{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OOEPLZ3U7I7WQ32OOB4ONIZJSC","short_pith_number":"pith:OOEPLZ3U","canonical_record":{"source":{"id":"1604.06152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-21T01:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"07185616a5da556272e28112be92fd307354b55380f3f8ef6ec57fe6f777a528","abstract_canon_sha256":"69c3663afde8c9667aeb9d069fd9958e42e1ce68f106497547065fadbce750c4"},"schema_version":"1.0"},"canonical_sha256":"7388f5e774fa3f686f4e7078e6a32990be6160ca1404c26ff142c2be39f469e3","source":{"kind":"arxiv","id":"1604.06152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06152","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06152v1","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06152","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"OOEPLZ3U7I7W","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OOEPLZ3U7I7WQ32O","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OOEPLZ3U","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OOEPLZ3U7I7WQ32OOB4ONIZJSC","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-21T01:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"07185616a5da556272e28112be92fd307354b55380f3f8ef6ec57fe6f777a528","abstract_canon_sha256":"69c3663afde8c9667aeb9d069fd9958e42e1ce68f106497547065fadbce750c4"},"schema_version":"1.0"},"canonical_sha256":"7388f5e774fa3f686f4e7078e6a32990be6160ca1404c26ff142c2be39f469e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:32.482803Z","signature_b64":"6JMcWF6fHnAkZm3DVGxeajwHELW6++r8BcHUfodrhpTIxNSR8FHu7XRAgyjwf/InWm0eVH8ofVQgwCzodjwMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7388f5e774fa3f686f4e7078e6a32990be6160ca1404c26ff142c2be39f469e3","last_reissued_at":"2026-05-18T01:16:32.482076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:32.482076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06152","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"738XRkCNV2MajQVDVvXSlL/jPwClVekVKF+LAquM6NRxMbbTW837hCOVpgQP/uu9Nl/9UTT6JzZ0ltAmQWZsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:13:51.755627Z"},"content_sha256":"839b76d43aa6ae1595511d3711216cf64188ae9a21a96739c9c07f473bd1abe4","schema_version":"1.0","event_id":"sha256:839b76d43aa6ae1595511d3711216cf64188ae9a21a96739c9c07f473bd1abe4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OOEPLZ3U7I7WQ32OOB4ONIZJSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Permanental random variables, ${M}$-matrices and $\\alpha$-permanents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jay Rosen, Michael B. Marcus","submitted_at":"2016-04-21T01:15:03Z","abstract_excerpt":"We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06152","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOy/TSMMC8RAjXijDf6GooTiktR53eCdtBMN7Lcawe2Q0X8JAFaRPm/x+FKoiwkTcYpiBQUvz5eIVsHcSY1BDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:13:51.755983Z"},"content_sha256":"93d72759ee680bcb7f172a742101669847dfa63e26e18d45dd35135ff44cab8e","schema_version":"1.0","event_id":"sha256:93d72759ee680bcb7f172a742101669847dfa63e26e18d45dd35135ff44cab8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC/bundle.json","state_url":"https://pith.science/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T15:13:51Z","links":{"resolver":"https://pith.science/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC","bundle":"https://pith.science/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC/bundle.json","state":"https://pith.science/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOEPLZ3U7I7WQ32OOB4ONIZJSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OOEPLZ3U7I7WQ32OOB4ONIZJSC","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":"69c3663afde8c9667aeb9d069fd9958e42e1ce68f106497547065fadbce750c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-21T01:15:03Z","title_canon_sha256":"07185616a5da556272e28112be92fd307354b55380f3f8ef6ec57fe6f777a528"},"schema_version":"1.0","source":{"id":"1604.06152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06152","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06152v1","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06152","created_at":"2026-05-18T01:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"OOEPLZ3U7I7W","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OOEPLZ3U7I7WQ32O","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OOEPLZ3U","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:93d72759ee680bcb7f172a742101669847dfa63e26e18d45dd35135ff44cab8e","target":"graph","created_at":"2026-05-18T01:16:32Z","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 explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.","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":"2016-04-21T01:15:03Z","title":"Permanental random variables, ${M}$-matrices and $\\alpha$-permanents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06152","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":"sha256:839b76d43aa6ae1595511d3711216cf64188ae9a21a96739c9c07f473bd1abe4","target":"record","created_at":"2026-05-18T01:16:32Z","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":"69c3663afde8c9667aeb9d069fd9958e42e1ce68f106497547065fadbce750c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-04-21T01:15:03Z","title_canon_sha256":"07185616a5da556272e28112be92fd307354b55380f3f8ef6ec57fe6f777a528"},"schema_version":"1.0","source":{"id":"1604.06152","kind":"arxiv","version":1}},"canonical_sha256":"7388f5e774fa3f686f4e7078e6a32990be6160ca1404c26ff142c2be39f469e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7388f5e774fa3f686f4e7078e6a32990be6160ca1404c26ff142c2be39f469e3","first_computed_at":"2026-05-18T01:16:32.482076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:32.482076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6JMcWF6fHnAkZm3DVGxeajwHELW6++r8BcHUfodrhpTIxNSR8FHu7XRAgyjwf/InWm0eVH8ofVQgwCzodjwMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:32.482803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:839b76d43aa6ae1595511d3711216cf64188ae9a21a96739c9c07f473bd1abe4","sha256:93d72759ee680bcb7f172a742101669847dfa63e26e18d45dd35135ff44cab8e"],"state_sha256":"78f0d7f29069169896d5743ec9a6e12f34b95278d03056119151adf5433cbfbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wU45zpoTM12jw1gQAZQV1sqVci/vc11V+cZYRxXPJ4+SHmCU0HBsNECRloaD33QNAgFEetBBT/kuI1CiIPsRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T15:13:51.758201Z","bundle_sha256":"149dd5ecf85642a4c1741f9801a642ee0e2ca4ded6205c13360d29935dad93cb"}}