{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XZJH6AXZIY2RTZBAQRURVKG7TY","short_pith_number":"pith:XZJH6AXZ","canonical_record":{"source":{"id":"1511.09016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-29T14:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"f1dc0adffc54929d9ced07cf26adec5b9c0d49af2010cdaa4c9a7d00dfab1b58","abstract_canon_sha256":"b80d721c281221f27f730f7d356154f87322369b8d14f7d2ed4d3d0cc0878de0"},"schema_version":"1.0"},"canonical_sha256":"be527f02f9463519e42084691aa8df9e31cac12d7c148e35c8bd37f521827bc0","source":{"kind":"arxiv","id":"1511.09016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09016","created_at":"2026-05-18T01:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09016v1","created_at":"2026-05-18T01:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09016","created_at":"2026-05-18T01:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"XZJH6AXZIY2R","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZJH6AXZIY2RTZBA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZJH6AXZ","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XZJH6AXZIY2RTZBAQRURVKG7TY","target":"record","payload":{"canonical_record":{"source":{"id":"1511.09016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-29T14:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"f1dc0adffc54929d9ced07cf26adec5b9c0d49af2010cdaa4c9a7d00dfab1b58","abstract_canon_sha256":"b80d721c281221f27f730f7d356154f87322369b8d14f7d2ed4d3d0cc0878de0"},"schema_version":"1.0"},"canonical_sha256":"be527f02f9463519e42084691aa8df9e31cac12d7c148e35c8bd37f521827bc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:45.848682Z","signature_b64":"FK4u1MDGQfaChjgkoKjmmLR7siv+5h34jWPu3uQ4Yk3XYfG3IfQ/oVISOV3j8e57rSRtGNF0BFta0kfg603FAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be527f02f9463519e42084691aa8df9e31cac12d7c148e35c8bd37f521827bc0","last_reissued_at":"2026-05-18T01:25:45.848197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:45.848197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.09016","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SXNVwjX9bfKasMAjGf/CY8BOBC0TrWaiYQKPb7vhsiQ2gFSjc3xkDBnYq2zGrMd0+P8L5yE2ci1chY2QYZw8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:00:23.090260Z"},"content_sha256":"b7920323501ce3703a7c079fc124de10665afd03cb1d49dbd87721abfcdc4d19","schema_version":"1.0","event_id":"sha256:b7920323501ce3703a7c079fc124de10665afd03cb1d49dbd87721abfcdc4d19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XZJH6AXZIY2RTZBAQRURVKG7TY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the spectral radius of nonregular uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Changjiang Bu, Jiang Zhou, Lizhu Sun","submitted_at":"2015-11-29T14:32:09Z","abstract_excerpt":"Let $G$ be a connected uniform hypergraphs with maximum degree $\\Delta$, spectral radius $\\lambda$ and minimum H-eigenvalue $\\mu$. In this paper, we give some lower bounds for $\\Delta-\\lambda$, which extend the result of [S.M. Cioab\\u{a}, D.A. Gregory, V. Nikiforov, Extreme eigenvalues of nonregular graphs, J. Combin. Theory, Ser. B 97 (2007) 483-486] to hypergraphs. Applying these bounds, we also obtain a lower bound for $\\Delta+\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09016","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LjkfO8pXlO29QeRVkLaAYdnb/+ZeiheSr3PKTvFFeFOso6ToheQDoJLhG7HIX4LN9fBnVE+J4WvJDHZq/JvQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:00:23.090613Z"},"content_sha256":"5fa0bacc3953f30928dd7ca8b5ca9d0351e36a76e9400cf18c6f0e46b70042bb","schema_version":"1.0","event_id":"sha256:5fa0bacc3953f30928dd7ca8b5ca9d0351e36a76e9400cf18c6f0e46b70042bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZJH6AXZIY2RTZBAQRURVKG7TY/bundle.json","state_url":"https://pith.science/pith/XZJH6AXZIY2RTZBAQRURVKG7TY