{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XUH2WVPFI3BMAUU4CC3ZQ6UVYJ","short_pith_number":"pith:XUH2WVPF","canonical_record":{"source":{"id":"1904.05335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-05T15:49:06Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"c99b28c4a71a2df7228c627b98d5b00a958bd37d7e5d7c11b1eb5d0f460d6800","abstract_canon_sha256":"f3a1f9da7df0aac87a84bfc8f3c13233849c6262da7dccbb620e92330c179098"},"schema_version":"1.0"},"canonical_sha256":"bd0fab55e546c2c0529c10b7987a95c27235813e1b33bfae22b0073cac9b7536","source":{"kind":"arxiv","id":"1904.05335","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05335","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05335v1","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05335","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"XUH2WVPFI3BM","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XUH2WVPFI3BMAUU4","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XUH2WVPF","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XUH2WVPFI3BMAUU4CC3ZQ6UVYJ","target":"record","payload":{"canonical_record":{"source":{"id":"1904.05335","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-05T15:49:06Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"c99b28c4a71a2df7228c627b98d5b00a958bd37d7e5d7c11b1eb5d0f460d6800","abstract_canon_sha256":"f3a1f9da7df0aac87a84bfc8f3c13233849c6262da7dccbb620e92330c179098"},"schema_version":"1.0"},"canonical_sha256":"bd0fab55e546c2c0529c10b7987a95c27235813e1b33bfae22b0073cac9b7536","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:53.442251Z","signature_b64":"CeINXEXPqmRGSxIBSu1OFWBabFpsAtD8VUz1Xzx1P7PAF/Y8AH+aCH+Izp6NTtSqFtvOa476bCH6E9Hp+WFqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd0fab55e546c2c0529c10b7987a95c27235813e1b33bfae22b0073cac9b7536","last_reissued_at":"2026-05-17T23:48:53.441693Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:53.441693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.05335","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":"2026-05-17T23:48:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWcNWD/br7RicNdH3AZ8natqajOObKAQD81gDV3AQae47grCvQLVetlPlyQgczsciOli3zqpeBIzo6kHM0MbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:28:20.501304Z"},"content_sha256":"0023f4ea157d12df79d691fcc6662db548edfad544f7f821e6bbf5bbe8035f99","schema_version":"1.0","event_id":"sha256:0023f4ea157d12df79d691fcc6662db548edfad544f7f821e6bbf5bbe8035f99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XUH2WVPFI3BMAUU4CC3ZQ6UVYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adapting Stochastic Block Models to Power-Law Degree Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.SI","authors_text":"Dacheng Tao, Jun Yu, Maoying Qiao, Qiang Li, Wei Bian","submitted_at":"2019-04-05T15:49:06Z","abstract_excerpt":"Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new variant of SBM, termed power-law degree SBM (PLD-SBM), by introducing degree decay variables to explicitly encode the varying degree distribution over all nodes. With an exponential prior, it is proved that PLD-SBM approximately preserves the scale-free feature in real networks. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05335","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":"2026-05-17T23:48:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kj0a5x0E7ppDrXJ6frBHnHHuGr1tJOcvI+v9w4uvFa53UjLhiaJm87YAfJL2G0j7ZaY9DeueF6LBHYNNJLdBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:28:20.502029Z"},"content_sha256":"256463bd73b7a6ef6694d3c5398c7afeb8e7db9da97e63099f307995fcb5fbe1","schema_version":"1.0","event_id":"sha256:256463bd73b7a6ef6694d3c5398c7afeb8e7db9da97e63099f307995fcb5fbe1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ/bundle.json","state_url":"https://pith.science/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ/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":"2026-05-30T19:28:20Z","links":{"resolver":"https://pith.science/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ","bundle":"https://pith.science/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ/bundle.json","state":"https://pith.science/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUH2WVPFI3BMAUU4CC3ZQ6UVYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XUH2WVPFI3BMAUU4CC3ZQ6UVYJ","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":"f3a1f9da7df0aac87a84bfc8f3c13233849c6262da7dccbb620e92330c179098","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-05T15:49:06Z","title_canon_sha256":"c99b28c4a71a2df7228c627b98d5b00a958bd37d7e5d7c11b1eb5d0f460d6800"},"schema_version":"1.0","source":{"id":"1904.05335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05335","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05335v1","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05335","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"XUH2WVPFI3BM","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XUH2WVPFI3BMAUU4","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XUH2WVPF","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:256463bd73b7a6ef6694d3c5398c7afeb8e7db9da97e63099f307995fcb5fbe1","target":"graph","created_at":"2026-05-17T23:48:53Z","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":"Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new variant of SBM, termed power-law degree SBM (PLD-SBM), by introducing degree decay variables to explicitly encode the varying degree distribution over all nodes. With an exponential prior, it is proved that PLD-SBM approximately preserves the scale-free feature in real networks. In ","authors_text":"Dacheng Tao, Jun Yu, Maoying Qiao, Qiang Li, Wei Bian","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-05T15:49:06Z","title":"Adapting Stochastic Block Models to Power-Law Degree Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05335","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":"sha256:0023f4ea157d12df79d691fcc6662db548edfad544f7f821e6bbf5bbe8035f99","target":"record","created_at":"2026-05-17T23:48:53Z","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":"f3a1f9da7df0aac87a84bfc8f3c13233849c6262da7dccbb620e92330c179098","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-05T15:49:06Z","title_canon_sha256":"c99b28c4a71a2df7228c627b98d5b00a958bd37d7e5d7c11b1eb5d0f460d6800"},"schema_version":"1.0","source":{"id":"1904.05335","kind":"arxiv","version":1}},"canonical_sha256":"bd0fab55e546c2c0529c10b7987a95c27235813e1b33bfae22b0073cac9b7536","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd0fab55e546c2c0529c10b7987a95c27235813e1b33bfae22b0073cac9b7536","first_computed_at":"2026-05-17T23:48:53.441693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:53.441693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CeINXEXPqmRGSxIBSu1OFWBabFpsAtD8VUz1Xzx1P7PAF/Y8AH+aCH+Izp6NTtSqFtvOa476bCH6E9Hp+WFqDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:53.442251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.05335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0023f4ea157d12df79d691fcc6662db548edfad544f7f821e6bbf5bbe8035f99","sha256:256463bd73b7a6ef6694d3c5398c7afeb8e7db9da97e63099f307995fcb5fbe1"],"state_sha256":"b9d2f111518bbe7e847e4acd6da528f6abcba2b808fb935f9dd63711064b44e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZddeq31HMKxRc0g/hqUI5yPgCGrmphl2eDFDwS+eczMx0TpMnNjrnyQgUppvQjTTKPsdcIRaIuoid8p0kIlDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:28:20.519183Z","bundle_sha256":"857f67664a540e02d56ad0942a1a5e901341644e4fcf5b80b346534350b05ee4"}}