{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YWV6JQ2CW4NG6LZG4QRWTNVAI5","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":"99a218dfacc89475dc6756af58349393ad99110b20f5c204313e2b4ae75584bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-30T11:52:53Z","title_canon_sha256":"04e63c8679b81be5b37a022f67e6f6a5fa58b8c6c427fd342e130d902d949f80"},"schema_version":"1.0","source":{"id":"1106.6197","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.6197","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1106.6197v2","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6197","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"YWV6JQ2CW4NG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YWV6JQ2CW4NG6LZG","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YWV6JQ2C","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:64594893581073045aefe8039b1c0139c8e157c7f9cd109c5ce05204b71b97cd","target":"graph","created_at":"2026-05-18T03:45:21Z","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 characterize the rank of edge connection matrices of partition functions of real vertex models, as the dimension of the homogeneous components of the algebra of $G$-invariant tensors. Here $G$ is the sub- group of the real orthogonal group that stabilizes the vertex model. This answers a question of Bal\\'azs Szegedy from 2007.","authors_text":"Guus Regts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-30T11:52:53Z","title":"The rank of edge connection matrices and the dimension of algebras of invariant tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6197","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":"sha256:8ecb4471a98dea05c1d15a86bbe4bca572e7a4501c33a9f815a075c14d30c20b","target":"record","created_at":"2026-05-18T03:45:21Z","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":"99a218dfacc89475dc6756af58349393ad99110b20f5c204313e2b4ae75584bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-30T11:52:53Z","title_canon_sha256":"04e63c8679b81be5b37a022f67e6f6a5fa58b8c6c427fd342e130d902d949f80"},"schema_version":"1.0","source":{"id":"1106.6197","kind":"arxiv","version":2}},"canonical_sha256":"c5abe4c342b71a6f2f26e42369b6a04776485042b59aa545c87533831c3fe029","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5abe4c342b71a6f2f26e42369b6a04776485042b59aa545c87533831c3fe029","first_computed_at":"2026-05-18T03:45:21.257725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:21.257725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AuR76r2ZyFg2Ah4akfMQv8zEoLeH7D9NOIJwXc4QsSoPshSG7ESil1jfTrIfKbRf/sFwPpcbGP8aSU2kdzJAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:21.258200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.6197","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ecb4471a98dea05c1d15a86bbe4bca572e7a4501c33a9f815a075c14d30c20b","sha256:64594893581073045aefe8039b1c0139c8e157c7f9cd109c5ce05204b71b97cd"],"state_sha256":"e7983b67cc91675ea291ac0f1a5eaa4b94c4a027f1c2f823ab7e94e9ada7eb54"}