{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GZXPNFM2ZU2TRH5EMROYVYSUNY","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":"d34becfa5f14f9cc532d315b0413d9762175dad1d751a3b29f55faaa13f7693c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T10:49:09Z","title_canon_sha256":"cc253599b539c9bd3847a0efaa71404537fdc5b7386409eaf36561828bcb7075"},"schema_version":"1.0","source":{"id":"1412.1613","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1613","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1613v3","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1613","created_at":"2026-05-18T00:40:41Z"},{"alias_kind":"pith_short_12","alias_value":"GZXPNFM2ZU2T","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZXPNFM2ZU2TRH5E","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZXPNFM2","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:c27cb2556a1febb4470ec539fd8d0f55a3f22f5c2619ca01a81d8d8615b1ad2c","target":"graph","created_at":"2026-05-18T00:40:41Z","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":"The structure signature of a system made up of $n$ components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the $n$-tuple whose $k$-th coordinate is the probability that the $k$-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order $n$ whose $(k,l)$-entry is the probability that the $k$-th failure causes the first system to fail and th","authors_text":"Christian Paroissin, Jean-Luc Marichal, Jorge Navarro, Pierre Mathonet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T10:49:09Z","title":"Joint signature of two or more systems with applications to multistate systems made up of two-state components"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1613","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:e26b59a4f7cc06290adacefa8c4a4f52aca9108ec0368e93190978f3c10ee74a","target":"record","created_at":"2026-05-18T00:40:41Z","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":"d34becfa5f14f9cc532d315b0413d9762175dad1d751a3b29f55faaa13f7693c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-04T10:49:09Z","title_canon_sha256":"cc253599b539c9bd3847a0efaa71404537fdc5b7386409eaf36561828bcb7075"},"schema_version":"1.0","source":{"id":"1412.1613","kind":"arxiv","version":3}},"canonical_sha256":"366ef6959acd35389fa4645d8ae2546e2e56d62c98c9e919a90f74a207187d8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"366ef6959acd35389fa4645d8ae2546e2e56d62c98c9e919a90f74a207187d8b","first_computed_at":"2026-05-18T00:40:41.949381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:41.949381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPRfEMa8GvoN5QPWvmkPtuAjEeNy5RIG0Xb3bAaycyx8can75/yeFgssfBogUOLMyv1sTVUmE7ddHKYQ6ijoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:41.950100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1613","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e26b59a4f7cc06290adacefa8c4a4f52aca9108ec0368e93190978f3c10ee74a","sha256:c27cb2556a1febb4470ec539fd8d0f55a3f22f5c2619ca01a81d8d8615b1ad2c"],"state_sha256":"b10ca02514634e74462b4e14e224bec6f12f4e216ff0fec83054d2855c0599db"}