{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q3KLUS2T2ISOG57EWXOCDI2VLK","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":"31197e3c5ae1734ba75107b47ae6d9176beea7e03c98a6d4d88877d2d464fd64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-04T18:08:42Z","title_canon_sha256":"7264435046c6ed9b2e4628fa0bad34c072bf19c992991cf2c980890d22651f30"},"schema_version":"1.0","source":{"id":"1111.1200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1200","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1200v1","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1200","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"Q3KLUS2T2ISO","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3KLUS2T2ISOG57E","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3KLUS2T","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:c87033c3245fb0f0416f774db41b5e52566d0014ee243882a138f0fbeeaf9a7d","target":"graph","created_at":"2026-05-18T04:09:35Z","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 introduce a new invariant, the coronal of a graph, and use it to compute the spectrum of the corona $G\\circ H$ of two graphs $G$ and $H$. In particular, we show that this spectrum is completely determined by the spectra of $G$ and $H$ and the coronal of $H$. Previous work has computed the spectrum of a corona only in the case that $H$ is regular. We then explicitly compute the coronals for several families of graphs, including regular graphs, complete $n$-partite graphs, and paths. Finally, we use the corona construction to generate many infinite families of pairs of cospectral graphs.","authors_text":"Cam McLeman, Erin McNicholas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-04T18:08:42Z","title":"Spectra of Coronae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1200","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:c27d5e8623267bcc767f642463b531d24eb7199c11875973e26b4914c11dbcd7","target":"record","created_at":"2026-05-18T04:09:35Z","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":"31197e3c5ae1734ba75107b47ae6d9176beea7e03c98a6d4d88877d2d464fd64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-04T18:08:42Z","title_canon_sha256":"7264435046c6ed9b2e4628fa0bad34c072bf19c992991cf2c980890d22651f30"},"schema_version":"1.0","source":{"id":"1111.1200","kind":"arxiv","version":1}},"canonical_sha256":"86d4ba4b53d224e377e4b5dc21a3555a999e8485fd0e8bec167e93e2b1e81be4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86d4ba4b53d224e377e4b5dc21a3555a999e8485fd0e8bec167e93e2b1e81be4","first_computed_at":"2026-05-18T04:09:35.530254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:35.530254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4rRqgZrRBOqtLrJL1rR9JoAykLUJ1wwRsk03Nr3uCU6UhmMSM6Zexn45Gj8oirYhq5rYOLbjVSJWgVbM/eWHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:35.530836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c27d5e8623267bcc767f642463b531d24eb7199c11875973e26b4914c11dbcd7","sha256:c87033c3245fb0f0416f774db41b5e52566d0014ee243882a138f0fbeeaf9a7d"],"state_sha256":"e81199ac56dea5ab1e612757024b1aa96437cd9bdeab1f70a616af593fbd286a"}