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZJH6AXZIY2RTZBAQRURVKG7TY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T23:00:23Z","links":{"resolver":"https://pith.science/pith/XZJH6AXZIY2RTZBAQRURVKG7TY","bundle":"https://pith.science/pith/XZJH6AXZIY2RTZBAQRURVKG7TY/bundle.json","state":"https://pith.science/pith/XZJH6AXZIY2RTZBAQRURVKG7TY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZJH6AXZIY2RTZBAQRURVKG7TY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XZJH6AXZIY2RTZBAQRURVKG7TY","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":"b80d721c281221f27f730f7d356154f87322369b8d14f7d2ed4d3d0cc0878de0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-29T14:32:09Z","title_canon_sha256":"f1dc0adffc54929d9ced07cf26adec5b9c0d49af2010cdaa4c9a7d00dfab1b58"},"schema_version":"1.0","source":{"id":"1511.09016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09016","created_at":"2026-05-18T01:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09016v1","created_at":"2026-05-18T01:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09016","created_at":"2026-05-18T01:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"XZJH6AXZIY2R","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XZJH6AXZIY2RTZBA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XZJH6AXZ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:5fa0bacc3953f30928dd7ca8b5ca9d0351e36a76e9400cf18c6f0e46b70042bb","target":"graph","created_at":"2026-05-18T01:25:45Z","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"},"paper":{"abstract_excerpt":"Let $G$ be a connected uniform hypergraphs with maximum degree $\\Delta$, spectral radius $\\lambda$ and minimum H-eigenvalue $\\mu$. In this paper, we give some lower bounds for $\\Delta-\\lambda$, which extend the result of [S.M. Cioab\\u{a}, D.A. Gregory, V. Nikiforov, Extreme eigenvalues of nonregular graphs, J. Combin. Theory, Ser. B 97 (2007) 483-486] to hypergraphs. Applying these bounds, we also obtain a lower bound for $\\Delta+\\mu$.","authors_text":"Changjiang Bu, Jiang Zhou, Lizhu Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-29T14:32:09Z","title":"On the spectral radius of nonregular uniform hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09016","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:b7920323501ce3703a7c079fc124de10665afd03cb1d49dbd87721abfcdc4d19","target":"record","created_at":"2026-05-18T01:25:45Z","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":"b80d721c281221f27f730f7d356154f87322369b8d14f7d2ed4d3d0cc0878de0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-29T14:32:09Z","title_canon_sha256":"f1dc0adffc54929d9ced07cf26adec5b9c0d49af2010cdaa4c9a7d00dfab1b58"},"schema_version":"1.0","source":{"id":"1511.09016","kind":"arxiv","version":1}},"canonical_sha256":"be527f02f9463519e42084691aa8df9e31cac12d7c148e35c8bd37f521827bc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be527f02f9463519e42084691aa8df9e31cac12d7c148e35c8bd37f521827bc0","first_computed_at":"2026-05-18T01:25:45.848197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:45.848197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FK4u1MDGQfaChjgkoKjmmLR7siv+5h34jWPu3uQ4Yk3XYfG3IfQ/oVISOV3j8e57rSRtGNF0BFta0kfg603FAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:45.848682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7920323501ce3703a7c079fc124de10665afd03cb1d49dbd87721abfcdc4d19","sha256:5fa0bacc3953f30928dd7ca8b5ca9d0351e36a76e9400cf18c6f0e46b70042bb"],"state_sha256":"22acb711e63f7da71ffceaacfb7cc89c04863f0803c8b094691ffdbd7fae260d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/KQxPLvFzT8K3Mukia85tVpd5oDdMB9rQwMGiFjt37RbXbObxJhBaJdaScawqHD/LqxcmIkF16BDzfHkFwFBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:00:23.092585Z","bundle_sha256":"4963024de02554b4e5d7687d6ad58a8abe88c1489e95ea6ef971619a5efcfa20"}}