{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UV37JHLEVAONXKUJTFQGF4AZZG","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":"13822668cc21aa5e01f4b54f793db67583d1695292d2ff0f8840017455bcd85f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T05:08:59Z","title_canon_sha256":"34d16781d70637b33a305fcd6ebfe9374fda884fcbe4c3daf8a3050add6c7a57"},"schema_version":"1.0","source":{"id":"1601.07647","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07647","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07647v2","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07647","created_at":"2026-05-17T23:56:56Z"},{"alias_kind":"pith_short_12","alias_value":"UV37JHLEVAON","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UV37JHLEVAONXKUJ","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UV37JHLE","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:de24996a9e1c8eaa58ebd479e370d4c93bce6196f4dfd93d8fdb7b3d1462984f","target":"graph","created_at":"2026-05-17T23:56:56Z","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":"Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$ is denoted by $H(t)$ and it is defined by $H(t):=\\exp{\\left(itA\\right)},\\;t\\in\\mathbb{R}.$ The graph $G$ has perfect state transfer (PST) from a vertex $u$ to another vertex $v$ if there exist $\\tau\\left(\\neq0\\right)\\in\\mathbb{R}$ such that the $uv$-th entry of $H(\\tau)$ has unit modulus. In case when $u=v$, we say that $G$ is periodic at the vertex $u$ at time $\\tau$. The graph $G$ is said to be periodic if it is periodic at all vertices at the same time. A gcd-graph is a Cayley graph over a finite abelian group define","authors_text":"Bikash Bhattacharjya, Hiranmoy Pal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T05:08:59Z","title":"Perfect State Transfer on gcd-graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07647","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:e53df1d9b5125e81a7f7a4614b61be72452c05c1b690db59d87c4c905cfcccbd","target":"record","created_at":"2026-05-17T23:56:56Z","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":"13822668cc21aa5e01f4b54f793db67583d1695292d2ff0f8840017455bcd85f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-28T05:08:59Z","title_canon_sha256":"34d16781d70637b33a305fcd6ebfe9374fda884fcbe4c3daf8a3050add6c7a57"},"schema_version":"1.0","source":{"id":"1601.07647","kind":"arxiv","version":2}},"canonical_sha256":"a577f49d64a81cdbaa89996062f019c98293281a4cb15b559a79c72c5f93e7f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a577f49d64a81cdbaa89996062f019c98293281a4cb15b559a79c72c5f93e7f8","first_computed_at":"2026-05-17T23:56:56.261020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:56.261020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ylHbtg3TyxdB08uozx1AmRUKBlmRXODQWIdue+mxwy+yJDuJAMnP6HZaheuo1VSEMe96lKoSKxG6Vgsfk1u/Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:56.261608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07647","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e53df1d9b5125e81a7f7a4614b61be72452c05c1b690db59d87c4c905cfcccbd","sha256:de24996a9e1c8eaa58ebd479e370d4c93bce6196f4dfd93d8fdb7b3d1462984f"],"state_sha256":"a5ec17afcbd29dd29fcdce26298c3f62c838152d3dbef7ae9c3ce1bae4cfb73c"}