{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AMET4KLEI44KQGZ2EVG6VDCEUN","short_pith_number":"pith:AMET4KLE","canonical_record":{"source":{"id":"1406.5404","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-20T14:34:28Z","cross_cats_sorted":[],"title_canon_sha256":"c59dcef4e35b1b118a59ef9382773efbc4af39a57de0db8e318d7df8e8e5d12c","abstract_canon_sha256":"50f3225e6decc8a2b5889829c9366682e5648fb231c9b399c08efc2950442434"},"schema_version":"1.0"},"canonical_sha256":"03093e29644738a81b3a254dea8c44a37d29a2b394c543a5e58226fa7aa5a764","source":{"kind":"arxiv","id":"1406.5404","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5404","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5404v4","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5404","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"AMET4KLEI44K","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AMET4KLEI44KQGZ2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AMET4KLE","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AMET4KLEI44KQGZ2EVG6VDCEUN","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5404","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-20T14:34:28Z","cross_cats_sorted":[],"title_canon_sha256":"c59dcef4e35b1b118a59ef9382773efbc4af39a57de0db8e318d7df8e8e5d12c","abstract_canon_sha256":"50f3225e6decc8a2b5889829c9366682e5648fb231c9b399c08efc2950442434"},"schema_version":"1.0"},"canonical_sha256":"03093e29644738a81b3a254dea8c44a37d29a2b394c543a5e58226fa7aa5a764","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.366002Z","signature_b64":"7HymdmemeZQZSxdsqUPbZ5rjFBzL7rA/JgfBycmGzyHuQgchatRWlddXYgEJozEYe4f5kI9mDMVhdHSFUE9FBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03093e29644738a81b3a254dea8c44a37d29a2b394c543a5e58226fa7aa5a764","last_reissued_at":"2026-05-18T00:54:58.365584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.365584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5404","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zmkf+QR6A/dIk+tZleiekEsOKP5Wrvgvo1gTxTRyNBclwPRHDSww2Yc5j9EMvrga58D/mnVE5uq71e/8cUyTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:02:01.775491Z"},"content_sha256":"1cb8db4f279bacdc244e2ffb1ae0f5fc09e194fa54213e7e78772f030c4a4165","schema_version":"1.0","event_id":"sha256:1cb8db4f279bacdc244e2ffb1ae0f5fc09e194fa54213e7e78772f030c4a4165"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AMET4KLEI44KQGZ2EVG6VDCEUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral radius and traceability of connected claw-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Binlong Li, Bo Ning","submitted_at":"2014-06-20T14:34:28Z","abstract_excerpt":"Let $G$ be a connected claw-free graph on $n$ vertices and $\\overline{G}$ be its complement graph. Let $\\mu(G)$ be the spectral radius of $G$. Denote by $N_{n-3,3}$ the graph consisting of $K_{n-3}$ and three disjoint pendent edges. In this note we prove that: (1) If $\\mu(G)\\geq n-4$, then $G$ is traceable unless $G=N_{n-3,3}$. (2) If $\\mu(\\overline{G})\\leq \\mu(\\overline{N_{n-3,3}})$ and $n\\geq 24$, then $G$ is traceable unless $G=N_{n-3,3}$. Our works are counterparts on claw-free graphs of previous theorems due to Lu et al., and Fiedler and Nikiforov, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5404","kind":"arxiv","version":4},"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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFO4Xj9NNHQpDSw4rJOWYf+g+s/Jt3lot3bVE+tO+cRbMyiuQ8sLtLGflOXQk1jpTfqFjy7yvQsKFAal/VNYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:02:01.775841Z"},"content_sha256":"1624386b6ee5150bceb1b17ed810d230322545300ef14fbe783b259ec0ad0706","schema_version":"1.0","event_id":"sha256:1624386b6ee5150bceb1b17ed810d230322545300ef14fbe783b259ec0ad0706"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/bundle.json","state_url":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/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":"2026-06-04T15:02:01Z","links":{"resolver":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN","bundle":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/bundle.json","state":"https://pith.science/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AMET4KLEI44KQGZ2EVG6VDCEUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AMET4KLEI44KQGZ2EVG6VDCEUN","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":"50f3225e6decc8a2b5889829c9366682e5648fb231c9b399c08efc2950442434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-20T14:34:28Z","title_canon_sha256":"c59dcef4e35b1b118a59ef9382773efbc4af39a57de0db8e318d7df8e8e5d12c"},"schema_version":"1.0","source":{"id":"1406.5404","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5404","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5404v4","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5404","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"AMET4KLEI44K","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AMET4KLEI44KQGZ2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AMET4KLE","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:1624386b6ee5150bceb1b17ed810d230322545300ef14fbe783b259ec0ad0706","target":"graph","created_at":"2026-05-18T00:54:58Z","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 claw-free graph on $n$ vertices and $\\overline{G}$ be its complement graph. Let $\\mu(G)$ be the spectral radius of $G$. Denote by $N_{n-3,3}$ the graph consisting of $K_{n-3}$ and three disjoint pendent edges. In this note we prove that: (1) If $\\mu(G)\\geq n-4$, then $G$ is traceable unless $G=N_{n-3,3}$. (2) If $\\mu(\\overline{G})\\leq \\mu(\\overline{N_{n-3,3}})$ and $n\\geq 24$, then $G$ is traceable unless $G=N_{n-3,3}$. Our works are counterparts on claw-free graphs of previous theorems due to Lu et al., and Fiedler and Nikiforov, respectively.","authors_text":"Binlong Li, Bo Ning","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-20T14:34:28Z","title":"Spectral radius and traceability of connected claw-free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5404","kind":"arxiv","version":4},"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":"sha256:1cb8db4f279bacdc244e2ffb1ae0f5fc09e194fa54213e7e78772f030c4a4165","target":"record","created_at":"2026-05-18T00:54:58Z","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":"50f3225e6decc8a2b5889829c9366682e5648fb231c9b399c08efc2950442434","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-20T14:34:28Z","title_canon_sha256":"c59dcef4e35b1b118a59ef9382773efbc4af39a57de0db8e318d7df8e8e5d12c"},"schema_version":"1.0","source":{"id":"1406.5404","kind":"arxiv","version":4}},"canonical_sha256":"03093e29644738a81b3a254dea8c44a37d29a2b394c543a5e58226fa7aa5a764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03093e29644738a81b3a254dea8c44a37d29a2b394c543a5e58226fa7aa5a764","first_computed_at":"2026-05-18T00:54:58.365584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:58.365584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7HymdmemeZQZSxdsqUPbZ5rjFBzL7rA/JgfBycmGzyHuQgchatRWlddXYgEJozEYe4f5kI9mDMVhdHSFUE9FBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:58.366002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5404","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cb8db4f279bacdc244e2ffb1ae0f5fc09e194fa54213e7e78772f030c4a4165","sha256:1624386b6ee5150bceb1b17ed810d230322545300ef14fbe783b259ec0ad0706"],"state_sha256":"b9c85749169d81ecb930f1aaedd28dee75f4b5ae7d00799cfe07a7e82a5973a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W9TV6EPZWx92y6H0ti+ExHqdiYoA9eW1ma7mweuVzAox0f/h53ccjT19a5QOKZhD43Rh0Who9yYGFTtv2NqiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:02:01.778172Z","bundle_sha256":"00b0ef3a694e9a4d9183bd2bf3dd8944e697576201c39b05d125d1696684f71c"}}