{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:74JFYCUWYFU3AIOZC25DTXBLXL","short_pith_number":"pith:74JFYCUW","canonical_record":{"source":{"id":"1807.11224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T08:23:18Z","cross_cats_sorted":[],"title_canon_sha256":"7f6372fe80ed008b24dee368248c75dc20f98d1f98b781d42438e11cb25561e3","abstract_canon_sha256":"72c215286b88324eb5b09d7b791beac3f59efba75537592753bd62d0c10c8e26"},"schema_version":"1.0"},"canonical_sha256":"ff125c0a96c169b021d916ba39dc2bbafc30c9e8bb4927243a58314d5adbea4c","source":{"kind":"arxiv","id":"1807.11224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11224","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11224v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11224","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"74JFYCUWYFU3","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"74JFYCUWYFU3AIOZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"74JFYCUW","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:74JFYCUWYFU3AIOZC25DTXBLXL","target":"record","payload":{"canonical_record":{"source":{"id":"1807.11224","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T08:23:18Z","cross_cats_sorted":[],"title_canon_sha256":"7f6372fe80ed008b24dee368248c75dc20f98d1f98b781d42438e11cb25561e3","abstract_canon_sha256":"72c215286b88324eb5b09d7b791beac3f59efba75537592753bd62d0c10c8e26"},"schema_version":"1.0"},"canonical_sha256":"ff125c0a96c169b021d916ba39dc2bbafc30c9e8bb4927243a58314d5adbea4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:32.576390Z","signature_b64":"rOSof3L72bt+4eummRQ74FQIlVE5HBgCbujhJGPpqiu5kGRx3ucZ8z8215k2htNnf9gClgPDeYt3rBxRsPufDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff125c0a96c169b021d916ba39dc2bbafc30c9e8bb4927243a58314d5adbea4c","last_reissued_at":"2026-05-18T00:09:32.575845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:32.575845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.11224","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KbDxiUits76B9fMgNX6SukYUsIx8SUIglwHaP8wGAGBkQkddAJHcFKfMhD4QGfPoNq9OJnU9NNwi3JVje+cJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:50:55.820672Z"},"content_sha256":"9a235d067b116e0f366b579510b6ef0f491ac655ab3d52a1623ea0e6d60acb89","schema_version":"1.0","event_id":"sha256:9a235d067b116e0f366b579510b6ef0f491ac655ab3d52a1623ea0e6d60acb89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:74JFYCUWYFU3AIOZC25DTXBLXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lihua You, Xiaohua Huang, Xiying Yuan","submitted_at":"2018-07-30T08:23:18Z","abstract_excerpt":"In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor. We also apply these bounds to the adjacency spectral radius and signless Laplacian spectral radius of a uniform hypergraph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11224","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":"2026-05-18T00:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XbGWPaMr/yGxTQ1H6eXpa0X0R3UAhF62RRf5l6qkWXCtdWzuH5zGekhNQ4NSOeB+Tt86+4atZeCuQSCP0OeGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:50:55.821019Z"},"content_sha256":"abb9c62a793ec1de7c75b0a4d775a1c0322328c36e24a416fbb153cc1466589f","schema_version":"1.0","event_id":"sha256:abb9c62a793ec1de7c75b0a4d775a1c0322328c36e24a416fbb153cc1466589f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74JFYCUWYFU3AIOZC25DTXBLXL/bundle.json","state_url":"https://pith.science/pith/74JFYCUWYFU3AIOZC25DTXBLXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74JFYCUWYFU3AIOZC25DTXBLXL/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":"2026-06-10T21:50:55Z","links":{"resolver":"https://pith.science/pith/74JFYCUWYFU3AIOZC25DTXBLXL","bundle":"https://pith.science/pith/74JFYCUWYFU3AIOZC25DTXBLXL/bundle.json","state":"https://pith.science/pith/74JFYCUWYFU3AIOZC25DTXBLXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74JFYCUWYFU3AIOZC25DTXBLXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:74JFYCUWYFU3AIOZC25DTXBLXL","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":"72c215286b88324eb5b09d7b791beac3f59efba75537592753bd62d0c10c8e26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T08:23:18Z","title_canon_sha256":"7f6372fe80ed008b24dee368248c75dc20f98d1f98b781d42438e11cb25561e3"},"schema_version":"1.0","source":{"id":"1807.11224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11224","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11224v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11224","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"74JFYCUWYFU3","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"74JFYCUWYFU3AIOZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"74JFYCUW","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:abb9c62a793ec1de7c75b0a4d775a1c0322328c36e24a416fbb153cc1466589f","target":"graph","created_at":"2026-05-18T00:09:32Z","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":"In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor. We also apply these bounds to the adjacency spectral radius and signless Laplacian spectral radius of a uniform hypergraph.","authors_text":"Lihua You, Xiaohua Huang, Xiying Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T08:23:18Z","title":"Sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11224","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":"sha256:9a235d067b116e0f366b579510b6ef0f491ac655ab3d52a1623ea0e6d60acb89","target":"record","created_at":"2026-05-18T00:09:32Z","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":"72c215286b88324eb5b09d7b791beac3f59efba75537592753bd62d0c10c8e26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-30T08:23:18Z","title_canon_sha256":"7f6372fe80ed008b24dee368248c75dc20f98d1f98b781d42438e11cb25561e3"},"schema_version":"1.0","source":{"id":"1807.11224","kind":"arxiv","version":1}},"canonical_sha256":"ff125c0a96c169b021d916ba39dc2bbafc30c9e8bb4927243a58314d5adbea4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff125c0a96c169b021d916ba39dc2bbafc30c9e8bb4927243a58314d5adbea4c","first_computed_at":"2026-05-18T00:09:32.575845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:32.575845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOSof3L72bt+4eummRQ74FQIlVE5HBgCbujhJGPpqiu5kGRx3ucZ8z8215k2htNnf9gClgPDeYt3rBxRsPufDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:32.576390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a235d067b116e0f366b579510b6ef0f491ac655ab3d52a1623ea0e6d60acb89","sha256:abb9c62a793ec1de7c75b0a4d775a1c0322328c36e24a416fbb153cc1466589f"],"state_sha256":"2ea7224a4627b7cd7b2f2d52f47d0cbdca8f7fd2ebe12b02677dc464014247b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w24cS9+qRtScJxQ7CNVwFltqLqqXjTlFXmKsJJpim9WFBzqtYk1Dx4Ro45ivKAz+OCaCrhcWOox7w+pDkNEhAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:50:55.823173Z","bundle_sha256":"443fbf5bfc2d673e379446dd9ae0b47948b7e2ea20235d62767de14c1871840a"}}