{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S7O45DTQN2IR5MJZC6SM3QAGD3","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":"2c60acfd9e9b8e1d1ef4e19393fb52e3331dae721b216d718fdc02c1b022131d","cross_cats_sorted":["stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-20T16:56:28Z","title_canon_sha256":"18adfab78389de8bccc5f5a7a4e63ebee3d926572fc94fa62b02d37b679b584c"},"schema_version":"1.0","source":{"id":"2606.22148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22148","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22148v1","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22148","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"S7O45DTQN2IR","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"pith_short_16","alias_value":"S7O45DTQN2IR5MJZ","created_at":"2026-06-23T02:13:29Z"},{"alias_kind":"pith_short_8","alias_value":"S7O45DTQ","created_at":"2026-06-23T02:13:29Z"}],"graph_snapshots":[{"event_id":"sha256:a3784ac74a93c73452912c979ccc1ea283b8e8e990acf99c4da4889f553680b3","target":"graph","created_at":"2026-06-23T02:13:29Z","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/2606.22148/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In directed networks, nodes may form groups with similar interaction patterns, while these groups may themselves follow an ordered structure. Existing methods typically treat these features separately, either clustering nodes without enforcing a coherent block order, or ranking individual nodes without allowing for structurally equivalent groups. We introduce the Transitive Stochastic Block Model (TSBM), a Bayesian model for directed weighted networks that uses transitivity-inducing priors to infer ordered blocks. The model separates the total volume of interaction between two nodes from the d","authors_text":"Lapo Santi, Nial Friel, Pierpaolo De Blasi","cross_cats":["stat.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-20T16:56:28Z","title":"Ordering Stochastic Block Models via prior transitivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22148","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":"sha256:4b2b18fb442c162631947e0d5e6f90441c9ba7b039616d3c9ea5cca17055bad9","target":"record","created_at":"2026-06-23T02:13:29Z","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":"2c60acfd9e9b8e1d1ef4e19393fb52e3331dae721b216d718fdc02c1b022131d","cross_cats_sorted":["stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-06-20T16:56:28Z","title_canon_sha256":"18adfab78389de8bccc5f5a7a4e63ebee3d926572fc94fa62b02d37b679b584c"},"schema_version":"1.0","source":{"id":"2606.22148","kind":"arxiv","version":1}},"canonical_sha256":"97ddce8e706e911eb13917a4cdc0061ed2d2335a0fe7cb57104ea84d88e16918","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97ddce8e706e911eb13917a4cdc0061ed2d2335a0fe7cb57104ea84d88e16918","first_computed_at":"2026-06-23T02:13:29.633517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:29.633517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C8s3L+xHjLmRuSCVhgSwt8RbvcQY/6Xl5XIPdBCHHwit8aAQ5DkNXcq4SD8w/dgCtUqropddamUJsAdvLQT4BQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:29.633905Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b2b18fb442c162631947e0d5e6f90441c9ba7b039616d3c9ea5cca17055bad9","sha256:a3784ac74a93c73452912c979ccc1ea283b8e8e990acf99c4da4889f553680b3"],"state_sha256":"f1968792f744aa625c2cb1f5a7a80644a7046665d934d852c884758dac3d9bdf"}