{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZMQZR2Q3CZPECG4QZQQA3IHIWX","short_pith_number":"pith:ZMQZR2Q3","schema_version":"1.0","canonical_sha256":"cb2198ea1b165e411b90cc200da0e8b5eae0a3959e278695c51f7b529746e7fa","source":{"kind":"arxiv","id":"1712.00150","version":1},"attestation_state":"computed","paper":{"title":"Computing upper bounds for optimal density of $(t,r)$ broadcasts on the infinite grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin F. Drews, Pamela E. Harris, Timothy W. Randolph","submitted_at":"2017-12-01T01:54:01Z","abstract_excerpt":"The domination number of a finite graph $G$ with vertex set $V$ is the cardinality of the smallest set $S\\subseteq V$ such that for every vertex $v\\in V$ either $v\\in S$ or $v$ is adjacent to a vertex in $S$. A set $S$ satisfying these conditions is called a dominating set. In 2015 Blessing, Insko, Johnson, and Mauretour introduced $(t,r)$ broadcast domination, a generalization of graph domination parameterized by the nonnegative integers $t$ and $r$. In this setting, we say that the signal a vertex $v\\in V$ receives from a tower of strength $t$ located at vertex $T$ is defined by $sig(v,T)=ma"},"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":"1712.00150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-01T01:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"186eee9a355093d4d0c074f206c60cfe5ef9f3a93ca69b8e08bea7ca29833fc9","abstract_canon_sha256":"44db278e232ae77c1b0873bfe6bb0388017010c77aedb8eb8072218bd31ea824"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:07.166630Z","signature_b64":"giXJy8v/L79Ar3vrV2ZJYwyf2UgbX4kky71ng4x7/T+BrtmaTR2S6XlnCwXcCsVo9os78q+z/SbZrvXwq/YHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb2198ea1b165e411b90cc200da0e8b5eae0a3959e278695c51f7b529746e7fa","last_reissued_at":"2026-05-18T00:29:07.165965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:07.165965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing upper bounds for optimal density of $(t,r)$ broadcasts on the infinite grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin F. Drews, Pamela E. Harris, Timothy W. Randolph","submitted_at":"2017-12-01T01:54:01Z","abstract_excerpt":"The domination number of a finite graph $G$ with vertex set $V$ is the cardinality of the smallest set $S\\subseteq V$ such that for every vertex $v\\in V$ either $v\\in S$ or $v$ is adjacent to a vertex in $S$. A set $S$ satisfying these conditions is called a dominating set. In 2015 Blessing, Insko, Johnson, and Mauretour introduced $(t,r)$ broadcast domination, a generalization of graph domination parameterized by the nonnegative integers $t$ and $r$. In this setting, we say that the signal a vertex $v\\in V$ receives from a tower of strength $t$ located at vertex $T$ is defined by $sig(v,T)=ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00150","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":"1712.00150","created_at":"2026-05-18T00:29:07.166077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00150v1","created_at":"2026-05-18T00:29:07.166077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00150","created_at":"2026-05-18T00:29:07.166077+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMQZR2Q3CZPE","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMQZR2Q3CZPECG4Q","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMQZR2Q3","created_at":"2026-05-18T12:31:59.375834+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/ZMQZR2Q3CZPECG4QZQQA3IHIWX","json":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX.json","graph_json":"https://pith.science/api/pith-number/ZMQZR2Q3CZPECG4QZQQA3IHIWX/graph.json","events_json":"https://pith.science/api/pith-number/ZMQZR2Q3CZPECG4QZQQA3IHIWX/events.json","paper":"https://pith.science/paper/ZMQZR2Q3"},"agent_actions":{"view_html":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX","download_json":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX.json","view_paper":"https://pith.science/paper/ZMQZR2Q3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00150&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMQZR2Q3CZPECG4QZQQA3IHIWX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMQZR2Q3CZPECG4QZQQA3IHIWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX/action/storage_attestation","attest_author":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX/action/author_attestation","sign_citation":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX/action/citation_signature","submit_replication":"https://pith.science/pith/ZMQZR2Q3CZPECG4QZQQA3IHIWX/action/replication_record"}},"created_at":"2026-05-18T00:29:07.166077+00:00","updated_at":"2026-05-18T00:29:07.166077+00:00"}