{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:GZ4P6FLPIUUH2JYIIWV5AKCNOG","short_pith_number":"pith:GZ4P6FLP","schema_version":"1.0","canonical_sha256":"3678ff156f45287d270845abd0284d71b3d20a2a3989e0f8b14895baf368867d","source":{"kind":"arxiv","id":"0910.5380","version":2},"attestation_state":"computed","paper":{"title":"On the SIG dimension of trees under $L_{\\infty}$ metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"L. Sunil Chandran, Rajesh Chitnis, Ramanjit Kumar","submitted_at":"2009-10-28T13:55:42Z","abstract_excerpt":"We study the $SIG$ dimension of trees under $L_{\\infty}$ metric and answer an open problem posed by Michael and Quint (Discrete Applied Mathematics: 127, pages 447-460, 2003). Let $T$ be a tree with atleast two vertices. For each $v\\in V(T)$, let leaf-degree$(v)$ denote the number of neighbours of $v$ that are leaves. We define the maximum leaf-degree as $\\alpha(T) = \\max_{x \\in V(T)}$ leaf-degree$(x)$. Let $S = \\{v\\in V(T) |$ leaf-degree$(v) = \\alpha\\}$. If $|S| = 1$, we define $\\beta(T) = \\alpha(T) - 1$. Otherwise define $\\beta(T) = \\alpha(T)$. We show that for a tree $T$, $SIG_\\infty(T) = \\"},"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":"0910.5380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-28T13:55:42Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"4be076faa58f6360eec735ab159612daca9b3331afeb1de0d5f55b474efa2cfc","abstract_canon_sha256":"4d30a5f7ca58c766b0f601f1dedd314f63322b4473ef6eab2d37451d2b9550e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:29.070527Z","signature_b64":"Eqg7maB1tDe9uUdqF6YkrelBIV9FaEDDBsyzC9bi/MYV/kd5/CDigPG0cYlsRz2MowI5+FbJ6KgW7wpg5cZSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3678ff156f45287d270845abd0284d71b3d20a2a3989e0f8b14895baf368867d","last_reissued_at":"2026-05-18T04:11:29.069789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:29.069789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the SIG dimension of trees under $L_{\\infty}$ metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"L. Sunil Chandran, Rajesh Chitnis, Ramanjit Kumar","submitted_at":"2009-10-28T13:55:42Z","abstract_excerpt":"We study the $SIG$ dimension of trees under $L_{\\infty}$ metric and answer an open problem posed by Michael and Quint (Discrete Applied Mathematics: 127, pages 447-460, 2003). Let $T$ be a tree with atleast two vertices. For each $v\\in V(T)$, let leaf-degree$(v)$ denote the number of neighbours of $v$ that are leaves. We define the maximum leaf-degree as $\\alpha(T) = \\max_{x \\in V(T)}$ leaf-degree$(x)$. Let $S = \\{v\\in V(T) |$ leaf-degree$(v) = \\alpha\\}$. If $|S| = 1$, we define $\\beta(T) = \\alpha(T) - 1$. Otherwise define $\\beta(T) = \\alpha(T)$. We show that for a tree $T$, $SIG_\\infty(T) = \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5380","kind":"arxiv","version":2},"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":"0910.5380","created_at":"2026-05-18T04:11:29.069903+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.5380v2","created_at":"2026-05-18T04:11:29.069903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5380","created_at":"2026-05-18T04:11:29.069903+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZ4P6FLPIUUH","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZ4P6FLPIUUH2JYI","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZ4P6FLP","created_at":"2026-05-18T12:25:59.703012+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/GZ4P6FLPIUUH2JYIIWV5AKCNOG","json":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG.json","graph_json":"https://pith.science/api/pith-number/GZ4P6FLPIUUH2JYIIWV5AKCNOG/graph.json","events_json":"https://pith.science/api/pith-number/GZ4P6FLPIUUH2JYIIWV5AKCNOG/events.json","paper":"https://pith.science/paper/GZ4P6FLP"},"agent_actions":{"view_html":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG","download_json":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG.json","view_paper":"https://pith.science/paper/GZ4P6FLP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.5380&json=true","fetch_graph":"https://pith.science/api/pith-number/GZ4P6FLPIUUH2JYIIWV5AKCNOG/graph.json","fetch_events":"https://pith.science/api/pith-number/GZ4P6FLPIUUH2JYIIWV5AKCNOG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG/action/storage_attestation","attest_author":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG/action/author_attestation","sign_citation":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG/action/citation_signature","submit_replication":"https://pith.science/pith/GZ4P6FLPIUUH2JYIIWV5AKCNOG/action/replication_record"}},"created_at":"2026-05-18T04:11:29.069903+00:00","updated_at":"2026-05-18T04:11:29.069903+00:00"}