{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7EHXU7M7AGWN75AP6DPWQVWT6L","short_pith_number":"pith:7EHXU7M7","canonical_record":{"source":{"id":"1611.07185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-22T08:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"25b4dbbb254dd709299c254c717bd651f595156c682f7b64e5c96af5ebb2092b","abstract_canon_sha256":"dfeb4dc38c3b323c743a5f022a0f05094fdd0f7c4d07cc4661e7fe832fea1d57"},"schema_version":"1.0"},"canonical_sha256":"f90f7a7d9f01acdff40ff0df6856d3f2d960925c972876cd88ef4322c6733da8","source":{"kind":"arxiv","id":"1611.07185","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07185","created_at":"2026-05-18T00:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07185v1","created_at":"2026-05-18T00:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07185","created_at":"2026-05-18T00:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"7EHXU7M7AGWN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EHXU7M7AGWN75AP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EHXU7M7","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7EHXU7M7AGWN75AP6DPWQVWT6L","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-22T08:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"25b4dbbb254dd709299c254c717bd651f595156c682f7b64e5c96af5ebb2092b","abstract_canon_sha256":"dfeb4dc38c3b323c743a5f022a0f05094fdd0f7c4d07cc4661e7fe832fea1d57"},"schema_version":"1.0"},"canonical_sha256":"f90f7a7d9f01acdff40ff0df6856d3f2d960925c972876cd88ef4322c6733da8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:24.664065Z","signature_b64":"CtgztmdSh44NgkHjB079J9PvotH9eJls4VmYKEv2ReZbw4ukhbDYXauG0TDKZPPOBvXeWGOYoyVg7xSPxZaoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f90f7a7d9f01acdff40ff0df6856d3f2d960925c972876cd88ef4322c6733da8","last_reissued_at":"2026-05-18T00:57:24.663493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:24.663493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07185","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":"2026-05-18T00:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGNy+El2n0oaJCoLMCvdWbgPK2WNG2ywCCjw27gfZUrRxRDi1mq5OYy2x00w3GAmcwKzMXv1zZ/mqosng+XXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:48:34.269142Z"},"content_sha256":"6cc0141f6ec933149eed0f97a69aa34268c3e4ee247b0d5de271cddaba2aef1f","schema_version":"1.0","event_id":"sha256:6cc0141f6ec933149eed0f97a69aa34268c3e4ee247b0d5de271cddaba2aef1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7EHXU7M7AGWN75AP6DPWQVWT6L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp lower bounds on the spectral radius of uniform hypergraphs concerning degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Erfang Shan, Lele Liu, Liying Kang","submitted_at":"2016-11-22T08:10:46Z","abstract_excerpt":"Let $\\mathcal{A}(H)$ and $\\mathcal{Q}(H)$ be the adjacency tensor and signless Laplacian tensor of an $r$-uniform hypergraph $H$. Denote by $\\rho(H)$ and $\\rho(\\mathcal{Q}(H))$ the spectral radii of $\\mathcal{A}(H)$ and $\\mathcal{Q}(H)$, respectively. In this paper we present a lower bound on $\\rho(H)$ in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound, which solves a problem posed by Nikiforov [V. Nikiforov, Analytic methods for uniform hypergraphs, Linear Algebra Appl. 457 (2014) 455-535]. Also, we prove a lower bound on $\\rho(\\mathcal{Q}(H))$ concern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07185","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":"2026-05-18T00:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OTlTei25bC5DuiDSrX5wa8WsBOnUW5pBE4SjYI/luf0S/nNcKYhpnl92vesiUExC0MVxaYqP2l3FD4VVfnyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:48:34.269833Z"},"content_sha256":"89d6a5baf257f2f09486d1eae28f257cbd181a69db7faf16c07bdd19f1858fa6","schema_version":"1.0","event_id":"sha256:89d6a5baf257f2f09486d1eae28f257cbd181a69db7faf16c07bdd19f1858fa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EHXU7M7AGWN75AP6DPWQVWT6L/bundle.json","state_url":"https://pith.science/pith/7EHXU7M7AGWN75AP6DPWQVWT6L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EHXU7M7AGWN75AP6DPWQVWT6L/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":"2026-05-27T04:48:34Z","links":{"resolver":"https://pith.science/pith/7EHXU7M7AGWN75AP6DPWQVWT6L","bundle":"https://pith.science/pith/7EHXU7M7AGWN75AP6DPWQVWT6L/bundle.json","state":"https://pith.science/pith/7EHXU7M7AGWN75AP6DPWQVWT6L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EHXU7M7AGWN75AP6DPWQVWT6L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7EHXU7M7AGWN75AP6DPWQVWT6L","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":"dfeb4dc38c3b323c743a5f022a0f05094fdd0f7c4d07cc4661e7fe832fea1d57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-22T08:10:46Z","title_canon_sha256":"25b4dbbb254dd709299c254c717bd651f595156c682f7b64e5c96af5ebb2092b"},"schema_version":"1.0","source":{"id":"1611.07185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07185","created_at":"2026-05-18T00:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07185v1","created_at":"2026-05-18T00:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07185","created_at":"2026-05-18T00:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"7EHXU7M7AGWN","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EHXU7M7AGWN75AP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EHXU7M7","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:89d6a5baf257f2f09486d1eae28f257cbd181a69db7faf16c07bdd19f1858fa6","target":"graph","created_at":"2026-05-18T00:57:24Z","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 $\\mathcal{A}(H)$ and $\\mathcal{Q}(H)$ be the adjacency tensor and signless Laplacian tensor of an $r$-uniform hypergraph $H$. Denote by $\\rho(H)$ and $\\rho(\\mathcal{Q}(H))$ the spectral radii of $\\mathcal{A}(H)$ and $\\mathcal{Q}(H)$, respectively. In this paper we present a lower bound on $\\rho(H)$ in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound, which solves a problem posed by Nikiforov [V. Nikiforov, Analytic methods for uniform hypergraphs, Linear Algebra Appl. 457 (2014) 455-535]. Also, we prove a lower bound on $\\rho(\\mathcal{Q}(H))$ concern","authors_text":"Erfang Shan, Lele Liu, Liying Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-22T08:10:46Z","title":"Sharp lower bounds on the spectral radius of uniform hypergraphs concerning degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07185","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":"sha256:6cc0141f6ec933149eed0f97a69aa34268c3e4ee247b0d5de271cddaba2aef1f","target":"record","created_at":"2026-05-18T00:57:24Z","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":"dfeb4dc38c3b323c743a5f022a0f05094fdd0f7c4d07cc4661e7fe832fea1d57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-11-22T08:10:46Z","title_canon_sha256":"25b4dbbb254dd709299c254c717bd651f595156c682f7b64e5c96af5ebb2092b"},"schema_version":"1.0","source":{"id":"1611.07185","kind":"arxiv","version":1}},"canonical_sha256":"f90f7a7d9f01acdff40ff0df6856d3f2d960925c972876cd88ef4322c6733da8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f90f7a7d9f01acdff40ff0df6856d3f2d960925c972876cd88ef4322c6733da8","first_computed_at":"2026-05-18T00:57:24.663493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:24.663493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CtgztmdSh44NgkHjB079J9PvotH9eJls4VmYKEv2ReZbw4ukhbDYXauG0TDKZPPOBvXeWGOYoyVg7xSPxZaoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:24.664065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cc0141f6ec933149eed0f97a69aa34268c3e4ee247b0d5de271cddaba2aef1f","sha256:89d6a5baf257f2f09486d1eae28f257cbd181a69db7faf16c07bdd19f1858fa6"],"state_sha256":"5293f2f7527e7a7be3166867fdc95b4711fab3b9126a5d0a7d778cb8d6c160a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xwKSw2Y82ESQw3RMGvI4gC5f0yg5GWxxXBI7OtGEXo3gsw+/3PFJO1uyTdxw1iqLxwRl8zcx1j0EzyFHHo56Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:48:34.273942Z","bundle_sha256":"80871d2d75ca9981be6e223f46b35fca1c38ba66ab26b4486745915cab15a282"}}