{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JWPRGBXT5OWOP7WYEG2KD2LGL4","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":"31750074cfdb090b75e58a0a765001a4c1cbc5d546035f0d86930d853c2bca5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-30T09:10:28Z","title_canon_sha256":"c9b611ee50d79629cc5758a14d62257e7e6c0f573b70b060f0a443978382a216"},"schema_version":"1.0","source":{"id":"2505.24381","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24381","created_at":"2026-07-05T11:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24381v1","created_at":"2026-07-05T11:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24381","created_at":"2026-07-05T11:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"JWPRGBXT5OWO","created_at":"2026-07-05T11:12:48Z"},{"alias_kind":"pith_short_16","alias_value":"JWPRGBXT5OWOP7WY","created_at":"2026-07-05T11:12:48Z"},{"alias_kind":"pith_short_8","alias_value":"JWPRGBXT","created_at":"2026-07-05T11:12:48Z"}],"graph_snapshots":[{"event_id":"sha256:0c4ac168ce3e68e5d250ca5f2d27dc27979f8589654bcab42282bc9420ba0fff","target":"graph","created_at":"2026-07-05T11:12:48Z","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/2505.24381/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The independence polynomial of a graph is termed {\\it stable} if all its roots are located in the left half-plane $\\{z \\in \\mathbb{C} : \\mathrm{Re}(z) \\leq 0\\}$, and the graph itself is also referred to as stable. Brown and Cameron (Electron. J. Combin. 25(1) (2018) \\#P1.46) proved that the complete bipartite graph $K_{1,n}$ is stable and posed the question: \\textbf{Are all complete bipartite graphs stable?}\n  We answer this question by establishing the following results:\n  \\begin{itemize}\n  \\item The complete bipartite graphs $K_{2,n}$ and $K_{3,n}$ are stable.\n  \\item For any integer $k\\geq0","authors_text":"Bo Ning, Guo Chen, Jianhua Tu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-30T09:10:28Z","title":"The stability of independence polynomials of complete bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24381","kind":"arxiv","version":1},"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":"sha256:2dd8595039f1517b5e2ca41ae001518dabb9d4d90cb0384a851ffd78624d4ec4","target":"record","created_at":"2026-07-05T11:12:48Z","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":"31750074cfdb090b75e58a0a765001a4c1cbc5d546035f0d86930d853c2bca5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-30T09:10:28Z","title_canon_sha256":"c9b611ee50d79629cc5758a14d62257e7e6c0f573b70b060f0a443978382a216"},"schema_version":"1.0","source":{"id":"2505.24381","kind":"arxiv","version":1}},"canonical_sha256":"4d9f1306f3ebace7fed821b4a1e9665f212946f361a85ff4194dadefa6b2202a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d9f1306f3ebace7fed821b4a1e9665f212946f361a85ff4194dadefa6b2202a","first_computed_at":"2026-07-05T11:12:48.034158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:48.034158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6yBGmQx/PLvqtYxQmXwJ1l8CZo7PCw0VdJEP6HpMbIHoC0iI3Z4Q/Wn5frR8ntpTVYOQWinuEjlZhD3OjMhAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:48.034681Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24381","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2dd8595039f1517b5e2ca41ae001518dabb9d4d90cb0384a851ffd78624d4ec4","sha256:0c4ac168ce3e68e5d250ca5f2d27dc27979f8589654bcab42282bc9420ba0fff"],"state_sha256":"158b6cfe8103a54251a0569e6200072167c94f8265f5e390571410571f2154f6"}