{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OFPXMN4LFIM46UJ3NTW5QOB4LJ","short_pith_number":"pith:OFPXMN4L","schema_version":"1.0","canonical_sha256":"715f76378b2a19cf513b6cedd8383c5a76a086af5222c63036b5105f8d9bf388","source":{"kind":"arxiv","id":"1503.01541","version":3},"attestation_state":"computed","paper":{"title":"Groups all of whose undirected Cayley graphs are determined by their spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.SP"],"primary_cat":"math.CO","authors_text":"Alireza Abdollahi, Mojtaba Jazaeri, Shahrooz Janbaz","submitted_at":"2015-03-05T05:22:47Z","abstract_excerpt":"Let $G$ be a finite group, and $S$ be a subset of $G\\setminus\\{1\\}$ such that $S=S^{-1}$. Suppose that $Cay(G,S)$ is the Cayley graph on $G$ with respect to the set $S$ which is the graph whose vertex set is $G$ and two vertices $a,b\\in G$ are adjacent if and only if $ab^{-1}\\in S$. The adjacency spectrum $Spec(\\Gamma)$ of a graph $\\Gamma$ is the multiset of eigenvalues of its adjacency matrix. A graph $\\Gamma$ is called \"determined by its spectrum\" (or for short DS) whenever if a graph $\\Gamma'$ has the same spectrum as $\\Gamma$, then $\\Gamma \\cong \\Gamma'$. We say that the group $G$ is DS (C"},"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":"1503.01541","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-05T05:22:47Z","cross_cats_sorted":["math.GR","math.SP"],"title_canon_sha256":"cb3c7da917c4df0b85f2e8d2fca92b2ef7607ffabda5df1fad657b4a78b9b721","abstract_canon_sha256":"41ef2e534a0125895201e92a0ab27c49c86e9f9b69cf7a6544d2197eeb4eb765"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:11.088579Z","signature_b64":"yW70/7ROlWgDxIu3GIw09FGsVdnDbYEtEmx7O95p3YYyIQYVlbPNZOI4XDDxV7jkqfnIyUx8Jr26dHYomHP+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"715f76378b2a19cf513b6cedd8383c5a76a086af5222c63036b5105f8d9bf388","last_reissued_at":"2026-05-18T02:17:11.087929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:11.087929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groups all of whose undirected Cayley graphs are determined by their spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.SP"],"primary_cat":"math.CO","authors_text":"Alireza Abdollahi, Mojtaba Jazaeri, Shahrooz Janbaz","submitted_at":"2015-03-05T05:22:47Z","abstract_excerpt":"Let $G$ be a finite group, and $S$ be a subset of $G\\setminus\\{1\\}$ such that $S=S^{-1}$. Suppose that $Cay(G,S)$ is the Cayley graph on $G$ with respect to the set $S$ which is the graph whose vertex set is $G$ and two vertices $a,b\\in G$ are adjacent if and only if $ab^{-1}\\in S$. The adjacency spectrum $Spec(\\Gamma)$ of a graph $\\Gamma$ is the multiset of eigenvalues of its adjacency matrix. A graph $\\Gamma$ is called \"determined by its spectrum\" (or for short DS) whenever if a graph $\\Gamma'$ has the same spectrum as $\\Gamma$, then $\\Gamma \\cong \\Gamma'$. We say that the group $G$ is DS (C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01541","kind":"arxiv","version":3},"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":"1503.01541","created_at":"2026-05-18T02:17:11.088023+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01541v3","created_at":"2026-05-18T02:17:11.088023+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01541","created_at":"2026-05-18T02:17:11.088023+00:00"},{"alias_kind":"pith_short_12","alias_value":"OFPXMN4LFIM4","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OFPXMN4LFIM46UJ3","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OFPXMN4L","created_at":"2026-05-18T12:29:34.919912+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/OFPXMN4LFIM46UJ3NTW5QOB4LJ","json":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ.json","graph_json":"https://pith.science/api/pith-number/OFPXMN4LFIM46UJ3NTW5QOB4LJ/graph.json","events_json":"https://pith.science/api/pith-number/OFPXMN4LFIM46UJ3NTW5QOB4LJ/events.json","paper":"https://pith.science/paper/OFPXMN4L"},"agent_actions":{"view_html":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ","download_json":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ.json","view_paper":"https://pith.science/paper/OFPXMN4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01541&json=true","fetch_graph":"https://pith.science/api/pith-number/OFPXMN4LFIM46UJ3NTW5QOB4LJ/graph.json","fetch_events":"https://pith.science/api/pith-number/OFPXMN4LFIM46UJ3NTW5QOB4LJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ/action/storage_attestation","attest_author":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ/action/author_attestation","sign_citation":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ/action/citation_signature","submit_replication":"https://pith.science/pith/OFPXMN4LFIM46UJ3NTW5QOB4LJ/action/replication_record"}},"created_at":"2026-05-18T02:17:11.088023+00:00","updated_at":"2026-05-18T02:17:11.088023+00:00"}