{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4OU442W5X7PCXQ6UQEDUUWSOTB","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":"4c64c302a30e73f2bd15512c3d676f90f6bf92ec2d4094dc28982474773c151d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T15:27:13Z","title_canon_sha256":"df50e2b876a9d520238026d2cf6cb182e7e81aa2a55885b6f97b42013f117a1b"},"schema_version":"1.0","source":{"id":"1405.0188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0188","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0188v1","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0188","created_at":"2026-05-18T02:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"4OU442W5X7PC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4OU442W5X7PCXQ6U","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4OU442W5","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:d71de62eef83f6c95fb464b68f79836978bdd8b46458c41e6c4fd15441118f66","target":"graph","created_at":"2026-05-18T02:52:48Z","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":"We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal spaces in the general case, classify all the monomial spaces in the case of tensor products of cyclic algebras of degree 3 using graph theory, and provide an upper bound for the dimension in the generic tensor product of cyclic algebras of degree 3.","authors_text":"Adam Chapman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T15:27:13Z","title":"Kummer Subspaces of Tensor Products of Cyclic Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0188","kind":"arxiv","version":1},"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":"sha256:2875cc68330de0735a0bca1587a1b9534db23fa1836c5c14afcc6f3d7677f692","target":"record","created_at":"2026-05-18T02:52:48Z","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":"4c64c302a30e73f2bd15512c3d676f90f6bf92ec2d4094dc28982474773c151d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-01T15:27:13Z","title_canon_sha256":"df50e2b876a9d520238026d2cf6cb182e7e81aa2a55885b6f97b42013f117a1b"},"schema_version":"1.0","source":{"id":"1405.0188","kind":"arxiv","version":1}},"canonical_sha256":"e3a9ce6addbfde2bc3d481074a5a4e984703b83de649d345980fb9ec16767b4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3a9ce6addbfde2bc3d481074a5a4e984703b83de649d345980fb9ec16767b4a","first_computed_at":"2026-05-18T02:52:48.803581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:48.803581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"62mZpEPmjabZl5VVnXjp2z0AX6mPoTMqcsoVyLQoAl6T/NMkKh6UqbMndh50S1OepGWy3HMO9DrUqH2/8PLeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:48.804053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2875cc68330de0735a0bca1587a1b9534db23fa1836c5c14afcc6f3d7677f692","sha256:d71de62eef83f6c95fb464b68f79836978bdd8b46458c41e6c4fd15441118f66"],"state_sha256":"daa23a9694c3c1bc4a9b6326ce3879f9367c85a4d29985ce9deb6e93bc7571cb"}