{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GAC3VMNKP36GVXSWH64FP3KQOE","short_pith_number":"pith:GAC3VMNK","canonical_record":{"source":{"id":"1802.02146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T15:29:51Z","cross_cats_sorted":[],"title_canon_sha256":"1ee991746617d894d38fe32a6d6c5c26d64a4de50f5b84e763e480e7bfee6678","abstract_canon_sha256":"32dfdfc00932c8abad540afa464ef7be02376d732c8919b32be696ab0d608b59"},"schema_version":"1.0"},"canonical_sha256":"3005bab1aa7efc6ade563fb857ed507110a387f9539f7bb185f58c7b97859501","source":{"kind":"arxiv","id":"1802.02146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02146","created_at":"2026-05-18T00:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02146v1","created_at":"2026-05-18T00:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02146","created_at":"2026-05-18T00:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"GAC3VMNKP36G","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GAC3VMNKP36GVXSW","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GAC3VMNK","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GAC3VMNKP36GVXSWH64FP3KQOE","target":"record","payload":{"canonical_record":{"source":{"id":"1802.02146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T15:29:51Z","cross_cats_sorted":[],"title_canon_sha256":"1ee991746617d894d38fe32a6d6c5c26d64a4de50f5b84e763e480e7bfee6678","abstract_canon_sha256":"32dfdfc00932c8abad540afa464ef7be02376d732c8919b32be696ab0d608b59"},"schema_version":"1.0"},"canonical_sha256":"3005bab1aa7efc6ade563fb857ed507110a387f9539f7bb185f58c7b97859501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:09.194712Z","signature_b64":"7o31sbxwP9YZN9r94ebtqTD7or55U4vkJVJ3V0Nfy0IipvB2cT6RxK7RzpoMnUfEOCd3jrimywyb2ANBTy6XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3005bab1aa7efc6ade563fb857ed507110a387f9539f7bb185f58c7b97859501","last_reissued_at":"2026-05-18T00:24:09.194127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:09.194127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.02146","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":"2026-05-18T00:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZwNdB6kBSvoQd6zSs6s2v/J3JnQUETKM2Jde2zvGK6WZZPhVtgOOHuDAmeqlZEBQRB83IGnYPvV4zsshY8RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:25:17.515363Z"},"content_sha256":"d0cb082bd50eaf802f4feceb182896d752651d9902b1ce64a1b37d51c708bc49","schema_version":"1.0","event_id":"sha256:d0cb082bd50eaf802f4feceb182896d752651d9902b1ce64a1b37d51c708bc49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GAC3VMNKP36GVXSWH64FP3KQOE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the irregularity of uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Lele Liu, Liying Kang","submitted_at":"2018-02-06T15:29:51Z","abstract_excerpt":"Let $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\\in V(H)$. Denote by $\\varepsilon(H)$ the difference of the spectral radius of $H$ and the average degree of $H$. Also, denote \\[ s(H)=\\sum_{i\\in V(H)}\\left|d_i-\\frac{rm}{n}\\right|,~ v(H)=\\frac{1}{n}\\sum_{i\\in V(H)}d_i^{\\frac{r}{r-1}}-\\left(\\frac{rm}{n}\\right)^{\\frac{r}{r-1}}. \\] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02146","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":"2026-05-18T00:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jssNh1E1RcJ4810LXarVc+jSo4W7s8tfZCxiMLLxdCRPKBY7IoyoZZ+fJfzhQVceilQPL0F+TIb8RDzWFXmGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:25:17.515720Z"},"content_sha256":"60ec5ccfdd145312898e8504ef9971cd9c37e451c8fad74a38d5f51484005788","schema_version":"1.0","event_id":"sha256:60ec5ccfdd145312898e8504ef9971cd9c37e451c8fad74a38d5f51484005788"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/bundle.json","state_url":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAC3VMNKP36GVXSWH64FP3KQOE/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":"2026-05-27T06:25:17Z","links":{"resolver":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE","bundle":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/bundle.json","state":"https://pith.science/pith/GAC3VMNKP36GVXSWH64FP3KQOE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAC3VMNKP36GVXSWH64FP3KQOE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GAC3VMNKP36GVXSWH64FP3KQOE","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":"32dfdfc00932c8abad540afa464ef7be02376d732c8919b32be696ab0d608b59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T15:29:51Z","title_canon_sha256":"1ee991746617d894d38fe32a6d6c5c26d64a4de50f5b84e763e480e7bfee6678"},"schema_version":"1.0","source":{"id":"1802.02146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02146","created_at":"2026-05-18T00:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02146v1","created_at":"2026-05-18T00:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02146","created_at":"2026-05-18T00:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"GAC3VMNKP36G","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GAC3VMNKP36GVXSW","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GAC3VMNK","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:60ec5ccfdd145312898e8504ef9971cd9c37e451c8fad74a38d5f51484005788","target":"graph","created_at":"2026-05-18T00:24:09Z","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 $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\\in V(H)$. Denote by $\\varepsilon(H)$ the difference of the spectral radius of $H$ and the average degree of $H$. Also, denote \\[ s(H)=\\sum_{i\\in V(H)}\\left|d_i-\\frac{rm}{n}\\right|,~ v(H)=\\frac{1}{n}\\sum_{i\\in V(H)}d_i^{\\frac{r}{r-1}}-\\left(\\frac{rm}{n}\\right)^{\\frac{r}{r-1}}. \\] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs.","authors_text":"Erfang Shan, Lele Liu, Liying Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T15:29:51Z","title":"On the irregularity of uniform hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02146","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:d0cb082bd50eaf802f4feceb182896d752651d9902b1ce64a1b37d51c708bc49","target":"record","created_at":"2026-05-18T00:24:09Z","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":"32dfdfc00932c8abad540afa464ef7be02376d732c8919b32be696ab0d608b59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-06T15:29:51Z","title_canon_sha256":"1ee991746617d894d38fe32a6d6c5c26d64a4de50f5b84e763e480e7bfee6678"},"schema_version":"1.0","source":{"id":"1802.02146","kind":"arxiv","version":1}},"canonical_sha256":"3005bab1aa7efc6ade563fb857ed507110a387f9539f7bb185f58c7b97859501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3005bab1aa7efc6ade563fb857ed507110a387f9539f7bb185f58c7b97859501","first_computed_at":"2026-05-18T00:24:09.194127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:09.194127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7o31sbxwP9YZN9r94ebtqTD7or55U4vkJVJ3V0Nfy0IipvB2cT6RxK7RzpoMnUfEOCd3jrimywyb2ANBTy6XAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:09.194712Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0cb082bd50eaf802f4feceb182896d752651d9902b1ce64a1b37d51c708bc49","sha256:60ec5ccfdd145312898e8504ef9971cd9c37e451c8fad74a38d5f51484005788"],"state_sha256":"7c5499c47c1d6b8800111f98034f043d94a2d941785651db94cc2816ebf81578"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xWOx2un9ii0Eh1LssLDEYHk+Pxv90TX9nHY23nc7BmcWB3HNSv1gF034Swv5T4xXM+BSNMP4SQ/OGZ4dc8qBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:25:17.517766Z","bundle_sha256":"c92809b5b7bdae818bb4bcbb8b7d588865eb456dde1c064b75df716185c63bad"}}