{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QFSC35UF67PSI272JTRFA5LDS2","short_pith_number":"pith:QFSC35UF","canonical_record":{"source":{"id":"1705.01204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-02T23:55:26Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"53c3e8f95d97346b9254584e858a8e3056c5f9e5c938cb8234b2c186406465ca","abstract_canon_sha256":"980c7b8b04da62728280d771313dc6fd0770496b304cbaa2239deeaa55e2a2a8"},"schema_version":"1.0"},"canonical_sha256":"81642df685f7df246bfa4ce250756396b92396d7a192a5cf1046efbb6d8b976e","source":{"kind":"arxiv","id":"1705.01204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01204","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01204v1","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01204","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"QFSC35UF67PS","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFSC35UF67PSI272","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFSC35UF","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QFSC35UF67PSI272JTRFA5LDS2","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-02T23:55:26Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"53c3e8f95d97346b9254584e858a8e3056c5f9e5c938cb8234b2c186406465ca","abstract_canon_sha256":"980c7b8b04da62728280d771313dc6fd0770496b304cbaa2239deeaa55e2a2a8"},"schema_version":"1.0"},"canonical_sha256":"81642df685f7df246bfa4ce250756396b92396d7a192a5cf1046efbb6d8b976e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:05.685088Z","signature_b64":"3/r3QqCD8Fu6P9ho6KDcUK5qITAdX/5mXIyHtQh+I7Rzo6mL+EB1DdAtEciWvWJA1NMjA2pw3nTB/7Ao9B9tDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81642df685f7df246bfa4ce250756396b92396d7a192a5cf1046efbb6d8b976e","last_reissued_at":"2026-05-18T00:45:05.684691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:05.684691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01204","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":"2026-05-18T00:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1xGmmKaVFd0A7p9vBq2WYBORUun4NFubLyxt57EQwU0rMTjaPwPtL6B0bvEwft7aYKRM+Kz74JquhiX87KyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:11:38.095806Z"},"content_sha256":"4f29299d80c2f6e43fe11fa7027ee9ee27e6b13845f31aa695f4d4519be85fc6","schema_version":"1.0","event_id":"sha256:4f29299d80c2f6e43fe11fa7027ee9ee27e6b13845f31aa695f4d4519be85fc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QFSC35UF67PSI272JTRFA5LDS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral clustering in the dynamic stochastic block model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"stat.ME","authors_text":"Marianna Pensky, Teng Zhang","submitted_at":"2017-05-02T23:55:26Z","abstract_excerpt":"In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type procedure and extract the group memberships of the nodes by spectral clustering. The procedure is computationally viable, adaptive to the unknown smoothness of the functional connection probabilities, to the rate $s$ of membership switching and to the unknown number of clusters. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01204","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":"2026-05-18T00:45:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOk2BsyaFQASAIqJAV2+9FDPNMI4g2XCSQelezhwvM+LontWPpzy5k3EPj5yiUzdTKHF5aaDgapOr7W5dG/OAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:11:38.096436Z"},"content_sha256":"97ae75089c778dac65e524e826ad486b33082c948f5463117bb1cb243f7e3dd8","schema_version":"1.0","event_id":"sha256:97ae75089c778dac65e524e826ad486b33082c948f5463117bb1cb243f7e3dd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFSC35UF67PSI272JTRFA5LDS2/bundle.json","state_url":"https://pith.science/pith/QFSC35UF67PSI272JTRFA5LDS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFSC35UF67PSI272JTRFA5LDS2/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":"2026-06-02T13:11:38Z","links":{"resolver":"https://pith.science/pith/QFSC35UF67PSI272JTRFA5LDS2","bundle":"https://pith.science/pith/QFSC35UF67PSI272JTRFA5LDS2/bundle.json","state":"https://pith.science/pith/QFSC35UF67PSI272JTRFA5LDS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFSC35UF67PSI272JTRFA5LDS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QFSC35UF67PSI272JTRFA5LDS2","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":"980c7b8b04da62728280d771313dc6fd0770496b304cbaa2239deeaa55e2a2a8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-02T23:55:26Z","title_canon_sha256":"53c3e8f95d97346b9254584e858a8e3056c5f9e5c938cb8234b2c186406465ca"},"schema_version":"1.0","source":{"id":"1705.01204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01204","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01204v1","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01204","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"QFSC35UF67PS","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QFSC35UF67PSI272","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QFSC35UF","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:97ae75089c778dac65e524e826ad486b33082c948f5463117bb1cb243f7e3dd8","target":"graph","created_at":"2026-05-18T00:45:05Z","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":"In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type procedure and extract the group memberships of the nodes by spectral clustering. The procedure is computationally viable, adaptive to the unknown smoothness of the functional connection probabilities, to the rate $s$ of membership switching and to the unknown number of clusters. I","authors_text":"Marianna Pensky, Teng Zhang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-02T23:55:26Z","title":"Spectral clustering in the dynamic stochastic block model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01204","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":"sha256:4f29299d80c2f6e43fe11fa7027ee9ee27e6b13845f31aa695f4d4519be85fc6","target":"record","created_at":"2026-05-18T00:45:05Z","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":"980c7b8b04da62728280d771313dc6fd0770496b304cbaa2239deeaa55e2a2a8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2017-05-02T23:55:26Z","title_canon_sha256":"53c3e8f95d97346b9254584e858a8e3056c5f9e5c938cb8234b2c186406465ca"},"schema_version":"1.0","source":{"id":"1705.01204","kind":"arxiv","version":1}},"canonical_sha256":"81642df685f7df246bfa4ce250756396b92396d7a192a5cf1046efbb6d8b976e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81642df685f7df246bfa4ce250756396b92396d7a192a5cf1046efbb6d8b976e","first_computed_at":"2026-05-18T00:45:05.684691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:05.684691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3/r3QqCD8Fu6P9ho6KDcUK5qITAdX/5mXIyHtQh+I7Rzo6mL+EB1DdAtEciWvWJA1NMjA2pw3nTB/7Ao9B9tDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:05.685088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f29299d80c2f6e43fe11fa7027ee9ee27e6b13845f31aa695f4d4519be85fc6","sha256:97ae75089c778dac65e524e826ad486b33082c948f5463117bb1cb243f7e3dd8"],"state_sha256":"62305e2d8ece7beb12a78837d50551891591b49325eb0c8b4688a977daa30967"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHc2lNwY7ACIkM0CYGgB0xuumt9AN24+Zr53nbP5Z7+Mkpl4SAlG13nalP88z36L3hd5eITwjI1iW/BjDdh5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:11:38.099656Z","bundle_sha256":"2b9bf3583308ee7ae3012e96017ed15b0fcffa91e3c37060dd765302f399330c"}}