{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IVEKLBE5MB3TB5HHHI65OSRNTD","short_pith_number":"pith:IVEKLBE5","canonical_record":{"source":{"id":"1507.04143","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2015-07-15T09:52:00Z","cross_cats_sorted":[],"title_canon_sha256":"21697210034723a93db8b351cea971bb78721e6f75735f0abb0cc152ad34c6dc","abstract_canon_sha256":"49e8f7ccc20dd6331ad5efa68990c936a27ab188f409e4bacb489c16ed10b1e3"},"schema_version":"1.0"},"canonical_sha256":"4548a5849d607730f4e73a3dd74a2d98cae070436a3b45b46813167a92b022f7","source":{"kind":"arxiv","id":"1507.04143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04143","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04143v1","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04143","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"IVEKLBE5MB3T","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IVEKLBE5MB3TB5HH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IVEKLBE5","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IVEKLBE5MB3TB5HHHI65OSRNTD","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04143","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2015-07-15T09:52:00Z","cross_cats_sorted":[],"title_canon_sha256":"21697210034723a93db8b351cea971bb78721e6f75735f0abb0cc152ad34c6dc","abstract_canon_sha256":"49e8f7ccc20dd6331ad5efa68990c936a27ab188f409e4bacb489c16ed10b1e3"},"schema_version":"1.0"},"canonical_sha256":"4548a5849d607730f4e73a3dd74a2d98cae070436a3b45b46813167a92b022f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:49.009927Z","signature_b64":"rKbl4QsiGYflM/ru09vDwAp0Ms+Lw4EkOasT1IB/XZIECeGpuO5N0VqGRXyl+z3UEdFMm9xMWI0NxLlAlmTsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4548a5849d607730f4e73a3dd74a2d98cae070436a3b45b46813167a92b022f7","last_reissued_at":"2026-05-18T01:36:49.009296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:49.009296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04143","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":"2026-05-18T01:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWwt3jKyD2TZ428C9E+BG5C6JkEZArewelPbtLAikTemvcD/Dbx7VixaCguhKKxjYzMQNk31Y27K33ZqM5zVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:48:18.246608Z"},"content_sha256":"fd3190d45aec40cc531f0f35a92ff496f1174681822aeb5747c391c6e2927ced","schema_version":"1.0","event_id":"sha256:fd3190d45aec40cc531f0f35a92ff496f1174681822aeb5747c391c6e2927ced"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IVEKLBE5MB3TB5HHHI65OSRNTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Shock Model Based Approach to Network Reliability","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"M. Asadi, S. Ashrafi, S. Zarezadeh","submitted_at":"2015-07-15T09:52:00Z","abstract_excerpt":"We consider a network consisting of $n$ components (links or nodes) and assume that the network has two states, up and down. We further suppose that the network is subject to shocks that appear according to a counting process and that each shock may lead to the component failures. Under some assumptions on the shock occurrences, we present a new variant of the notion of signature which we call it t-signature. Then t-signature based mixture representations for the reliability function of the network are obtained. Several stochastic properties of the network lifetime are investigated. In particu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04143","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":"2026-05-18T01:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPGYl4JOP3TGf59ziaDf7ghm7/jlNX3kligDkjmjX/tFCygrjwouKgdB2wMST6QdrkKSa7t7XfTdA2J60TQBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:48:18.247186Z"},"content_sha256":"b71f1c59c2e9f2c09a89eec3477b889f285741b16bafc2f7012ef9a8b22587c3","schema_version":"1.0","event_id":"sha256:b71f1c59c2e9f2c09a89eec3477b889f285741b16bafc2f7012ef9a8b22587c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVEKLBE5MB3TB5HHHI65OSRNTD/bundle.json","state_url":"https://pith.science/pith/IVEKLBE5MB3TB5HHHI65OSRNTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVEKLBE5MB3TB5HHHI65OSRNTD/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":"2026-06-05T18:48:18Z","links":{"resolver":"https://pith.science/pith/IVEKLBE5MB3TB5HHHI65OSRNTD","bundle":"https://pith.science/pith/IVEKLBE5MB3TB5HHHI65OSRNTD/bundle.json","state":"https://pith.science/pith/IVEKLBE5MB3TB5HHHI65OSRNTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVEKLBE5MB3TB5HHHI65OSRNTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IVEKLBE5MB3TB5HHHI65OSRNTD","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":"49e8f7ccc20dd6331ad5efa68990c936a27ab188f409e4bacb489c16ed10b1e3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2015-07-15T09:52:00Z","title_canon_sha256":"21697210034723a93db8b351cea971bb78721e6f75735f0abb0cc152ad34c6dc"},"schema_version":"1.0","source":{"id":"1507.04143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04143","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04143v1","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04143","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"IVEKLBE5MB3T","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IVEKLBE5MB3TB5HH","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IVEKLBE5","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:b71f1c59c2e9f2c09a89eec3477b889f285741b16bafc2f7012ef9a8b22587c3","target":"graph","created_at":"2026-05-18T01:36:49Z","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":"We consider a network consisting of $n$ components (links or nodes) and assume that the network has two states, up and down. We further suppose that the network is subject to shocks that appear according to a counting process and that each shock may lead to the component failures. Under some assumptions on the shock occurrences, we present a new variant of the notion of signature which we call it t-signature. Then t-signature based mixture representations for the reliability function of the network are obtained. Several stochastic properties of the network lifetime are investigated. In particu","authors_text":"M. Asadi, S. Ashrafi, S. Zarezadeh","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2015-07-15T09:52:00Z","title":"A Shock Model Based Approach to Network Reliability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04143","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:fd3190d45aec40cc531f0f35a92ff496f1174681822aeb5747c391c6e2927ced","target":"record","created_at":"2026-05-18T01:36:49Z","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":"49e8f7ccc20dd6331ad5efa68990c936a27ab188f409e4bacb489c16ed10b1e3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"stat.AP","submitted_at":"2015-07-15T09:52:00Z","title_canon_sha256":"21697210034723a93db8b351cea971bb78721e6f75735f0abb0cc152ad34c6dc"},"schema_version":"1.0","source":{"id":"1507.04143","kind":"arxiv","version":1}},"canonical_sha256":"4548a5849d607730f4e73a3dd74a2d98cae070436a3b45b46813167a92b022f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4548a5849d607730f4e73a3dd74a2d98cae070436a3b45b46813167a92b022f7","first_computed_at":"2026-05-18T01:36:49.009296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:49.009296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rKbl4QsiGYflM/ru09vDwAp0Ms+Lw4EkOasT1IB/XZIECeGpuO5N0VqGRXyl+z3UEdFMm9xMWI0NxLlAlmTsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:49.009927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd3190d45aec40cc531f0f35a92ff496f1174681822aeb5747c391c6e2927ced","sha256:b71f1c59c2e9f2c09a89eec3477b889f285741b16bafc2f7012ef9a8b22587c3"],"state_sha256":"23843bc08341d35f550554a3c162afa0f44f85abc9f7cfc7f373d66b6fabe3ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMT/We/NVkH2TpC93a3ocFLWkWNQXWQTuE9zdGcNRjWdI8/9jHpkbUuUgXGuBazPVaoCSZklfUfvgJZEAEKPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:48:18.250260Z","bundle_sha256":"650c6f1b5e48b2486fb51a204e7064216984408f8b7b30dc8843af8071a6394a"}}