{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Q3KLUS2T2ISOG57EWXOCDI2VLK","short_pith_number":"pith:Q3KLUS2T","schema_version":"1.0","canonical_sha256":"86d4ba4b53d224e377e4b5dc21a3555a999e8485fd0e8bec167e93e2b1e81be4","source":{"kind":"arxiv","id":"1111.1200","version":1},"attestation_state":"computed","paper":{"title":"Spectra of Coronae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cam McLeman, Erin McNicholas","submitted_at":"2011-11-04T18:08:42Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.1200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-04T18:08:42Z","cross_cats_sorted":[],"title_canon_sha256":"7264435046c6ed9b2e4628fa0bad34c072bf19c992991cf2c980890d22651f30","abstract_canon_sha256":"31197e3c5ae1734ba75107b47ae6d9176beea7e03c98a6d4d88877d2d464fd64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:35.530836Z","signature_b64":"4rRqgZrRBOqtLrJL1rR9JoAykLUJ1wwRsk03Nr3uCU6UhmMSM6Zexn45Gj8oirYhq5rYOLbjVSJWgVbM/eWHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86d4ba4b53d224e377e4b5dc21a3555a999e8485fd0e8bec167e93e2b1e81be4","last_reissued_at":"2026-05-18T04:09:35.530254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:35.530254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectra of Coronae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cam McLeman, Erin McNicholas","submitted_at":"2011-11-04T18:08:42Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1200","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.1200","created_at":"2026-05-18T04:09:35.530338+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1200v1","created_at":"2026-05-18T04:09:35.530338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1200","created_at":"2026-05-18T04:09:35.530338+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q3KLUS2T2ISO","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q3KLUS2T2ISOG57E","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q3KLUS2T","created_at":"2026-05-18T12:26:39.201973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK","json":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK.json","graph_json":"https://pith.science/api/pith-number/Q3KLUS2T2ISOG57EWXOCDI2VLK/graph.json","events_json":"https://pith.science/api/pith-number/Q3KLUS2T2ISOG57EWXOCDI2VLK/events.json","paper":"https://pith.science/paper/Q3KLUS2T"},"agent_actions":{"view_html":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK","download_json":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK.json","view_paper":"https://pith.science/paper/Q3KLUS2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1200&json=true","fetch_graph":"https://pith.science/api/pith-number/Q3KLUS2T2ISOG57EWXOCDI2VLK/graph.json","fetch_events":"https://pith.science/api/pith-number/Q3KLUS2T2ISOG57EWXOCDI2VLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK/action/storage_attestation","attest_author":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK/action/author_attestation","sign_citation":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK/action/citation_signature","submit_replication":"https://pith.science/pith/Q3KLUS2T2ISOG57EWXOCDI2VLK/action/replication_record"}},"created_at":"2026-05-18T04:09:35.530338+00:00","updated_at":"2026-05-18T04:09:35.530338+00:00"}