{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:4LD7PREUFYSXLULWEEVSQG4V43","short_pith_number":"pith:4LD7PREU","schema_version":"1.0","canonical_sha256":"e2c7f7c4942e2575d176212b281b95e6cb9d632fffa5e3f082437de6609f894e","source":{"kind":"arxiv","id":"2004.07918","version":4},"attestation_state":"computed","paper":{"title":"An upper bound for the $k$-power domination number in $r$-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Franklin Kenter, Joseph S. Alameda, Karen Meagher, Michael Young","submitted_at":"2020-04-16T20:16:33Z","abstract_excerpt":"Generalizing work on graphs, Chang and Roussel introduced $k$-power domination in hypergraphs and conjectured the upper bound for the $k$-power domination number for $r$-uniform hypergraphs on $n$ vertices was $\\frac{n}{r+k}$. This upper bound was shown to be true for simple graphs ($r=2$) and it was further conjectured that only a family of hypergraphs, known as the squid hypergraphs, attained this upper bound. In this paper, the conjecture is proven to hold for hypergraphs with $r=3$ or $4$; but is shown to be false, by a counterexample, for $r\\geq 7$. Furthermore, we show that the squid hyp"},"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":"2004.07918","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-04-16T20:16:33Z","cross_cats_sorted":[],"title_canon_sha256":"4bbe803ae9c46d85f6feffccd750e51b34b764d524caebad62f0206d342cbc53","abstract_canon_sha256":"3fdaf8edbf0620a48d37e27971120ebf61541ea1f426a665c986319a878d033a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:28:25.203486Z","signature_b64":"442UI44z2dWXZU1vWP3CL+GIuVznZ2ZCVwy9DIK9t8CNIgXXKqze2NHBlBwbFgsN+o0sinDmZ89mVVlZyqDjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2c7f7c4942e2575d176212b281b95e6cb9d632fffa5e3f082437de6609f894e","last_reissued_at":"2026-07-05T04:28:25.202975Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:28:25.202975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An upper bound for the $k$-power domination number in $r$-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Franklin Kenter, Joseph S. Alameda, Karen Meagher, Michael Young","submitted_at":"2020-04-16T20:16:33Z","abstract_excerpt":"Generalizing work on graphs, Chang and Roussel introduced $k$-power domination in hypergraphs and conjectured the upper bound for the $k$-power domination number for $r$-uniform hypergraphs on $n$ vertices was $\\frac{n}{r+k}$. This upper bound was shown to be true for simple graphs ($r=2$) and it was further conjectured that only a family of hypergraphs, known as the squid hypergraphs, attained this upper bound. In this paper, the conjecture is proven to hold for hypergraphs with $r=3$ or $4$; but is shown to be false, by a counterexample, for $r\\geq 7$. Furthermore, we show that the squid hyp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.07918","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.07918/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2004.07918","created_at":"2026-07-05T04:28:25.203035+00:00"},{"alias_kind":"arxiv_version","alias_value":"2004.07918v4","created_at":"2026-07-05T04:28:25.203035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.07918","created_at":"2026-07-05T04:28:25.203035+00:00"},{"alias_kind":"pith_short_12","alias_value":"4LD7PREUFYSX","created_at":"2026-07-05T04:28:25.203035+00:00"},{"alias_kind":"pith_short_16","alias_value":"4LD7PREUFYSXLULW","created_at":"2026-07-05T04:28:25.203035+00:00"},{"alias_kind":"pith_short_8","alias_value":"4LD7PREU","created_at":"2026-07-05T04:28:25.203035+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/4LD7PREUFYSXLULWEEVSQG4V43","json":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43.json","graph_json":"https://pith.science/api/pith-number/4LD7PREUFYSXLULWEEVSQG4V43/graph.json","events_json":"https://pith.science/api/pith-number/4LD7PREUFYSXLULWEEVSQG4V43/events.json","paper":"https://pith.science/paper/4LD7PREU"},"agent_actions":{"view_html":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43","download_json":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43.json","view_paper":"https://pith.science/paper/4LD7PREU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2004.07918&json=true","fetch_graph":"https://pith.science/api/pith-number/4LD7PREUFYSXLULWEEVSQG4V43/graph.json","fetch_events":"https://pith.science/api/pith-number/4LD7PREUFYSXLULWEEVSQG4V43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43/action/storage_attestation","attest_author":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43/action/author_attestation","sign_citation":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43/action/citation_signature","submit_replication":"https://pith.science/pith/4LD7PREUFYSXLULWEEVSQG4V43/action/replication_record"}},"created_at":"2026-07-05T04:28:25.203035+00:00","updated_at":"2026-07-05T04:28:25.203035+00:00"}