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A graph $G$ is called $\\Theta_\\alpha$-maximal in a class of connected simple graphs $\\mathcal {G}$ if $\\Theta(G,\\alpha)$ is maximal among all graphs of $\\mathcal {G}$. A $t$-cone $c$-cyclic graph is the join of a complete graph $K_t$ and a $c$-cyclic connected simple graph. 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A graph $G$ is called $\\Theta_\\alpha$-maximal in a class of connected simple graphs $\\mathcal {G}$ if $\\Theta(G,\\alpha)$ is maximal among all graphs of $\\mathcal {G}$. A $t$-cone $c$-cyclic graph is the join of a complete graph $K_t$ and a $c$-cyclic connected simple graph. Let $\\pi=\\big(d_1,d_2,\\ldots,d_n\\big)$ and $\\pi'=\\big(d'_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06224","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06224/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":"1908.06224","created_at":"2026-07-04T23:58:13.559454+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06224v1","created_at":"2026-07-04T23:58:13.559454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06224","created_at":"2026-07-04T23:58:13.559454+00:00"},{"alias_kind":"pith_short_12","alias_value":"67KODJQ7HTYL","created_at":"2026-07-04T23:58:13.559454+00:00"},{"alias_kind":"pith_short_16","alias_value":"67KODJQ7HTYL2W7Q","created_at":"2026-07-04T23:58:13.559454+00:00"},{"alias_kind":"pith_short_8","alias_value":"67KODJQ7","created_at":"2026-07-04T23:58:13.559454+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/67KODJQ7HTYL2W7QXJTFW725QP","json":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP.json","graph_json":"https://pith.science/api/pith-number/67KODJQ7HTYL2W7QXJTFW725QP/graph.json","events_json":"https://pith.science/api/pith-number/67KODJQ7HTYL2W7QXJTFW725QP/events.json","paper":"https://pith.science/paper/67KODJQ7"},"agent_actions":{"view_html":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP","download_json":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP.json","view_paper":"https://pith.science/paper/67KODJQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06224&json=true","fetch_graph":"https://pith.science/api/pith-number/67KODJQ7HTYL2W7QXJTFW725QP/graph.json","fetch_events":"https://pith.science/api/pith-number/67KODJQ7HTYL2W7QXJTFW725QP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP/action/storage_attestation","attest_author":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP/action/author_attestation","sign_citation":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP/action/citation_signature","submit_replication":"https://pith.science/pith/67KODJQ7HTYL2W7QXJTFW725QP/action/replication_record"}},"created_at":"2026-07-04T23:58:13.559454+00:00","updated_at":"2026-07-04T23:58:13.559454+00:00"}