{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:ZAFDGIV47SUVUNQ2J5SZFN7DVO","short_pith_number":"pith:ZAFDGIV4","canonical_record":{"source":{"id":"2010.15063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-10-28T16:16:14Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f9a15c4e35a23aef42d9cb82f8f48e91a142e4630d53007f99d0e054493809a3","abstract_canon_sha256":"a10e969341fb58c9702500d91cc40554cff428b0ef3bcbc6aa61a43e2dcd4b05"},"schema_version":"1.0"},"canonical_sha256":"c80a3322bcfca95a361a4f6592b7e3abbdf550a44945bad1f957d526046cbefe","source":{"kind":"arxiv","id":"2010.15063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.15063","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"arxiv_version","alias_value":"2010.15063v2","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.15063","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZAFDGIV47SUV","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZAFDGIV47SUVUNQ2","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZAFDGIV4","created_at":"2026-07-05T01:47:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:ZAFDGIV47SUVUNQ2J5SZFN7DVO","target":"record","payload":{"canonical_record":{"source":{"id":"2010.15063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-10-28T16:16:14Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"f9a15c4e35a23aef42d9cb82f8f48e91a142e4630d53007f99d0e054493809a3","abstract_canon_sha256":"a10e969341fb58c9702500d91cc40554cff428b0ef3bcbc6aa61a43e2dcd4b05"},"schema_version":"1.0"},"canonical_sha256":"c80a3322bcfca95a361a4f6592b7e3abbdf550a44945bad1f957d526046cbefe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:47:46.331174Z","signature_b64":"FM+msDh7PffpjC0dLHjGL2onQ8gKLEtpueWq8Z/DDVdLiqTkran4CJdangprQVi+84gm91NlWeN3OYdbB0gUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c80a3322bcfca95a361a4f6592b7e3abbdf550a44945bad1f957d526046cbefe","last_reissued_at":"2026-07-05T01:47:46.330704Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:47:46.330704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.15063","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:47:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFfVcK1yd9wT9ugn0T1gmpOvF+ot3Xi4cxG2fb2OpkOGK63Rxq3zYhs//bVXVuVX1NnFS6iYZ9YDmfd8bN5nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:18:48.009119Z"},"content_sha256":"7e46fafe7bbdc3a0f4262a1ba215ea78333537a0282bf3e5a7f150f1635a1098","schema_version":"1.0","event_id":"sha256:7e46fafe7bbdc3a0f4262a1ba215ea78333537a0282bf3e5a7f150f1635a1098"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:ZAFDGIV47SUVUNQ2J5SZFN7DVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial-Probabilistic Trade-Off: Community Properties Test in the Stochastic Block Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Junwei Lu, Shuting Shen","submitted_at":"2020-10-28T16:16:14Z","abstract_excerpt":"In this paper, we propose an inferential framework testing the general community combinatorial properties of the stochastic block model. Instead of estimating the community assignments, we aim to test the hypothesis on whether a certain community property is satisfied. For instance, we propose to test whether a given set of nodes belong to the same community or whether different network communities have the same size. We propose a general inference framework that can be applied to all symmetric community properties. To ease the challenges caused by the combinatorial nature of communities prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.15063","kind":"arxiv","version":2},"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/2010.15063/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":"2026-07-05T01:47:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"du+MiUypSFwTQyTu3L3r3kVbzRsvuqJwfiASjV6HeAQmoiihUQPcseML9RkheskD0FQ/hG7Oovpj5MLflWvnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:18:48.009701Z"},"content_sha256":"2f8363ef54103da834a6268bb4eae2c014180957a2959594f70b33d68c04a1b5","schema_version":"1.0","event_id":"sha256:2f8363ef54103da834a6268bb4eae2c014180957a2959594f70b33d68c04a1b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO/bundle.json","state_url":"https://pith.science/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO/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":"2026-08-07T12:18:48Z","links":{"resolver":"https://pith.science/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO","bundle":"https://pith.science/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO/bundle.json","state":"https://pith.science/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAFDGIV47SUVUNQ2J5SZFN7DVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ZAFDGIV47SUVUNQ2J5SZFN7DVO","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":"a10e969341fb58c9702500d91cc40554cff428b0ef3bcbc6aa61a43e2dcd4b05","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-10-28T16:16:14Z","title_canon_sha256":"f9a15c4e35a23aef42d9cb82f8f48e91a142e4630d53007f99d0e054493809a3"},"schema_version":"1.0","source":{"id":"2010.15063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.15063","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"arxiv_version","alias_value":"2010.15063v2","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.15063","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"pith_short_12","alias_value":"ZAFDGIV47SUV","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"pith_short_16","alias_value":"ZAFDGIV47SUVUNQ2","created_at":"2026-07-05T01:47:46Z"},{"alias_kind":"pith_short_8","alias_value":"ZAFDGIV4","created_at":"2026-07-05T01:47:46Z"}],"graph_snapshots":[{"event_id":"sha256:2f8363ef54103da834a6268bb4eae2c014180957a2959594f70b33d68c04a1b5","target":"graph","created_at":"2026-07-05T01:47:46Z","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/2010.15063/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose an inferential framework testing the general community combinatorial properties of the stochastic block model. Instead of estimating the community assignments, we aim to test the hypothesis on whether a certain community property is satisfied. For instance, we propose to test whether a given set of nodes belong to the same community or whether different network communities have the same size. We propose a general inference framework that can be applied to all symmetric community properties. To ease the challenges caused by the combinatorial nature of communities prope","authors_text":"Junwei Lu, Shuting Shen","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-10-28T16:16:14Z","title":"Combinatorial-Probabilistic Trade-Off: Community Properties Test in the Stochastic Block Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.15063","kind":"arxiv","version":2},"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":"sha256:7e46fafe7bbdc3a0f4262a1ba215ea78333537a0282bf3e5a7f150f1635a1098","target":"record","created_at":"2026-07-05T01:47:46Z","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":"a10e969341fb58c9702500d91cc40554cff428b0ef3bcbc6aa61a43e2dcd4b05","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2020-10-28T16:16:14Z","title_canon_sha256":"f9a15c4e35a23aef42d9cb82f8f48e91a142e4630d53007f99d0e054493809a3"},"schema_version":"1.0","source":{"id":"2010.15063","kind":"arxiv","version":2}},"canonical_sha256":"c80a3322bcfca95a361a4f6592b7e3abbdf550a44945bad1f957d526046cbefe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c80a3322bcfca95a361a4f6592b7e3abbdf550a44945bad1f957d526046cbefe","first_computed_at":"2026-07-05T01:47:46.330704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:47:46.330704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FM+msDh7PffpjC0dLHjGL2onQ8gKLEtpueWq8Z/DDVdLiqTkran4CJdangprQVi+84gm91NlWeN3OYdbB0gUBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:47:46.331174Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.15063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e46fafe7bbdc3a0f4262a1ba215ea78333537a0282bf3e5a7f150f1635a1098","sha256:2f8363ef54103da834a6268bb4eae2c014180957a2959594f70b33d68c04a1b5"],"state_sha256":"42b0fd3afa1e6a1791686bd4d9e3028ac6b1a2e5768688d84d2fb3e946941a42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfetj/PHxE3ujNgn0d4Z0QPtxZT9xiqN7TfGZFVIIffT5slcVl/qfWI9a9JboMRuOEIwBXeoiLsgdvAIIzWPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T12:18:48.014128Z","bundle_sha256":"8cc448e0520ab428bfc59710be09b7d6d8601d0ef4dad2fb509d84511a6e36ab"}}