{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6L3YAZMYDZT4DLK3S4KGHAQBUK","short_pith_number":"pith:6L3YAZMY","canonical_record":{"source":{"id":"2012.11372","kind":"arxiv","version":11},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-18T06:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"0cf69c67e49377b9580b3c832810b6d9c31e65d147cdbd16fe05b6e3df04e9d9","abstract_canon_sha256":"230341ba97838ff973fe327fa93ce65249f5bb9d77136669bed941c69ae857b3"},"schema_version":"1.0"},"canonical_sha256":"f2f78065981e67c1ad5b9714638201a29857f8a3d14fcb210132abef4e3527c8","source":{"kind":"arxiv","id":"2012.11372","version":11},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.11372","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"arxiv_version","alias_value":"2012.11372v11","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11372","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"pith_short_12","alias_value":"6L3YAZMYDZT4","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"pith_short_16","alias_value":"6L3YAZMYDZT4DLK3","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"pith_short_8","alias_value":"6L3YAZMY","created_at":"2026-07-05T09:40:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6L3YAZMYDZT4DLK3S4KGHAQBUK","target":"record","payload":{"canonical_record":{"source":{"id":"2012.11372","kind":"arxiv","version":11},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-18T06:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"0cf69c67e49377b9580b3c832810b6d9c31e65d147cdbd16fe05b6e3df04e9d9","abstract_canon_sha256":"230341ba97838ff973fe327fa93ce65249f5bb9d77136669bed941c69ae857b3"},"schema_version":"1.0"},"canonical_sha256":"f2f78065981e67c1ad5b9714638201a29857f8a3d14fcb210132abef4e3527c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:13.174495Z","signature_b64":"aGvQySBaQKupVT0X+puBgpI6UuxNVUCBYbL9zKv+KfDAEIk2fFykvjCtEJ+uXruTZhsU+8QXeaXjqOdNiVmODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2f78065981e67c1ad5b9714638201a29857f8a3d14fcb210132abef4e3527c8","last_reissued_at":"2026-07-05T09:40:13.174066Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:13.174066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.11372","source_version":11,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:40:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LCqLC4vpqlQt5LELKgiPrbGj4w0qQiDg2Mx44RPB4M2dafygY+WNd5M5zQqFeN369iQSKhrfnI8g33ekkRByCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:24:17.697893Z"},"content_sha256":"a4a7a049de569c04e149537a4c8341156990523564513acbd443e57625d7c5d2","schema_version":"1.0","event_id":"sha256:a4a7a049de569c04e149537a4c8341156990523564513acbd443e57625d7c5d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6L3YAZMYDZT4DLK3S4KGHAQBUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A study on Type-2 isomorphic circulant graphs and related Abelian groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"V. Vilfred Kamalappan","submitted_at":"2020-12-18T06:27:28Z","abstract_excerpt":"Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be \\emph{Adam's isomorphic} if there exist some $a\\in \\mathbb{Z}_n^*$ such that $S = a R$ under arithmetic reflexive modulo $n$. In 1970, Elspas and Turner \\cite{eltu} raised a question on the isomorphism of $C_{16}(1, 3, 7)$ and $C_{16}(2, 3, 5)$ and Vilfred \\cite{v96} gave its answer by defining Type-2 isomorphism, different from Adam's isomorphism or Type-1 isomorphism, of $C_n(R)$ w.r.t. $m$ where $m > 1$ is a divisor of $\\gcd(n, r)$ and $r\\in R$. This paper is an extensive study on Type-2 isomorphic circulant graphs. Vilfred and Wilson \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11372","kind":"arxiv","version":11},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.11372/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:40:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUim96lJa2C3sMbZUbYO86t9wgi+w3OJGtdqf8ZdnRVUSOAxJrMiSvWxxvJSZMfDDTULmTK6EGiY1SNMsAnDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:24:17.698389Z"},"content_sha256":"12599e3c4c9bcb9a8c5419e9c47d2b95cfa4cfe8a3a29789041e51cc48cfb834","schema_version":"1.0","event_id":"sha256:12599e3c4c9bcb9a8c5419e9c47d2b95cfa4cfe8a3a29789041e51cc48cfb834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK/bundle.json","state_url":"https://pith.science/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-14T17:24:17Z","links":{"resolver":"https://pith.science/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK","bundle":"https://pith.science/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK/bundle.json","state":"https://pith.science/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6L3YAZMYDZT4DLK3S4KGHAQBUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6L3YAZMYDZT4DLK3S4KGHAQBUK","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":"230341ba97838ff973fe327fa93ce65249f5bb9d77136669bed941c69ae857b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-18T06:27:28Z","title_canon_sha256":"0cf69c67e49377b9580b3c832810b6d9c31e65d147cdbd16fe05b6e3df04e9d9"},"schema_version":"1.0","source":{"id":"2012.11372","kind":"arxiv","version":11}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.11372","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"arxiv_version","alias_value":"2012.11372v11","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11372","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"pith_short_12","alias_value":"6L3YAZMYDZT4","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"pith_short_16","alias_value":"6L3YAZMYDZT4DLK3","created_at":"2026-07-05T09:40:13Z"},{"alias_kind":"pith_short_8","alias_value":"6L3YAZMY","created_at":"2026-07-05T09:40:13Z"}],"graph_snapshots":[{"event_id":"sha256:12599e3c4c9bcb9a8c5419e9c47d2b95cfa4cfe8a3a29789041e51cc48cfb834","target":"graph","created_at":"2026-07-05T09:40:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.11372/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be \\emph{Adam's isomorphic} if there exist some $a\\in \\mathbb{Z}_n^*$ such that $S = a R$ under arithmetic reflexive modulo $n$. In 1970, Elspas and Turner \\cite{eltu} raised a question on the isomorphism of $C_{16}(1, 3, 7)$ and $C_{16}(2, 3, 5)$ and Vilfred \\cite{v96} gave its answer by defining Type-2 isomorphism, different from Adam's isomorphism or Type-1 isomorphism, of $C_n(R)$ w.r.t. $m$ where $m > 1$ is a divisor of $\\gcd(n, r)$ and $r\\in R$. This paper is an extensive study on Type-2 isomorphic circulant graphs. Vilfred and Wilson \\c","authors_text":"V. Vilfred Kamalappan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-18T06:27:28Z","title":"A study on Type-2 isomorphic circulant graphs and related Abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11372","kind":"arxiv","version":11},"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:a4a7a049de569c04e149537a4c8341156990523564513acbd443e57625d7c5d2","target":"record","created_at":"2026-07-05T09:40:13Z","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":"230341ba97838ff973fe327fa93ce65249f5bb9d77136669bed941c69ae857b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-12-18T06:27:28Z","title_canon_sha256":"0cf69c67e49377b9580b3c832810b6d9c31e65d147cdbd16fe05b6e3df04e9d9"},"schema_version":"1.0","source":{"id":"2012.11372","kind":"arxiv","version":11}},"canonical_sha256":"f2f78065981e67c1ad5b9714638201a29857f8a3d14fcb210132abef4e3527c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2f78065981e67c1ad5b9714638201a29857f8a3d14fcb210132abef4e3527c8","first_computed_at":"2026-07-05T09:40:13.174066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:13.174066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aGvQySBaQKupVT0X+puBgpI6UuxNVUCBYbL9zKv+KfDAEIk2fFykvjCtEJ+uXruTZhsU+8QXeaXjqOdNiVmODw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:13.174495Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.11372","source_kind":"arxiv","source_version":11}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4a7a049de569c04e149537a4c8341156990523564513acbd443e57625d7c5d2","sha256:12599e3c4c9bcb9a8c5419e9c47d2b95cfa4cfe8a3a29789041e51cc48cfb834"],"state_sha256":"8e877db92d778ed041148dec5303d585180a4080e7d54b20a5b7e042861b63dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zeZqrwipsb57xhMIArNoaETU07GJwW/7sC47y3vEJRFWz6cYlpLIf4P3zmaJrd9K5NyqVmwAPesYmRqrLVe+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:24:17.703097Z","bundle_sha256":"7501f9bc598b57ebab11af3433a07019baf4d1f50737a5207e6bd5d639c341a9"}}