{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7HHAFYCFROQMLAO2EZUNO5FDC7","short_pith_number":"pith:7HHAFYCF","schema_version":"1.0","canonical_sha256":"f9ce02e0458ba0c581da2668d774a317dea54ba1fa6accad510fd4e7f34d96aa","source":{"kind":"arxiv","id":"1610.05250","version":1},"attestation_state":"computed","paper":{"title":"Upper broadcast domination of toroidal grids and a classification of diametrical trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bethany Kubik, Candice Price, Erik Insko","submitted_at":"2016-10-17T18:27:29Z","abstract_excerpt":"A broadcast on a graph $G=(V,E)$ is a function $f:V \\rightarrow \\{0,1, \\ldots, \\text{diam}(G)\\}$ satisfying $f(v) \\leq e(v)$ for all $v \\in V$, where $e(v)$ denotes the eccentricity of $v$ and $\\text{diam}(G)$ denotes the diameter of $G$. We say that a broadcast dominates $G$ if every vertex can hear at least one broadcasting node. The upper domination number is the maximum cost of all possible minimal broadcasts, where the cost of a broadcast is defined as $\\text{cost} (f)= \\sum_{v \\in V}f(v)$. In this paper we establish both the upper domination number and the upper broadcast domination numb"},"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":"1610.05250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-17T18:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"e5e64a1854325c3258d9e949d8cfe49fb58e7fe9beb2d76be76d2b1231c55be2","abstract_canon_sha256":"642cc14100078c707c9c03593b95c641b0d5ea809f6ba0148b9f4584eabd0381"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:05.702944Z","signature_b64":"+2xO9hMHFHzP+Wo0yVLTyDopnwPW2+FLkmg557b/wuiK13qDbHfL2Lvx3aZDlEPQZcZxQu6J4Nt1UsSbaBUZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9ce02e0458ba0c581da2668d774a317dea54ba1fa6accad510fd4e7f34d96aa","last_reissued_at":"2026-05-18T01:02:05.702470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:05.702470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper broadcast domination of toroidal grids and a classification of diametrical trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bethany Kubik, Candice Price, Erik Insko","submitted_at":"2016-10-17T18:27:29Z","abstract_excerpt":"A broadcast on a graph $G=(V,E)$ is a function $f:V \\rightarrow \\{0,1, \\ldots, \\text{diam}(G)\\}$ satisfying $f(v) \\leq e(v)$ for all $v \\in V$, where $e(v)$ denotes the eccentricity of $v$ and $\\text{diam}(G)$ denotes the diameter of $G$. We say that a broadcast dominates $G$ if every vertex can hear at least one broadcasting node. The upper domination number is the maximum cost of all possible minimal broadcasts, where the cost of a broadcast is defined as $\\text{cost} (f)= \\sum_{v \\in V}f(v)$. In this paper we establish both the upper domination number and the upper broadcast domination numb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05250","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":"1610.05250","created_at":"2026-05-18T01:02:05.702545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.05250v1","created_at":"2026-05-18T01:02:05.702545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05250","created_at":"2026-05-18T01:02:05.702545+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HHAFYCFROQM","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HHAFYCFROQMLAO2","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HHAFYCF","created_at":"2026-05-18T12:30:04.600751+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/7HHAFYCFROQMLAO2EZUNO5FDC7","json":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7.json","graph_json":"https://pith.science/api/pith-number/7HHAFYCFROQMLAO2EZUNO5FDC7/graph.json","events_json":"https://pith.science/api/pith-number/7HHAFYCFROQMLAO2EZUNO5FDC7/events.json","paper":"https://pith.science/paper/7HHAFYCF"},"agent_actions":{"view_html":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7","download_json":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7.json","view_paper":"https://pith.science/paper/7HHAFYCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.05250&json=true","fetch_graph":"https://pith.science/api/pith-number/7HHAFYCFROQMLAO2EZUNO5FDC7/graph.json","fetch_events":"https://pith.science/api/pith-number/7HHAFYCFROQMLAO2EZUNO5FDC7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7/action/storage_attestation","attest_author":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7/action/author_attestation","sign_citation":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7/action/citation_signature","submit_replication":"https://pith.science/pith/7HHAFYCFROQMLAO2EZUNO5FDC7/action/replication_record"}},"created_at":"2026-05-18T01:02:05.702545+00:00","updated_at":"2026-05-18T01:02:05.702545+00:00"}