{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K7APUBSYLX7TUT7QSENQHJZSVW","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":"35aba3b65bfdd1ab7f1a5414cc7f7a1c06f4d892eb128ec028d6854f6c4b8039","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-04T17:58:07Z","title_canon_sha256":"c9f88cdd03a20474e25837534da5dceadf77e4e0908edcfe94ef10e17aafde72"},"schema_version":"1.0","source":{"id":"2606.06482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06482","created_at":"2026-06-05T01:15:46Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06482v1","created_at":"2026-06-05T01:15:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06482","created_at":"2026-06-05T01:15:46Z"},{"alias_kind":"pith_short_12","alias_value":"K7APUBSYLX7T","created_at":"2026-06-05T01:15:46Z"},{"alias_kind":"pith_short_16","alias_value":"K7APUBSYLX7TUT7Q","created_at":"2026-06-05T01:15:46Z"},{"alias_kind":"pith_short_8","alias_value":"K7APUBSY","created_at":"2026-06-05T01:15:46Z"}],"graph_snapshots":[{"event_id":"sha256:09a4db14164409888404f22d9389589c5c5996b8a9d1e149b8bbca3a5e7ee7bf","target":"graph","created_at":"2026-06-05T01:15:46Z","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/2606.06482/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In many settings one is often interested in determining whether two networks share some joint structural connectivity patterns such as communities. However, while communities may be shared across networks, edge probabilities may differ significantly. Therefore, in this paper we consider testing a general null hypothesis that two networks have the same underlying subspace, which in particular includes the setting that communities are the same for either stochastic blockmodels or mixed-membership stochastic blockmodels (even if edge probabilities are different). We propose a test statistic based","authors_text":"Joshua Agterberg, Rajdeep Brahma, Yuguo Chen","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-04T17:58:07Z","title":"Two-Sample Hypothesis Testing for Subspace Equality in Network Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06482","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":"sha256:7718e55e4a00d50451827d7e893c796d84541b3ed742abb924b0c8a45882e985","target":"record","created_at":"2026-06-05T01:15:46Z","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":"35aba3b65bfdd1ab7f1a5414cc7f7a1c06f4d892eb128ec028d6854f6c4b8039","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-04T17:58:07Z","title_canon_sha256":"c9f88cdd03a20474e25837534da5dceadf77e4e0908edcfe94ef10e17aafde72"},"schema_version":"1.0","source":{"id":"2606.06482","kind":"arxiv","version":1}},"canonical_sha256":"57c0fa06585dff3a4ff0911b03a732ad8bf53fe87ca63e2cc77eb4c9bb3bbb5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57c0fa06585dff3a4ff0911b03a732ad8bf53fe87ca63e2cc77eb4c9bb3bbb5e","first_computed_at":"2026-06-05T01:15:46.869799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:46.869799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rdBhYGSrFcptMipz5SdIXGacUj4Pn8ftUufuLCj392L61lyBEDTYgJu/GYk2ZIKUKUDGzRVXDzX63n9badjCQ==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:46.870201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7718e55e4a00d50451827d7e893c796d84541b3ed742abb924b0c8a45882e985","sha256:09a4db14164409888404f22d9389589c5c5996b8a9d1e149b8bbca3a5e7ee7bf"],"state_sha256":"aedffe898cd5781b34f5454410d87e2f86794a4c19359b153703c638869170f2"}