{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RR5AATUMKMTCUT2HPTXF6KXSNV","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":"229f94de9546f435b89b942ab320fc35ecc96e1609dc79551a3a768e8cb1c21d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-01-26T07:57:16Z","title_canon_sha256":"c03fade516fbd81fd3631643647390fff3e9dd54e66dee9ef87d1a6705050cbf"},"schema_version":"1.0","source":{"id":"1601.06915","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06915","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06915v2","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06915","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"RR5AATUMKMTC","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RR5AATUMKMTCUT2H","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RR5AATUM","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:98d528c3f6b6af05a177f8cb6c7edddaf7118d7c5c3817f41904d8e4e3c27571","target":"graph","created_at":"2026-05-18T00:59:26Z","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":"Independent trees are used in building secure and/or fault-tolerant network communication protocols. They have been investigated for different network topologies including tori. Dense Gaussian networks are potential alternatives for 2-dimensional tori. They have similar topological properties; however, they are superiors in carrying communications due to their node-distance distributions and smaller diameters. In this paper, we present constructions of edge-disjoint node-independent spanning trees in dense Gaussian networks. Based on the constructed trees, we design algorithms that could be us","authors_text":"Anton Cerny, Bader AlBdaiwi, Robert Aldred, Zaid Hussain","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-01-26T07:57:16Z","title":"Edge-Disjoint Node-Independent Spanning Trees in Dense Gaussian Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06915","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":"sha256:2540eb8163fc837066de9418bb578c3b8036faea006a0689c68b79c3a887afe9","target":"record","created_at":"2026-05-18T00:59:26Z","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":"229f94de9546f435b89b942ab320fc35ecc96e1609dc79551a3a768e8cb1c21d","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-01-26T07:57:16Z","title_canon_sha256":"c03fade516fbd81fd3631643647390fff3e9dd54e66dee9ef87d1a6705050cbf"},"schema_version":"1.0","source":{"id":"1601.06915","kind":"arxiv","version":2}},"canonical_sha256":"8c7a004e8c53262a4f477cee5f2af26d4837e0fb1b82b4a525c482d967582d73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c7a004e8c53262a4f477cee5f2af26d4837e0fb1b82b4a525c482d967582d73","first_computed_at":"2026-05-18T00:59:26.040199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:26.040199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aFJiyRH2DE3vfC2Af9unB0YqFsF1Jkplq7Kf+odKrjYU/EIulGEbIsR8W/N0SeZ9PApBsU9GTwU/3KaWpGrRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:26.040902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06915","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2540eb8163fc837066de9418bb578c3b8036faea006a0689c68b79c3a887afe9","sha256:98d528c3f6b6af05a177f8cb6c7edddaf7118d7c5c3817f41904d8e4e3c27571"],"state_sha256":"7a5cde8095dfb22a657d1611b1fae7e8ca4ab75c4a2a25bf43def992fe530b86"}