{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CAE6FME5EDFQUPYGRMVSXVUMNS","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":"18d3510b73ada5c0fbdca923a248b980f568a66f2c9416a07ec514abc953bed8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-21T00:30:37Z","title_canon_sha256":"0fbb7f18d31bc181ba3f9dae00bfd10db9924aa0d43c8f1f8191c686cc214407"},"schema_version":"1.0","source":{"id":"1808.00050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00050","created_at":"2026-05-18T00:09:08Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00050v1","created_at":"2026-05-18T00:09:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00050","created_at":"2026-05-18T00:09:08Z"},{"alias_kind":"pith_short_12","alias_value":"CAE6FME5EDFQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CAE6FME5EDFQUPYG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CAE6FME5","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:3a609687fe97315217baf49d21279eaa7bbd5b16ecc070ee7804543361fbbb37","target":"graph","created_at":"2026-05-18T00:09:08Z","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":"A connected undirected graph $G=(V,E)$ is given. This paper presents an algorithm that samples (non-uniformly) a $K$ partition $U_1,\\ldots U_K$ of the graph nodes $V$, such that the subgraph induced by each $U_k$, with $k=1:K$, is connected. Moreover, the probability induced by the algorithm over the set ${\\mathcal C}_K$ of all such partitions is obtained in closed form.","authors_text":"Marina Meila","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-21T00:30:37Z","title":"How to sample connected $K$-partitions of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00050","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":"sha256:2c745844b72d0188c2ba55dbed66ae4687be90c00d0a6e7693d1d090d1ff9d48","target":"record","created_at":"2026-05-18T00:09:08Z","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":"18d3510b73ada5c0fbdca923a248b980f568a66f2c9416a07ec514abc953bed8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-21T00:30:37Z","title_canon_sha256":"0fbb7f18d31bc181ba3f9dae00bfd10db9924aa0d43c8f1f8191c686cc214407"},"schema_version":"1.0","source":{"id":"1808.00050","kind":"arxiv","version":1}},"canonical_sha256":"1009e2b09d20cb0a3f068b2b2bd68c6c8d797ba9c00bffdccda0bf5080026156","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1009e2b09d20cb0a3f068b2b2bd68c6c8d797ba9c00bffdccda0bf5080026156","first_computed_at":"2026-05-18T00:09:08.896136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:08.896136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TXygWKJ1EU8EJN8l5Qg+R4wVl/oAyiCFqAWDOj/a/hCJ71R//GnqNVqTszE+2OK6otDhNp6AtDV5FXWZBwuPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:08.896762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c745844b72d0188c2ba55dbed66ae4687be90c00d0a6e7693d1d090d1ff9d48","sha256:3a609687fe97315217baf49d21279eaa7bbd5b16ecc070ee7804543361fbbb37"],"state_sha256":"d47fafd9a0c3eb6328c1ced50ccf67cbf00296701e2e07e87b4d5a9c2de9f016"}