{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3EE4RUBQBZHUW77KMB7HZNC7XJ","short_pith_number":"pith:3EE4RUBQ","schema_version":"1.0","canonical_sha256":"d909c8d0300e4f4b7fea607e7cb45fba707b3e3c9f28956f30b4ecbb5ee87d4a","source":{"kind":"arxiv","id":"1602.05437","version":1},"attestation_state":"computed","paper":{"title":"Distributed Strong Diameter Network Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Elkin, Ofer Neiman","submitted_at":"2016-02-17T14:43:40Z","abstract_excerpt":"For a pair of positive parameters $D,\\chi$, a partition ${\\cal P}$ of the vertex set $V$ of an $n$-vertex graph $G = (V,E)$ into disjoint clusters of diameter at most $D$ each is called a $(D,\\chi)$ network decomposition, if the supergraph ${\\cal G}({\\cal P})$, obtained by contracting each of the clusters of ${\\cal P}$, can be properly $\\chi$-colored. The decomposition ${\\cal P}$ is said to be strong (resp., weak) if each of the clusters has strong (resp., weak) diameter at most $D$, i.e., if for every cluster $C \\in {\\cal P}$ and every two vertices $u,v \\in C$, the distance between them in th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.05437","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-17T14:43:40Z","cross_cats_sorted":[],"title_canon_sha256":"307aa24201c2d19f86a7252c972b35939bc19f11a49457f5b672647cac705d0c","abstract_canon_sha256":"90db1dc680050402d9ee0f17aa4345b06996701922504e1153db634881dbe512"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:28.203349Z","signature_b64":"5tj4hZ3wLJI7G1MIXl1I5pFEflnig1OMjbD950jmJtvoTtZcB8VsrNK5L84gj01UgQU3wnAg2olFhxviLovCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d909c8d0300e4f4b7fea607e7cb45fba707b3e3c9f28956f30b4ecbb5ee87d4a","last_reissued_at":"2026-05-18T01:20:28.202670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:28.202670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distributed Strong Diameter Network Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Elkin, Ofer Neiman","submitted_at":"2016-02-17T14:43:40Z","abstract_excerpt":"For a pair of positive parameters $D,\\chi$, a partition ${\\cal P}$ of the vertex set $V$ of an $n$-vertex graph $G = (V,E)$ into disjoint clusters of diameter at most $D$ each is called a $(D,\\chi)$ network decomposition, if the supergraph ${\\cal G}({\\cal P})$, obtained by contracting each of the clusters of ${\\cal P}$, can be properly $\\chi$-colored. The decomposition ${\\cal P}$ is said to be strong (resp., weak) if each of the clusters has strong (resp., weak) diameter at most $D$, i.e., if for every cluster $C \\in {\\cal P}$ and every two vertices $u,v \\in C$, the distance between them in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05437","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.05437","created_at":"2026-05-18T01:20:28.202777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05437v1","created_at":"2026-05-18T01:20:28.202777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05437","created_at":"2026-05-18T01:20:28.202777+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EE4RUBQBZHU","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EE4RUBQBZHUW77K","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EE4RUBQ","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ","json":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ.json","graph_json":"https://pith.science/api/pith-number/3EE4RUBQBZHUW77KMB7HZNC7XJ/graph.json","events_json":"https://pith.science/api/pith-number/3EE4RUBQBZHUW77KMB7HZNC7XJ/events.json","paper":"https://pith.science/paper/3EE4RUBQ"},"agent_actions":{"view_html":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ","download_json":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ.json","view_paper":"https://pith.science/paper/3EE4RUBQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05437&json=true","fetch_graph":"https://pith.science/api/pith-number/3EE4RUBQBZHUW77KMB7HZNC7XJ/graph.json","fetch_events":"https://pith.science/api/pith-number/3EE4RUBQBZHUW77KMB7HZNC7XJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ/action/storage_attestation","attest_author":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ/action/author_attestation","sign_citation":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ/action/citation_signature","submit_replication":"https://pith.science/pith/3EE4RUBQBZHUW77KMB7HZNC7XJ/action/replication_record"}},"created_at":"2026-05-18T01:20:28.202777+00:00","updated_at":"2026-05-18T01:20:28.202777+00:00"}