{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SED37HU3BAJ2JR3ODCOVTB4SGM","short_pith_number":"pith:SED37HU3","canonical_record":{"source":{"id":"2605.14743","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.SI","submitted_at":"2026-05-14T12:11:03Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"c6034f5bf4b206ee426f2e06718420e77d7c16a0a9614bc583b2a725a44f4971","abstract_canon_sha256":"a79b92646cb217ac851de1838c59a619f4766f7d497a239cb9b03615a2009a86"},"schema_version":"1.0"},"canonical_sha256":"9107bf9e9b0813a4c76e189d598792333111a4316faead705ecf743b11c6751d","source":{"kind":"arxiv","id":"2605.14743","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14743","created_at":"2026-05-17T23:38:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14743v1","created_at":"2026-05-17T23:38:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14743","created_at":"2026-05-17T23:38:58Z"},{"alias_kind":"pith_short_12","alias_value":"SED37HU3BAJ2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"SED37HU3BAJ2JR3O","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"SED37HU3","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SED37HU3BAJ2JR3ODCOVTB4SGM","target":"record","payload":{"canonical_record":{"source":{"id":"2605.14743","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.SI","submitted_at":"2026-05-14T12:11:03Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"c6034f5bf4b206ee426f2e06718420e77d7c16a0a9614bc583b2a725a44f4971","abstract_canon_sha256":"a79b92646cb217ac851de1838c59a619f4766f7d497a239cb9b03615a2009a86"},"schema_version":"1.0"},"canonical_sha256":"9107bf9e9b0813a4c76e189d598792333111a4316faead705ecf743b11c6751d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:58.919965Z","signature_b64":"zJg1NR+BhdN05Pl+fmxB6+alhI9XKxZBQKDp2+/7sPH8Ssmk+noDvC7U0z+FoaHFG66QOp8wgZeJ7P0rcKBvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9107bf9e9b0813a4c76e189d598792333111a4316faead705ecf743b11c6751d","last_reissued_at":"2026-05-17T23:38:58.919328Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:58.919328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.14743","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":"2026-05-17T23:38:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lMfdkDVIybmr6j2Ow09uD2/WPUoL1Yc7SVQFS+8oNiHrmhzlMjE9Di91bqQ+mCZVXpq2gE7YnYsROogfaOeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:47:09.062413Z"},"content_sha256":"0bacac895c0a3db36dfa0293db312ae3ddeb1c163e3446bcf6ac58dbc8f94821","schema_version":"1.0","event_id":"sha256:0bacac895c0a3db36dfa0293db312ae3ddeb1c163e3446bcf6ac58dbc8f94821"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SED37HU3BAJ2JR3ODCOVTB4SGM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Betweenness Central Nodes Under Uncertainty: An Absorbing Markov Chain Approach","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SI","authors_text":"Chrysafis Vogiatzis, Eleftheria Kontou, Wencheng Bao","submitted_at":"2026-05-14T12:11:03Z","abstract_excerpt":"We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This produces a way to study centrality under uncertainty, which can then be estimated with Monte Carlo simulation. We also analyze robustness when the transition kernel is only approximately known, using row-wise perturbations to assess sensitivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14743","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":"2026-05-17T23:38:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqCb73obOkcAznYVnvibbaCPFdfkl1NFJ4f8sUDR6y8KP6FlnkxqPgc3Pg7YyrD9FsAphffCQpQ7ihVDPwGYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:47:09.062763Z"},"content_sha256":"3c7aec30361737227384bb78f1d521e4dd8da4814838f69ee4c5012737cfa306","schema_version":"1.0","event_id":"sha256:3c7aec30361737227384bb78f1d521e4dd8da4814838f69ee4c5012737cfa306"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SED37HU3BAJ2JR3ODCOVTB4SGM/bundle.json","state_url":"https://pith.science/pith/SED37HU3BAJ2JR3ODCOVTB4SGM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SED37HU3BAJ2JR3ODCOVTB4SGM/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":"2026-06-04T10:47:09Z","links":{"resolver":"https://pith.science/pith/SED37HU3BAJ2JR3ODCOVTB4SGM","bundle":"https://pith.science/pith/SED37HU3BAJ2JR3ODCOVTB4SGM/bundle.json","state":"https://pith.science/pith/SED37HU3BAJ2JR3ODCOVTB4SGM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SED37HU3BAJ2JR3ODCOVTB4SGM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SED37HU3BAJ2JR3ODCOVTB4SGM","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":"a79b92646cb217ac851de1838c59a619f4766f7d497a239cb9b03615a2009a86","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.SI","submitted_at":"2026-05-14T12:11:03Z","title_canon_sha256":"c6034f5bf4b206ee426f2e06718420e77d7c16a0a9614bc583b2a725a44f4971"},"schema_version":"1.0","source":{"id":"2605.14743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14743","created_at":"2026-05-17T23:38:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14743v1","created_at":"2026-05-17T23:38:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14743","created_at":"2026-05-17T23:38:58Z"},{"alias_kind":"pith_short_12","alias_value":"SED37HU3BAJ2","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"SED37HU3BAJ2JR3O","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"SED37HU3","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:3c7aec30361737227384bb78f1d521e4dd8da4814838f69ee4c5012737cfa306","target":"graph","created_at":"2026-05-17T23:38:58Z","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 a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This produces a way to study centrality under uncertainty, which can then be estimated with Monte Carlo simulation. We also analyze robustness when the transition kernel is only approximately known, using row-wise perturbations to assess sensitivi","authors_text":"Chrysafis Vogiatzis, Eleftheria Kontou, Wencheng Bao","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.SI","submitted_at":"2026-05-14T12:11:03Z","title":"Betweenness Central Nodes Under Uncertainty: An Absorbing Markov Chain Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14743","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":"sha256:0bacac895c0a3db36dfa0293db312ae3ddeb1c163e3446bcf6ac58dbc8f94821","target":"record","created_at":"2026-05-17T23:38:58Z","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":"a79b92646cb217ac851de1838c59a619f4766f7d497a239cb9b03615a2009a86","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.SI","submitted_at":"2026-05-14T12:11:03Z","title_canon_sha256":"c6034f5bf4b206ee426f2e06718420e77d7c16a0a9614bc583b2a725a44f4971"},"schema_version":"1.0","source":{"id":"2605.14743","kind":"arxiv","version":1}},"canonical_sha256":"9107bf9e9b0813a4c76e189d598792333111a4316faead705ecf743b11c6751d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9107bf9e9b0813a4c76e189d598792333111a4316faead705ecf743b11c6751d","first_computed_at":"2026-05-17T23:38:58.919328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:38:58.919328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zJg1NR+BhdN05Pl+fmxB6+alhI9XKxZBQKDp2+/7sPH8Ssmk+noDvC7U0z+FoaHFG66QOp8wgZeJ7P0rcKBvBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:38:58.919965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bacac895c0a3db36dfa0293db312ae3ddeb1c163e3446bcf6ac58dbc8f94821","sha256:3c7aec30361737227384bb78f1d521e4dd8da4814838f69ee4c5012737cfa306"],"state_sha256":"2839caa8f907a428e38d04a123aa05f0b950900ecdfc96577ed88fa000683993"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wUGykKBjZ9df4PQNEOMtmkPHLGhsk9o89d2O4cMhLwTeKFPrTG22nkJ6SsXRe3QQyP71/495TGYSsAbiHyJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:47:09.064772Z","bundle_sha256":"656036cb3f48b2ba71db0249c1a752b2a2c451aa3b61b3462d64d747b396b623"}}