{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:WDVZ4ZVTCPBQ5HBHSII36LZTH2","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":"87727960fcf07b5f5563637b783aee503958cde3114bc1bed679d6e1adc289f1","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-09-02T18:00:00Z","title_canon_sha256":"8ff2be901fb70bfb481bcb332dc03a1b89e5ad36dcf59aeb84e64ec2ed98e0f2"},"schema_version":"1.0","source":{"id":"2009.01239","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.01239","created_at":"2026-07-05T02:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"2009.01239v2","created_at":"2026-07-05T02:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.01239","created_at":"2026-07-05T02:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"WDVZ4ZVTCPBQ","created_at":"2026-07-05T02:17:32Z"},{"alias_kind":"pith_short_16","alias_value":"WDVZ4ZVTCPBQ5HBH","created_at":"2026-07-05T02:17:32Z"},{"alias_kind":"pith_short_8","alias_value":"WDVZ4ZVT","created_at":"2026-07-05T02:17:32Z"}],"graph_snapshots":[{"event_id":"sha256:e10b84a763e278ba8b676412b79e9d50239f66d5e0e19c31c9e2f8cd48021b3b","target":"graph","created_at":"2026-07-05T02:17:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.01239/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $\\frak{su}(n)$ Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order $p^8$, as well as enumeration of $CP$-even, $CP$-odd, $C$-odd, and $P$-odd terms beg","authors_text":"Brian Henning, Hitoshi Murayama, Lukas Graf, Tom Melia, Xiaochuan Lu","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-09-02T18:00:00Z","title":"2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.01239","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":"sha256:83b009c22437a9da86502ded8a4915f95faa90290d9117604ab046aa35e8db7e","target":"record","created_at":"2026-07-05T02:17:32Z","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":"87727960fcf07b5f5563637b783aee503958cde3114bc1bed679d6e1adc289f1","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2020-09-02T18:00:00Z","title_canon_sha256":"8ff2be901fb70bfb481bcb332dc03a1b89e5ad36dcf59aeb84e64ec2ed98e0f2"},"schema_version":"1.0","source":{"id":"2009.01239","kind":"arxiv","version":2}},"canonical_sha256":"b0eb9e66b313c30e9c279211bf2f333eaadc25d4eadc02e98e31c42b92eb41d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0eb9e66b313c30e9c279211bf2f333eaadc25d4eadc02e98e31c42b92eb41d6","first_computed_at":"2026-07-05T02:17:32.503755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:17:32.503755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c3fHMKeMSy3F/yGU4z+UDpNdMu67czCrXec333zIoEIcV8YkmLyDbGH0srwH1E07gpPbaS85lKMEZ0Z6OL/TBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:17:32.504212Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.01239","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83b009c22437a9da86502ded8a4915f95faa90290d9117604ab046aa35e8db7e","sha256:e10b84a763e278ba8b676412b79e9d50239f66d5e0e19c31c9e2f8cd48021b3b"],"state_sha256":"69e8e38c01e15e221b3909b75fa6d2f6f88ca18088a90d168f8c4dc54b3d24b2"}