46a5bdc26bd485a8b768ce107d4dfebdbc7fdb6ef81bb006b5c8a5"}