{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AAPLEICWMFK3HEMZCWLYRDHMVR","short_pith_number":"pith:AAPLEICW","canonical_record":{"source":{"id":"1511.07537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-24T01:52:11Z","cross_cats_sorted":[],"title_canon_sha256":"c756d838097cdaea71d4bdde03e1c6583b83c62bfda149d4a2f96dd2feff61f1","abstract_canon_sha256":"530853ec905683b0a72c147272ce0a616de86e2cd5d0da12d8168e580968f5e1"},"schema_version":"1.0"},"canonical_sha256":"001eb220566155b391991597888cecac43736b46e9a138eae6f82d35ffb47ec2","source":{"kind":"arxiv","id":"1511.07537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07537","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07537v1","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07537","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"pith_short_12","alias_value":"AAPLEICWMFK3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AAPLEICWMFK3HEMZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AAPLEICW","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AAPLEICWMFK3HEMZCWLYRDHMVR","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-24T01:52:11Z","cross_cats_sorted":[],"title_canon_sha256":"c756d838097cdaea71d4bdde03e1c6583b83c62bfda149d4a2f96dd2feff61f1","abstract_canon_sha256":"530853ec905683b0a72c147272ce0a616de86e2cd5d0da12d8168e580968f5e1"},"schema_version":"1.0"},"canonical_sha256":"001eb220566155b391991597888cecac43736b46e9a138eae6f82d35ffb47ec2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:04.482733Z","signature_b64":"qwznPrKjtGoj37Gyfrx0//99IXksSMo/epPE7ehZqhM3jvvsfVOwcI/A/BBQ9LAUI2WJ1/hl0CdSITrYY8d8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"001eb220566155b391991597888cecac43736b46e9a138eae6f82d35ffb47ec2","last_reissued_at":"2026-05-18T01:26:04.482238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:04.482238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07537","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":"2026-05-18T01:26:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"loEk19QKzXr6Fm5BY1ZlU7lU2Tfaoiqb7VFKlb6jBrznk5wKxDvm1kC4GK0RxZiXYNKCyMuK2C49WBnyOYfYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:35:44.074921Z"},"content_sha256":"c7c65a6dcfc28f0e893660475d6e52fff410d635b056fe78e0989b8067881c12","schema_version":"1.0","event_id":"sha256:c7c65a6dcfc28f0e893660475d6e52fff410d635b056fe78e0989b8067881c12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AAPLEICWMFK3HEMZCWLYRDHMVR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hadi Kharaghani, Sho Suda","submitted_at":"2015-11-24T01:52:11Z","abstract_excerpt":"We extend Hoffman's coclique bound for regular digraphs with the property that its adjacency matrix is normal, and discuss cocliques attaining the inequality. As a consequence, we characterize skew-Bush-type Hadamard matrices in terms of digraphs. We present some normal digraphs whose vertex set is decomposed into disjoint cocliques attaining the bound. The digraphs provided here are relation graphs of some nonsymmetric association schemes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07537","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":"2026-05-18T01:26:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZIRtCGRORLr+WlFg24m/2QLF1/awmC04hYeHpQgVs+JMo5YyojEsgjf1msADU7DQrKOwEKnqgQaoDnLQDXN/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:35:44.075646Z"},"content_sha256":"eee4dcb0d330789aa7fe3ff43bb90c579a3842aad93c3e40cd3e811320f691fa","schema_version":"1.0","event_id":"sha256:eee4dcb0d330789aa7fe3ff43bb90c579a3842aad93c3e40cd3e811320f691fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAPLEICWMFK3HEMZCWLYRDHMVR/bundle.json","state_url":"https://pith.science/pith/AAPLEICWMFK3HEMZCWLYRDHMVR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAPLEICWMFK3HEMZCWLYRDHMVR/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":"2026-05-26T01:35:44Z","links":{"resolver":"https://pith.science/pith/AAPLEICWMFK3HEMZCWLYRDHMVR","bundle":"https://pith.science/pith/AAPLEICWMFK3HEMZCWLYRDHMVR/bundle.json","state":"https://pith.science/pith/AAPLEICWMFK3HEMZCWLYRDHMVR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAPLEICWMFK3HEMZCWLYRDHMVR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AAPLEICWMFK3HEMZCWLYRDHMVR","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":"530853ec905683b0a72c147272ce0a616de86e2cd5d0da12d8168e580968f5e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-24T01:52:11Z","title_canon_sha256":"c756d838097cdaea71d4bdde03e1c6583b83c62bfda149d4a2f96dd2feff61f1"},"schema_version":"1.0","source":{"id":"1511.07537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07537","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07537v1","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07537","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"pith_short_12","alias_value":"AAPLEICWMFK3","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AAPLEICWMFK3HEMZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AAPLEICW","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:eee4dcb0d330789aa7fe3ff43bb90c579a3842aad93c3e40cd3e811320f691fa","target":"graph","created_at":"2026-05-18T01:26:04Z","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 extend Hoffman's coclique bound for regular digraphs with the property that its adjacency matrix is normal, and discuss cocliques attaining the inequality. As a consequence, we characterize skew-Bush-type Hadamard matrices in terms of digraphs. We present some normal digraphs whose vertex set is decomposed into disjoint cocliques attaining the bound. The digraphs provided here are relation graphs of some nonsymmetric association schemes.","authors_text":"Hadi Kharaghani, Sho Suda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-24T01:52:11Z","title":"Hoffman's coclique bound for normal regular digraphs, and nonsymmetric association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07537","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:c7c65a6dcfc28f0e893660475d6e52fff410d635b056fe78e0989b8067881c12","target":"record","created_at":"2026-05-18T01:26:04Z","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":"530853ec905683b0a72c147272ce0a616de86e2cd5d0da12d8168e580968f5e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-24T01:52:11Z","title_canon_sha256":"c756d838097cdaea71d4bdde03e1c6583b83c62bfda149d4a2f96dd2feff61f1"},"schema_version":"1.0","source":{"id":"1511.07537","kind":"arxiv","version":1}},"canonical_sha256":"001eb220566155b391991597888cecac43736b46e9a138eae6f82d35ffb47ec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"001eb220566155b391991597888cecac43736b46e9a138eae6f82d35ffb47ec2","first_computed_at":"2026-05-18T01:26:04.482238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:04.482238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwznPrKjtGoj37Gyfrx0//99IXksSMo/epPE7ehZqhM3jvvsfVOwcI/A/BBQ9LAUI2WJ1/hl0CdSITrYY8d8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:04.482733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7c65a6dcfc28f0e893660475d6e52fff410d635b056fe78e0989b8067881c12","sha256:eee4dcb0d330789aa7fe3ff43bb90c579a3842aad93c3e40cd3e811320f691fa"],"state_sha256":"4d6d29aed9f89fa4f670d0954282d2531ce027359503053130a000b1c15ffd33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fsAAg1vdwtsfU708nWr+gZohFOAHG+WWKcpjLOcFjZuY0bdqTEqBxsJ0ncd9mqt1vj+dBfYZy41w6iqGEKMrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:35:44.079959Z","bundle_sha256":"ca0318a5a69253cd260a63b10b8bad35d1380743c874a97bd48347d8b6a85015"}}