{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NT5ZX7SLCCCZFYNZ3WFGMGXE6W","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":"189376293ab6c694656bd9bd51a44006a1d4c5991239e53b4a30084f3e49eb4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-28T17:49:25Z","title_canon_sha256":"e3694bb316b35fe3e45ca50a0acc053aa96ca6798844ff555bee076d41534619"},"schema_version":"1.0","source":{"id":"1411.7952","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7952","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7952v3","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7952","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"NT5ZX7SLCCCZ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NT5ZX7SLCCCZFYNZ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NT5ZX7SL","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a1a25e91c4fc8a96d8351d2fb2111a67b17cfc38a1fdfe885897f4dcc904344d","target":"graph","created_at":"2026-05-18T01:12:36Z","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 propose Mecke-Palm formulas for multiple integrals with respect to a Poisson random measure interlaced with its intensity measure. We apply such formulas to multiple mixed L\\'evy systems of L\\'evy processes and obtain moment formulas for products of interlaced multiple Poisson integrals.","authors_text":"Grzegorz Serafin, Jan Rosi\\'nski, Krzysztof Bogdan, {\\L}ukasz Wojciechowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-28T17:49:25Z","title":"L\\'evy systems and moment formulas for mixed Poisson integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7952","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":"sha256:74d4f12d4b635e558135b27813cd9faf7f4070e5a91aa86ff856b4ea59553219","target":"record","created_at":"2026-05-18T01:12:36Z","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":"189376293ab6c694656bd9bd51a44006a1d4c5991239e53b4a30084f3e49eb4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-28T17:49:25Z","title_canon_sha256":"e3694bb316b35fe3e45ca50a0acc053aa96ca6798844ff555bee076d41534619"},"schema_version":"1.0","source":{"id":"1411.7952","kind":"arxiv","version":3}},"canonical_sha256":"6cfb9bfe4b108592e1b9dd8a661ae4f580b3176ac35061a912333568634ca292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cfb9bfe4b108592e1b9dd8a661ae4f580b3176ac35061a912333568634ca292","first_computed_at":"2026-05-18T01:12:36.492900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:36.492900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNRYGmx6RE9/FvqOb/7xgXZCciv3xhbt1Hjwu57cKxhf7opg6v4c4K2wtKuj9MCKfTTR8ALx9OxHjkxBtjzWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:36.493476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7952","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74d4f12d4b635e558135b27813cd9faf7f4070e5a91aa86ff856b4ea59553219","sha256:a1a25e91c4fc8a96d8351d2fb2111a67b17cfc38a1fdfe885897f4dcc904344d"],"state_sha256":"c48dd100dd139df5641e430fda9349e441f4b79a2e64c1334aa2153af52ce741"}