{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:6WCBZ7NTROUFZ6W7H4A453L2EO","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":"474e2ff52ddfe9f603ea36f1e30727d1206c1fcbbdcb15df25fbd341fe9b6753","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-13T17:43:09Z","title_canon_sha256":"c96ddd586bad43897169653f65968bc70996d606d3d9a2b88274f678f2d49733"},"schema_version":"1.0","source":{"id":"2211.06970","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.06970","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"2211.06970v2","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.06970","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"6WCBZ7NTROUF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"6WCBZ7NTROUFZ6W7","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"6WCBZ7NT","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:5741a483b83bf248149cefc0bc6f67e4762ab05dd0893ab472693141ff83d238","target":"graph","created_at":"2026-05-17T23:39:19Z","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":"This study is the $10^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \\cite{v2-1}-\\cite{v2-10}. In this part, we obtain families of Type-2 isomorphic circulant graphs $C_{np^3}(R)$ w.r.t. $m$ = $p$, and related Abelian groups where $p$ is a prime number and $n\\in\\mathbb{N}$. In its main theorem, it is proved that for $i$ = 1 to $p$, circulant graphs $C_{np^3}(R^{np^3,x+yp}_i)$ are isomorphic of Type-2 w.r.t. $m$ = $p$ and they form Abelian group $(T2_{np^3,p}(C_{np^3}(R^{np^3,x+yp}_i)), \\circ)$ where $T2_{np^3,p}(C_{np^3}(R^{np^3,x+yp}_i))$ = $\\{\\theta_{np","authors_text":"Vilfred Kamalappan, Wilson Peraprakash","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-13T17:43:09Z","title":"A study on Type-2 isomorphic circulant graphs. Part 10: Type-2 isomorphic $C_{np^3}(R)$ w.r.t. $m$ = $p$ and related groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.06970","kind":"arxiv","version":2},"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":"sha256:42093ed98ec99a8dcb5e7b1e574d9aed65036ce4dc5d89f0800db3c20fd90d0b","target":"record","created_at":"2026-05-17T23:39:19Z","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":"474e2ff52ddfe9f603ea36f1e30727d1206c1fcbbdcb15df25fbd341fe9b6753","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-13T17:43:09Z","title_canon_sha256":"c96ddd586bad43897169653f65968bc70996d606d3d9a2b88274f678f2d49733"},"schema_version":"1.0","source":{"id":"2211.06970","kind":"arxiv","version":2}},"canonical_sha256":"f5841cfdb38ba85cfadf3f01ceed7a239f8bcb199c73af936587ce88cfa99f9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5841cfdb38ba85cfadf3f01ceed7a239f8bcb199c73af936587ce88cfa99f9d","first_computed_at":"2026-05-17T23:39:19.648257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:19.648257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2wBh/w/O7Y6RHqMt7LysAHtaFfsBKLsEqdb9VQvKDunbiNdxpFQsIym3uYpzR44120AVF4tueostDqF48oPsAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:19.648925Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.06970","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42093ed98ec99a8dcb5e7b1e574d9aed65036ce4dc5d89f0800db3c20fd90d0b","sha256:5741a483b83bf248149cefc0bc6f67e4762ab05dd0893ab472693141ff83d238"],"state_sha256":"99c1f806e72af6f21640acae63ed87d0f3d4ad714f62e5ef7e021c5cdce10120"}