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Combinatorial Theory,9(1970), 297-307","work_id":"d1c668b3-b8ac-436d-9047-2408b9c6f3ec","year":1970}],"snapshot_sha256":"3c828d45fe615bc80f52b71e5d470906c8f5bb07a007fc6198bdc9a232f59de2"},"source":{"id":"2605.14402","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T01:58:52.160054Z","id":"596cc171-3985-4f1f-b744-f90b945b1610","model_set":{"reader":"grok-4.3"},"one_line_summary":"Two families of circulant graphs C_432(R) and C_6750(S) each possess Type-2 isomorphic variants for two values of m.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Families of circulant graphs C_432(R) each admit Type-2 isomorphisms for both m=2 and m=3, and families C_6750(S) do so for both m=3 and m=5.","strongest_claim":"Family of circulant graphs C_432(R), each has isomorphic circulant graphs of Type-2 w.r.t. m = 2 as well as m = 3; and Family of circulant graphs C_6750(S), each has isomorphic circulant graphs of Type-2 w.r.t. m = 3 as well as m = 5.","weakest_assumption":"The specific connection sets R and S are assumed to produce the claimed Type-2 isomorphisms under the definitions established in the author's prior seven papers; this assumption is not independently verified or derived in the abstract."}},"verdict_id":"596cc171-3985-4f1f-b744-f90b945b1610"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9834ad25892f5348b2386aa6e6a8168d75799d8e9ffe6c70e0b3cbf1ace63586","target":"record","created_at":"2026-05-17T23:39:07Z","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":"2cfbb2d26806acb38f93ce895bace4064311355c787c466059d697c41209d92f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-14T05:39:20Z","title_canon_sha256":"50345caea557d9edcc86483cbf7797e07755b8bf420358a07b139454b546829b"},"schema_version":"1.0","source":{"id":"2605.14402","kind":"arxiv","version":1}},"canonical_sha256":"f94bcdffcd8290b17ad159318bdb3034cb97953b98f11d5aae0ed9c9e24da1b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f94bcdffcd8290b17ad159318bdb3034cb97953b98f11d5aae0ed9c9e24da1b9","first_computed_at":"2026-05-17T23:39:07.470464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:07.470464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KLlr/G5GqcZDX14gjhhR9Vyej3KHghrGkV/vgQf0Hu7d5akX5yf3c9x3qxhg3EaHTy4VtX/unebDgM13CQ01CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:07.471152Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9834ad25892f5348b2386aa6e6a8168d75799d8e9ffe6c70e0b3cbf1ace63586","sha256:66b96a2ee2617bb592232bc2c2866c9bddb5b900099d77887e56617a73ef41ae","sha256:69051fcb4580332e4365589e4855ba9e6abd611b0c378002faccff4e51a3f08d"],"state_sha256":"95aedcf3f05e2b74087f2bb6b2be6e6ddbfbece8a0b3ee906dd3c752009cd167"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpEHEFbr26jDCx6zDMRyEvNtMl2o6qbxYi6m2W22noWJ2bG0iPFMTtdqbl5Q+7GJ/qQcD6gp1DaepS30XvbXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T12:33:38.786857Z","bundle_sha256":"d6bc1947723d261c8b9e44085faf595f3e92d5f6a41f55faa4ededb37b5c466d"}}