{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WJGBWBU7YEHJYAXYKSVFJJB55M","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":"8a0eae44fd31e9da1bc1b1f3a1628177f6d37699c1b29326eeb9224b6c5a4025","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T14:31:53Z","title_canon_sha256":"a4818d1db4ff7e1d0b0062be423044941730163780f924f9d7e19c1996f08089"},"schema_version":"1.0","source":{"id":"1608.03188","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03188","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03188v3","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03188","created_at":"2026-05-18T00:51:47Z"},{"alias_kind":"pith_short_12","alias_value":"WJGBWBU7YEHJ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WJGBWBU7YEHJYAXY","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WJGBWBU7","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:b6f98d937563e212b70b03d45031b22f43944bd3b974c47e348bb22e8ca9dd6a","target":"graph","created_at":"2026-05-18T00:51:47Z","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":"Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group $SO(N_f)$ in $U(N_c)$ gauge theory by using Gelfand pairs and Schur-Weyl duality. The singlet operators, when specialised at $N_f =6$, belong to the scalar sector of ${\\cal N}=4$ SYM. A simple formula is given for the two-point functions in the free field limit of $g_{YM}^2 =0$. The free two-point functions are shown to be equal to the partition function on a 2-complex with boundaries and a defect, in a topological field theory of permutations","authors_text":"Ryo Suzuki, Sanjaye Ramgoolam, Yusuke Kimura","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T14:31:53Z","title":"Flavour singlets in gauge theory as Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03188","kind":"arxiv","version":3},"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:f1d04de510b4a32b6a1d98ed60f9ef980973b7ec2018493d385e754fdc517cdf","target":"record","created_at":"2026-05-18T00:51:47Z","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":"8a0eae44fd31e9da1bc1b1f3a1628177f6d37699c1b29326eeb9224b6c5a4025","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-08-10T14:31:53Z","title_canon_sha256":"a4818d1db4ff7e1d0b0062be423044941730163780f924f9d7e19c1996f08089"},"schema_version":"1.0","source":{"id":"1608.03188","kind":"arxiv","version":3}},"canonical_sha256":"b24c1b069fc10e9c02f854aa54a43deb0922135ec4d6a607798a11cb0e1e205b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b24c1b069fc10e9c02f854aa54a43deb0922135ec4d6a607798a11cb0e1e205b","first_computed_at":"2026-05-18T00:51:47.312933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:47.312933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OIWk+xgkFL8A3+a/+XL+o1jPpgatpnUzMYgo4KGDJowJWjfou6pqAKDyjfvc7F4VufopUqKfeG4EJ4MEFzKdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:47.313716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03188","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1d04de510b4a32b6a1d98ed60f9ef980973b7ec2018493d385e754fdc517cdf","sha256:b6f98d937563e212b70b03d45031b22f43944bd3b974c47e348bb22e8ca9dd6a"],"state_sha256":"e29ad59db9c7b258eb0d1a0608a812fdb0a428226f774525bf5098158a547c2a"}