{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OGPIKT4NN36YT5HRGD7RJGTVIW","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":"35858c9266c37c26be4e077ebbc398404fe0f180b0a785eb4c07693cbba17900","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-09-03T16:00:57Z","title_canon_sha256":"cf0aee444b541a3b484f13f2cb592ecd98d22adb52ae803274b5fd007530fe18"},"schema_version":"1.0","source":{"id":"1009.0706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0706","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0706v1","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0706","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"OGPIKT4NN36Y","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OGPIKT4NN36YT5HR","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OGPIKT4N","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:1d6d50c41e2a7641543efab901f258df3472f52be00e8011510bda98b5f31eb3","target":"graph","created_at":"2026-05-18T04:41:25Z","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":"This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\\it minimum normalized cuts}/{\\it isoperimteric numbers} defined through taking minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a {\\it partition}/{\\it subpartition}. Following the main result of [A. Daneshgar, {\\it et. al.}, {\\it On the isoperimetric spectrum of graphs and its approximations}, JCTB, (2010)], it is known","authors_text":"Amir Daneshgar, Ramin Javadi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-09-03T16:00:57Z","title":"On Complexity of Isoperimetric Problems on Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0706","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":"sha256:63517fbd7cce6f273534f6ffdb6bce690cf0b3d4effaaad306450896d5c39857","target":"record","created_at":"2026-05-18T04:41:25Z","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":"35858c9266c37c26be4e077ebbc398404fe0f180b0a785eb4c07693cbba17900","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-09-03T16:00:57Z","title_canon_sha256":"cf0aee444b541a3b484f13f2cb592ecd98d22adb52ae803274b5fd007530fe18"},"schema_version":"1.0","source":{"id":"1009.0706","kind":"arxiv","version":1}},"canonical_sha256":"719e854f8d6efd89f4f130ff149a75459f60b4dd726249d33278e35467ba86cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"719e854f8d6efd89f4f130ff149a75459f60b4dd726249d33278e35467ba86cd","first_computed_at":"2026-05-18T04:41:25.512203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:25.512203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3PxVtmBNombXwsdpYYxZuHKq3XoUT/a94ZtTaTrtMQxcyLkYvlzPl0sdio5PwC5ADCAEool2rxDB/6W2YRrWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:25.512653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63517fbd7cce6f273534f6ffdb6bce690cf0b3d4effaaad306450896d5c39857","sha256:1d6d50c41e2a7641543efab901f258df3472f52be00e8011510bda98b5f31eb3"],"state_sha256":"10290b47e620ac59d5d95a2ced470f3e1232ec091bcfcf6e0fdb5442bd6bdd28"}