{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UXN567BVWSF7UIKIRBT3U4FB5Z","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":"03ec04d4bb4d8696b6fbdda79f9b2532dec2075d508b798de5fee1e5c3af01bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T13:34:25Z","title_canon_sha256":"276d99a35a84bbbe9f69427263abb92a70476ce4bf52df9f16b614473f1ae087"},"schema_version":"1.0","source":{"id":"1104.4261","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4261","created_at":"2026-05-18T04:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4261v3","created_at":"2026-05-18T04:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4261","created_at":"2026-05-18T04:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"UXN567BVWSF7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UXN567BVWSF7UIKI","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UXN567BV","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:bc0bc600f382c5a1cb45a531886a21ad94df00b4d9cbd8857b589b6680c5860a","target":"graph","created_at":"2026-05-18T04:13:39Z","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":"Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The integral circulant graph $\\ICG_n (D)$ has the vertex set $Z_n = \\{0, 1, 2, ..., n - 1\\}$ and vertices $a$ and $b$ are adjacent if $\\gcd(a-b,n)\\in D$, where $D \\subseteq \\{d : d \\mid n,\\ 1\\leq d<n\\}$. These graphs are highly symmetric, have integral spectra and some remarkable properties connecting chemical graph theory and number theory. The energy of a gra","authors_text":"Aleksandar Ilic, Milan Basic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T13:34:25Z","title":"New results on the energy of integral circulant graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4261","kind":"arxiv","version":3},"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:ed85781a64bf5e6284e1145dd0ec9ee4015f573ab105100cc55f95743690f6c4","target":"record","created_at":"2026-05-18T04:13:39Z","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":"03ec04d4bb4d8696b6fbdda79f9b2532dec2075d508b798de5fee1e5c3af01bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T13:34:25Z","title_canon_sha256":"276d99a35a84bbbe9f69427263abb92a70476ce4bf52df9f16b614473f1ae087"},"schema_version":"1.0","source":{"id":"1104.4261","kind":"arxiv","version":3}},"canonical_sha256":"a5dbdf7c35b48bfa21488867ba70a1ee51bd657b625278a1222829073e6be4d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5dbdf7c35b48bfa21488867ba70a1ee51bd657b625278a1222829073e6be4d8","first_computed_at":"2026-05-18T04:13:39.132554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:39.132554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lV06+AFPp3P3pyOZnwM/BJICf/KSoZXoPqL6qNoRzercspSk48RGIHI5E1VXesntc1CFD1EyJ2ktPudG8dVWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:39.133047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4261","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed85781a64bf5e6284e1145dd0ec9ee4015f573ab105100cc55f95743690f6c4","sha256:bc0bc600f382c5a1cb45a531886a21ad94df00b4d9cbd8857b589b6680c5860a"],"state_sha256":"ac910e1a75e16b87fb6aad2bd3e9bbef9bad0b583e46e0fc91db5bb02145850f"}