{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GQNVQ4FY6HQ242TSIDOMBRXF5G","short_pith_number":"pith:GQNVQ4FY","canonical_record":{"source":{"id":"1506.02435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-08T10:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"f038f5641681ae81f74df60867349a308b7e6f6050504b79f7bc59701118fbab","abstract_canon_sha256":"f8cfcc22d1042a4b34b9aa49abdd7dbe99470d3e3484d6a30b8b121c3a3a6cfb"},"schema_version":"1.0"},"canonical_sha256":"341b5870b8f1e1ae6a7240dcc0c6e5e9ab90bbaefb9b2edc1126d848337af765","source":{"kind":"arxiv","id":"1506.02435","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02435","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02435v1","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02435","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"pith_short_12","alias_value":"GQNVQ4FY6HQ2","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GQNVQ4FY6HQ242TS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GQNVQ4FY","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GQNVQ4FY6HQ242TSIDOMBRXF5G","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-08T10:57:00Z","cross_cats_sorted":[],"title_canon_sha256":"f038f5641681ae81f74df60867349a308b7e6f6050504b79f7bc59701118fbab","abstract_canon_sha256":"f8cfcc22d1042a4b34b9aa49abdd7dbe99470d3e3484d6a30b8b121c3a3a6cfb"},"schema_version":"1.0"},"canonical_sha256":"341b5870b8f1e1ae6a7240dcc0c6e5e9ab90bbaefb9b2edc1126d848337af765","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:10.113585Z","signature_b64":"fNPPrQIvz8IgAAMedJVzdz7d6nF794MA6CuUhjsI169lJgC50lrWZI/qq3cUee8FmdicqtbmaWBdSkCAnobnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"341b5870b8f1e1ae6a7240dcc0c6e5e9ab90bbaefb9b2edc1126d848337af765","last_reissued_at":"2026-05-17T23:55:10.113151Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:10.113151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02435","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":"2026-05-17T23:55:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BW7N8O6M4IIGQxj/MoIJ7Rm/X2BOwDSsELTZ5M2K37vdoyXyZNxHVDJwNvVpkAKHjVvur4LKL96uVWMbYcH+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:18:21.864403Z"},"content_sha256":"996bb04e47ea6292c90df097247286f23402cf47fc3ade9b145662ab02bbbe80","schema_version":"1.0","event_id":"sha256:996bb04e47ea6292c90df097247286f23402cf47fc3ade9b145662ab02bbbe80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GQNVQ4FY6HQ242TSIDOMBRXF5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphs with three eigenvalues and second largest eigenvalue at most 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary R. W. Greaves, Jack H. Koolen, Xi-Ming Cheng","submitted_at":"2015-06-08T10:57:00Z","abstract_excerpt":"We classify the connected graphs with precisely three distinct eigenvalues and second largest eigenvalue at most 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02435","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":"2026-05-17T23:55:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bmq/WX4VzMG8bTxKm+L6QnMlzTAX8hqJ5r0zauPLjEjOzpTtGZhSYh13IBW+zOtlcSNShuryurxypHjw6EhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:18:21.864755Z"},"content_sha256":"d8763e32bc87c49dc01f51884108859c73de50cb31470b2dc3d836e432278e06","schema_version":"1.0","event_id":"sha256:d8763e32bc87c49dc01f51884108859c73de50cb31470b2dc3d836e432278e06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G/bundle.json","state_url":"https://pith.science/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G/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":"2026-06-24T10:18:21Z","links":{"resolver":"https://pith.science/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G","bundle":"https://pith.science/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G/bundle.json","state":"https://pith.science/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQNVQ4FY6HQ242TSIDOMBRXF5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GQNVQ4FY6HQ242TSIDOMBRXF5G","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":"f8cfcc22d1042a4b34b9aa49abdd7dbe99470d3e3484d6a30b8b121c3a3a6cfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-08T10:57:00Z","title_canon_sha256":"f038f5641681ae81f74df60867349a308b7e6f6050504b79f7bc59701118fbab"},"schema_version":"1.0","source":{"id":"1506.02435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02435","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02435v1","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02435","created_at":"2026-05-17T23:55:10Z"},{"alias_kind":"pith_short_12","alias_value":"GQNVQ4FY6HQ2","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GQNVQ4FY6HQ242TS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GQNVQ4FY","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:d8763e32bc87c49dc01f51884108859c73de50cb31470b2dc3d836e432278e06","target":"graph","created_at":"2026-05-17T23:55:10Z","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":"We classify the connected graphs with precisely three distinct eigenvalues and second largest eigenvalue at most 1.","authors_text":"Gary R. W. Greaves, Jack H. Koolen, Xi-Ming Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-08T10:57:00Z","title":"Graphs with three eigenvalues and second largest eigenvalue at most 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02435","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":"sha256:996bb04e47ea6292c90df097247286f23402cf47fc3ade9b145662ab02bbbe80","target":"record","created_at":"2026-05-17T23:55:10Z","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":"f8cfcc22d1042a4b34b9aa49abdd7dbe99470d3e3484d6a30b8b121c3a3a6cfb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-08T10:57:00Z","title_canon_sha256":"f038f5641681ae81f74df60867349a308b7e6f6050504b79f7bc59701118fbab"},"schema_version":"1.0","source":{"id":"1506.02435","kind":"arxiv","version":1}},"canonical_sha256":"341b5870b8f1e1ae6a7240dcc0c6e5e9ab90bbaefb9b2edc1126d848337af765","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"341b5870b8f1e1ae6a7240dcc0c6e5e9ab90bbaefb9b2edc1126d848337af765","first_computed_at":"2026-05-17T23:55:10.113151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:10.113151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fNPPrQIvz8IgAAMedJVzdz7d6nF794MA6CuUhjsI169lJgC50lrWZI/qq3cUee8FmdicqtbmaWBdSkCAnobnCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:10.113585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:996bb04e47ea6292c90df097247286f23402cf47fc3ade9b145662ab02bbbe80","sha256:d8763e32bc87c49dc01f51884108859c73de50cb31470b2dc3d836e432278e06"],"state_sha256":"062a88dd8ad5a8be71a18617a6f5457e7e8f2c32de0b7a05824bac6bf7af0b6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvmriDpLYCgGwaKljosLj+fXa8XweoLSdswt/coBxgkqyB1i//ED4Gt11oQlFUt5PPVF5Xdf6+0vRasji3+fBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:18:21.866859Z","bundle_sha256":"355373cf8e21ea3ca26bfaedcfbad5da032cf26e4dea501c16174d8be5dfe6b2"}}