{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OYIVULTU5WL56WAKJYUOK5K3I2","short_pith_number":"pith:OYIVULTU","canonical_record":{"source":{"id":"2506.07224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-08T17:17:41Z","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"title_canon_sha256":"f9de95bf30052dd9bff5be32e1c2b0f3c49a8f8af9928434d4454b6b532e392e","abstract_canon_sha256":"f27fd88e3e0bed4927e19463dde5863a671257c4d0c406a741c5844a897aebb4"},"schema_version":"1.0"},"canonical_sha256":"76115a2e74ed97df580a4e28e5755b468388e2bacd9d07a3135761ffaed66ef8","source":{"kind":"arxiv","id":"2506.07224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07224","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07224v1","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07224","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"OYIVULTU5WL5","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"pith_short_16","alias_value":"OYIVULTU5WL56WAK","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"pith_short_8","alias_value":"OYIVULTU","created_at":"2026-07-05T11:18:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OYIVULTU5WL56WAKJYUOK5K3I2","target":"record","payload":{"canonical_record":{"source":{"id":"2506.07224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-08T17:17:41Z","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"title_canon_sha256":"f9de95bf30052dd9bff5be32e1c2b0f3c49a8f8af9928434d4454b6b532e392e","abstract_canon_sha256":"f27fd88e3e0bed4927e19463dde5863a671257c4d0c406a741c5844a897aebb4"},"schema_version":"1.0"},"canonical_sha256":"76115a2e74ed97df580a4e28e5755b468388e2bacd9d07a3135761ffaed66ef8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:03.804774Z","signature_b64":"gRk2GtrKt+24cD0PXhz+BimX2M2OoXoKR9Ms85DkckAh5huGgNm4mjafmSEt/eobqJg9eA/A4bORk0p7/hhtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76115a2e74ed97df580a4e28e5755b468388e2bacd9d07a3135761ffaed66ef8","last_reissued_at":"2026-07-05T11:18:03.804279Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:03.804279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.07224","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":"2026-07-05T11:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7c1zoOGNrZOuXhVfxD1ePNdvC0B+18/L6Vv9S5Lv+RnxhTWbHoA2t4q2mi5xOHuFxAyqvr2qhJy7wkx1OTrlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:35:25.723231Z"},"content_sha256":"b762ab31336bc408c64978a28e5d7d70f09a18fa761dc2d03a75af26cd1578a9","schema_version":"1.0","event_id":"sha256:b762ab31336bc408c64978a28e5d7d70f09a18fa761dc2d03a75af26cd1578a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OYIVULTU5WL56WAKJYUOK5K3I2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly Consistent Community Detection in Popularity Adjusted Block Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ML","stat.TH"],"primary_cat":"stat.ME","authors_text":"Binghui Liu, Danning Li, Lingzhou Xue, Quan Yuan","submitted_at":"2025-06-08T17:17:41Z","abstract_excerpt":"The Popularity Adjusted Block Model (PABM) provides a flexible framework for community detection in network data by allowing heterogeneous node popularity across communities. However, this flexibility increases model complexity and raises key unresolved challenges, particularly in effectively adapting spectral clustering techniques and efficiently achieving strong consistency in label recovery. To address these challenges, we first propose the Thresholded Cosine Spectral Clustering (TCSC) algorithm and establish its weak consistency under the PABM. We then introduce the one-step Refined TCSC