{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FENJDL7XNHT4FKO6K5VJMRGCYB","short_pith_number":"pith:FENJDL7X","canonical_record":{"source":{"id":"1311.3096","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T12:03:02Z","cross_cats_sorted":[],"title_canon_sha256":"238f7f74c467e6e8acc7454a3c537974e9538e8ccbf315ad2a4463356f1650a3","abstract_canon_sha256":"81646527728e78a2a33c5b426d22194e2b86ac2e06bbd6ee2e61e4bd9ce77ad1"},"schema_version":"1.0"},"canonical_sha256":"291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154","source":{"kind":"arxiv","id":"1311.3096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3096","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3096v1","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3096","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"FENJDL7XNHT4","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FENJDL7XNHT4FKO6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FENJDL7X","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FENJDL7XNHT4FKO6K5VJMRGCYB","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3096","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T12:03:02Z","cross_cats_sorted":[],"title_canon_sha256":"238f7f74c467e6e8acc7454a3c537974e9538e8ccbf315ad2a4463356f1650a3","abstract_canon_sha256":"81646527728e78a2a33c5b426d22194e2b86ac2e06bbd6ee2e61e4bd9ce77ad1"},"schema_version":"1.0"},"canonical_sha256":"291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:13.111590Z","signature_b64":"NdnkxV7bmWcCqvHy7sxsvWWenT8uvImAClTudICisWMIDBckx+wANYc+bZIV1Y1q9LVM2mEQcHU4DOR5qsPQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154","last_reissued_at":"2026-05-18T03:07:13.110810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:13.110810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3096","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":"2026-05-18T03:07:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rIiYDA3/TN4JepoL6uCCI0EaCkg0YF4j862ex3Zpn3PtpEbTyUAZ+v0JbbZZ9JEOP2D/dksK9v/Srkq7maWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:03:43.506121Z"},"content_sha256":"808d7802f74fdd5dcc737ea07cabfff0c5615eeac9d1407021bba52a36691f3c","schema_version":"1.0","event_id":"sha256:808d7802f74fdd5dcc737ea07cabfff0c5615eeac9d1407021bba52a36691f3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FENJDL7XNHT4FKO6K5VJMRGCYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lower bound of the least signless Laplacian eigenvalue of a graph","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanglong Yu, Shu-Guang Guo, Yong-Gao Chen","submitted_at":"2013-11-13T12:03:02Z","abstract_excerpt":"Let $G$ be a simple connected graph on $n$ vertices and $m$ edges. In [Linear Algebra Appl. 435 (2011) 2570-2584], Lima et al. posed the following conjecture on the least eigenvalue $q_n(G)$ of the signless Laplacian of $G$: $\\displaystyle q_n(G)\\ge {2m}/{(n-1)}-n+2$. In this paper we prove a stronger result: For any graph with $n$ vertices and $m$ edges, we have $\\displaystyle q_n(G)\\ge {2m}/{(n-2)}-n+1 (n\\ge 6)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3096","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":"2026-05-18T03:07:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9FRD2yfzmKgSMhffF6UtMVb2m7rObFCWx6PWmPeS7ZIow9ceDoiJg5nSXDLJBLBrUaVK51OwS/RYYhjLTQdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:03:43.506850Z"},"content_sha256":"164ae35f1d90f4274f1e2fc8a088c7c1c9b6babc831631c5f3ee1bf883bf65b9","schema_version":"1.0","event_id":"sha256:164ae35f1d90f4274f1e2fc8a088c7c1c9b6babc831631c5f3ee1bf883bf65b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FENJDL7XNHT4FKO6K5VJMRGCYB/bundle.json","state_url":"https://pith.science/pith/FENJDL7XNHT4FKO6K5VJMRGCYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FENJDL7XNHT4FKO6K5VJMRGCYB/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":"2026-06-06T16:03:43Z","links":{"resolver":"https://pith.science/pith/FENJDL7XNHT4FKO6K5VJMRGCYB","bundle":"https://pith.science/pith/FENJDL7XNHT4FKO6K5VJMRGCYB/bundle.json","state":"https://pith.science/pith/FENJDL7XNHT4FKO6K5VJMRGCYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FENJDL7XNHT4FKO6K5VJMRGCYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FENJDL7XNHT4FKO6K5VJMRGCYB","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":"81646527728e78a2a33c5b426d22194e2b86ac2e06bbd6ee2e61e4bd9ce77ad1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T12:03:02Z","title_canon_sha256":"238f7f74c467e6e8acc7454a3c537974e9538e8ccbf315ad2a4463356f1650a3"},"schema_version":"1.0","source":{"id":"1311.3096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3096","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3096v1","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3096","created_at":"2026-05-18T03:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"FENJDL7XNHT4","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FENJDL7XNHT4FKO6","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FENJDL7X","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:164ae35f1d90f4274f1e2fc8a088c7c1c9b6babc831631c5f3ee1bf883bf65b9","target":"graph","created_at":"2026-05-18T03:07:13Z","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 simple connected graph on $n$ vertices and $m$ edges. In [Linear Algebra Appl. 435 (2011) 2570-2584], Lima et al. posed the following conjecture on the least eigenvalue $q_n(G)$ of the signless Laplacian of $G$: $\\displaystyle q_n(G)\\ge {2m}/{(n-1)}-n+2$. In this paper we prove a stronger result: For any graph with $n$ vertices and $m$ edges, we have $\\displaystyle q_n(G)\\ge {2m}/{(n-2)}-n+1 (n\\ge 6)$.","authors_text":"Guanglong Yu, Shu-Guang Guo, Yong-Gao Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T12:03:02Z","title":"A lower bound of the least signless Laplacian eigenvalue of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3096","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":"sha256:808d7802f74fdd5dcc737ea07cabfff0c5615eeac9d1407021bba52a36691f3c","target":"record","created_at":"2026-05-18T03:07:13Z","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":"81646527728e78a2a33c5b426d22194e2b86ac2e06bbd6ee2e61e4bd9ce77ad1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CO","submitted_at":"2013-11-13T12:03:02Z","title_canon_sha256":"238f7f74c467e6e8acc7454a3c537974e9538e8ccbf315ad2a4463356f1650a3"},"schema_version":"1.0","source":{"id":"1311.3096","kind":"arxiv","version":1}},"canonical_sha256":"291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"291a91aff769e7c2a9de576a9644c2c04a2cda073fc855511a1cf498ba861154","first_computed_at":"2026-05-18T03:07:13.110810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:13.110810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NdnkxV7bmWcCqvHy7sxsvWWenT8uvImAClTudICisWMIDBckx+wANYc+bZIV1Y1q9LVM2mEQcHU4DOR5qsPQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:13.111590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:808d7802f74fdd5dcc737ea07cabfff0c5615eeac9d1407021bba52a36691f3c","sha256:164ae35f1d90f4274f1e2fc8a088c7c1c9b6babc831631c5f3ee1bf883bf65b9"],"state_sha256":"8bc089472fc07b1a28643547654091b80ca039f9d167653f30fcc642d9e639dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3MV88p9GMqnu1DDRuZ/m7TqkQuz3hwbIDHxTP2q5FQwdvY2zn6FPzXHX1Vilasfylk0UuHzlAoePwEdbgfzBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:03:43.510591Z","bundle_sha256":"7f46120291c1271e34ba7bf996d21b7a6d149f08ea33901207ec9fd3d2ce35a4"}}