{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BAOGGVQ7IECRQI3UK4SG6TLCHZ","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":"29da46f916e1180528d2c2e87a2da6e632fc486350119fd60460b197e29e3ac9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:04:28Z","title_canon_sha256":"c814213281914dffdd139c1c34730f1cf6d3236aa5b778d2ee6ceb9bea7c32bb"},"schema_version":"1.0","source":{"id":"1511.05172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05172","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05172v1","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05172","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"BAOGGVQ7IECR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BAOGGVQ7IECRQI3U","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BAOGGVQ7","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:e8e0fa13b4a6c3d49c54c3f9ae99b9ada4dc05d8e6e06bf7a912f7b27716320b","target":"graph","created_at":"2026-05-18T01:26:49Z","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":"An $\\al$-permanental process $\\{X_{ t},t\\in T \\}$ is a stochastic process determined by a kernel $K=\\{K(s,t),s,t\\in T \\}$, with the property that for all $t_{1},\\ldots,t_{n}\\in T $, $ |I+K( t_{1},\\ldots,t_{n}) S|^{- \\al} $ is the Laplace transform of $(X_{t_{1}},\\ldots,X_{t_{n}})$, where $ K( t_{1},\\ldots,t_{n})$ denotes the matrix $\\{K(t_{i}, t_{j})\\}_{i,j=1}^{n}$ and $S$ is the diagonal matrix with entries $s_{1},\\ldots,s_{n} $. $ (X_{t_{1}},\\ldots,X_{t_{n}})$ is called a permanental vector.\n  Under the condition that $K$ is the potential density of a transient Markov process,\n  $(X_{t_{1}},","authors_text":"Jay Rosen, Michael B. Marcus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:04:28Z","title":"Conditions for permanental processes to be unbounded"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05172","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:c8f42abf64889a97735a00cfd30f12babbcc0706295bd6eeb97850704904d1e1","target":"record","created_at":"2026-05-18T01:26:49Z","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":"29da46f916e1180528d2c2e87a2da6e632fc486350119fd60460b197e29e3ac9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-16T21:04:28Z","title_canon_sha256":"c814213281914dffdd139c1c34730f1cf6d3236aa5b778d2ee6ceb9bea7c32bb"},"schema_version":"1.0","source":{"id":"1511.05172","kind":"arxiv","version":1}},"canonical_sha256":"081c63561f410518237457246f4d623e67d5775d4579d45231fc0d55b56af654","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"081c63561f410518237457246f4d623e67d5775d4579d45231fc0d55b56af654","first_computed_at":"2026-05-18T01:26:49.884884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:49.884884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d7XJK5ztZgXd622ul4++sdGO+PM4AgdakMZVLreolKhFYa6/lXdo7v80zDNy0rAmrcGsDqLgVdcsN1TI7rm1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:49.885620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8f42abf64889a97735a00cfd30f12babbcc0706295bd6eeb97850704904d1e1","sha256:e8e0fa13b4a6c3d49c54c3f9ae99b9ada4dc05d8e6e06bf7a912f7b27716320b"],"state_sha256":"779a3b2dec32a5e31419482778084617d749b1d0fe2e7d08f69664b1fdd8be41"}