a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07224","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KBu84Vw7akZTd8qabq4KYd/kjF0hYmIgWdmhWFpFMQB2PjmTUWnBm7/s3yXdCqOMU4V+YyUcdL3wnEQgBb7QBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T22:35:25.723770Z"},"content_sha256":"3227dbe00d11727a53c2f037159b067ab4cc7302aeb4fd8f5f7eee8d112d130e","schema_version":"1.0","event_id":"sha256:3227dbe00d11727a53c2f037159b067ab4cc7302aeb4fd8f5f7eee8d112d130e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYIVULTU5WL56WAKJYUOK5K3I2/bundle.json","state_url":"https://pith.science/pith/OYIVULTU5WL56WAKJYUOK5K3I2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYIVULTU5WL56WAKJYUOK5K3I2/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":"2026-08-04T22:35:25Z","links":{"resolver":"https://pith.science/pith/OYIVULTU5WL56WAKJYUOK5K3I2","bundle":"https://pith.science/pith/OYIVULTU5WL56WAKJYUOK5K3I2/bundle.json","state":"https://pith.science/pith/OYIVULTU5WL56WAKJYUOK5K3I2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYIVULTU5WL56WAKJYUOK5K3I2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OYIVULTU5WL56WAKJYUOK5K3I2","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":"f27fd88e3e0bed4927e19463dde5863a671257c4d0c406a741c5844a897aebb4","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-08T17:17:41Z","title_canon_sha256":"f9de95bf30052dd9bff5be32e1c2b0f3c49a8f8af9928434d4454b6b532e392e"},"schema_version":"1.0","source":{"id":"2506.07224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.07224","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"2506.07224v1","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07224","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"OYIVULTU5WL5","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"pith_short_16","alias_value":"OYIVULTU5WL56WAK","created_at":"2026-07-05T11:18:03Z"},{"alias_kind":"pith_short_8","alias_value":"OYIVULTU","created_at":"2026-07-05T11:18:03Z"}],"graph_snapshots":[{"event_id":"sha256:3227dbe00d11727a53c2f037159b067ab4cc7302aeb4fd8f5f7eee8d112d130e","target":"graph","created_at":"2026-07-05T11:18:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.07224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Popularity Adjusted Block Model (PABM) provides a flexible framework for community detection in network data by allowing heterogeneous node popularity across communities. However, this flexibility increases model complexity and raises key unresolved challenges, particularly in effectively adapting spectral clustering techniques and efficiently achieving strong consistency in label recovery. To address these challenges, we first propose the Thresholded Cosine Spectral Clustering (TCSC) algorithm and establish its weak consistency under the PABM. We then introduce the one-step Refined TCSC a","authors_text":"Binghui Liu, Danning Li, Lingzhou Xue, Quan Yuan","cross_cats":["math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-08T17:17:41Z","title":"Strongly Consistent Community Detection in Popularity Adjusted Block Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07224","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:b762ab31336bc408c64978a28e5d7d70f09a18fa761dc2d03a75af26cd1578a9","target":"record","created_at":"2026-07-05T11:18:03Z","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":"f27fd88e3e0bed4927e19463dde5863a671257c4d0c406a741c5844a897aebb4","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-08T17:17:41Z","title_canon_sha256":"f9de95bf30052dd9bff5be32e1c2b0f3c49a8f8af9928434d4454b6b532e392e"},"schema_version":"1.0","source":{"id":"2506.07224","kind":"arxiv","version":1}},"canonical_sha256":"76115a2e74ed97df580a4e28e5755b468388e2bacd9d07a3135761ffaed66ef8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76115a2e74ed97df580a4e28e5755b468388e2bacd9d07a3135761ffaed66ef8","first_computed_at":"2026-07-05T11:18:03.804279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:18:03.804279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gRk2GtrKt+24cD0PXhz+BimX2M2OoXoKR9Ms85DkckAh5huGgNm4mjafmSEt/eobqJg9eA/A4bORk0p7/hhtCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:18:03.804774Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.07224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b762ab31336bc408c64978a28e5d7d70f09a18fa761dc2d03a75af26cd1578a9","sha256:3227dbe00d11727a53c2f037159b067ab4cc7302aeb4fd8f5f7eee8d112d130e"],"state_sha256":"be15cbb1eb70044aa68d75312244e29fa2a1431f37568a168f6452a9408bfc14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KiXNPiBFOssNvaqPK6RGOA7Iz/vDrxn6s4gl6Ef0RCbIzZ4ntRSAIWUwlVgZXw0rbvhncYR1teTAJWYEht89CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T22:35:25.727864Z","bundle_sha256":"29257af9903cf06ac3edfd8b82c7ac87a4b57b4532da11aa20b4c94db7a60d5e"}}