{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4DDZUOCGPVEDLJDNAPUD3NNP3I","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":"2f8fe6cf56c4ef7e45b602cfece6d26cdfb7fa89fc9de5702b440d684c6952d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-20T19:49:39Z","title_canon_sha256":"9df2704ccce33caeb3b0dda941fc3e0ad622db7d87c45d854ebad99566d9540f"},"schema_version":"1.0","source":{"id":"1908.07586","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07586","created_at":"2026-07-05T06:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07586v6","created_at":"2026-07-05T06:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07586","created_at":"2026-07-05T06:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"4DDZUOCGPVED","created_at":"2026-07-05T06:22:51Z"},{"alias_kind":"pith_short_16","alias_value":"4DDZUOCGPVEDLJDN","created_at":"2026-07-05T06:22:51Z"},{"alias_kind":"pith_short_8","alias_value":"4DDZUOCG","created_at":"2026-07-05T06:22:51Z"}],"graph_snapshots":[{"event_id":"sha256:eab8df97ab0ff9262a05f1b43a1f89e5fa10a2ac382c6b481b20e73d16e741b2","target":"graph","created_at":"2026-07-05T06:22:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07586/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study a variant of graph domination known as $(t, r)$ broadcast domination, first defined in Blessing, Insko, Johnson, and Mauretour in 2015. In this variant, each broadcast provides $t-d$ reception to each vertex a distance $d < t$ from the broadcast. If $d \\ge t$ then no reception is provided. A vertex is considered dominated if it receives $r$ total reception from all broadcasts. Our main results provide some upper and lower bounds on the density of a $(t, r)$ dominating pattern of an infinite grid, as well as methods of computing them. Also, when $r \\ge 2$ we describe a f","authors_text":"Tom Shlomi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-20T19:49:39Z","title":"Bounds On $(t,r)$ Broadcast Domination of $n$-Dimensional Grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07586","kind":"arxiv","version":6},"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:e5e1e344da62d0d502fd5e55eec53e2cbd66b5acd7ccc79854e0d6e41fd232c0","target":"record","created_at":"2026-07-05T06:22:51Z","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":"2f8fe6cf56c4ef7e45b602cfece6d26cdfb7fa89fc9de5702b440d684c6952d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-20T19:49:39Z","title_canon_sha256":"9df2704ccce33caeb3b0dda941fc3e0ad622db7d87c45d854ebad99566d9540f"},"schema_version":"1.0","source":{"id":"1908.07586","kind":"arxiv","version":6}},"canonical_sha256":"e0c79a38467d4835a46d03e83db5afda0211f28d1a1a076503d409eb056989aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0c79a38467d4835a46d03e83db5afda0211f28d1a1a076503d409eb056989aa","first_computed_at":"2026-07-05T06:22:51.661686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:22:51.661686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I64xGcQZX/xKMyM8Ub1HeCtyPJuvrptNMVm9aQtTdu9x9NAVT5r8fXSaCT2ur9s/JdJBH3SSj87Si4kaHPWnDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:22:51.662137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07586","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5e1e344da62d0d502fd5e55eec53e2cbd66b5acd7ccc79854e0d6e41fd232c0","sha256:eab8df97ab0ff9262a05f1b43a1f89e5fa10a2ac382c6b481b20e73d16e741b2"],"state_sha256":"f214a4ade6e5ffd49073df66e1ad568d204ff92de1cfd28bd8243038a6d173da"}