{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PLKAWJMHSON2Y6MSYNUUEFCQ7W","short_pith_number":"pith:PLKAWJMH","canonical_record":{"source":{"id":"1912.01896","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:12:37Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"186803caec01775a93594a322044bcd2762420644ec7cd5954b1c564619d8310","abstract_canon_sha256":"ff611e0412cd978797dde684a2a2ef9cf2851a9ada2ff2ee22799926a3d6c7fd"},"schema_version":"1.0"},"canonical_sha256":"7ad40b2587939bac7992c369421450fd8ca6438103f825bea17cb405e526f411","source":{"kind":"arxiv","id":"1912.01896","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.01896","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1912.01896v4","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.01896","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"PLKAWJMHSON2","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"pith_short_16","alias_value":"PLKAWJMHSON2Y6MS","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"pith_short_8","alias_value":"PLKAWJMH","created_at":"2026-07-05T01:13:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PLKAWJMHSON2Y6MSYNUUEFCQ7W","target":"record","payload":{"canonical_record":{"source":{"id":"1912.01896","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:12:37Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"186803caec01775a93594a322044bcd2762420644ec7cd5954b1c564619d8310","abstract_canon_sha256":"ff611e0412cd978797dde684a2a2ef9cf2851a9ada2ff2ee22799926a3d6c7fd"},"schema_version":"1.0"},"canonical_sha256":"7ad40b2587939bac7992c369421450fd8ca6438103f825bea17cb405e526f411","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:13:56.487240Z","signature_b64":"R85OkjPA0Cn5t/r0P9QeJMgc9cfsBa5OtgqjhSPUiF8VC/R/zKSUgKmY4bQYf/PyAAhgGhCwayTgQIlOt1I7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ad40b2587939bac7992c369421450fd8ca6438103f825bea17cb405e526f411","last_reissued_at":"2026-07-05T01:13:56.486850Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:13:56.486850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.01896","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBHJ8Iat813/22UP2EpFtbRf2zJ6m2LO2/MyaF0Ot+0T1QzTZuaVqKiM+R397TFMITOmfx2kSA5CsnemNAJxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T19:25:37.207750Z"},"content_sha256":"0b3108b67529d6f59659396b4a01ddda89d89e493b7ec0d53b000eaebb514b7b","schema_version":"1.0","event_id":"sha256:0b3108b67529d6f59659396b4a01ddda89d89e493b7ec0d53b000eaebb514b7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PLKAWJMHSON2Y6MSYNUUEFCQ7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed form fermionic expressions for the Macdonald index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Omar Foda, Rui-Dong Zhu","submitted_at":"2019-12-04T11:12:37Z","abstract_excerpt":"We interpret aspects of the Schur indices, that were identified with characters of highest weight modules in Virasoro $(p,p')=(2,2k+3)$ minimal models for $k=1,2,\\dots$, in terms of paths that first appeared in exact solutions in statistical mechanics. From that, we propose closed-form fermionic sum expressions, that is, $q, t$-series with manifestly non-negative coefficients, for two infinite-series of Macdonald indices of $(A_1,A_{2k})$ Argyres-Douglas theories that correspond to $t$-refinements of Virasoro $(p,p')=(2,2k+3)$ minimal model characters, and two rank-2 Macdonald indices that cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01896","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.01896/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:13:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YJp+fVNCh8WjjavGw08JEi0HmkUFU6DfXTSZVEE9gXncecykanTIaj/lY0dTFlTlQcm5zZUz9jkCEQQpDmzmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T19:25:37.208408Z"},"content_sha256":"dd40184216142ca3e9cc2e721f4be1f04f9fb2bf5aa3f6d1687fe0f789a6345f","schema_version":"1.0","event_id":"sha256:dd40184216142ca3e9cc2e721f4be1f04f9fb2bf5aa3f6d1687fe0f789a6345f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W/bundle.json","state_url":"https://pith.science/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-02T19:25:37Z","links":{"resolver":"https://pith.science/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W","bundle":"https://pith.science/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W/bundle.json","state":"https://pith.science/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PLKAWJMHSON2Y6MSYNUUEFCQ7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PLKAWJMHSON2Y6MSYNUUEFCQ7W","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":"ff611e0412cd978797dde684a2a2ef9cf2851a9ada2ff2ee22799926a3d6c7fd","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:12:37Z","title_canon_sha256":"186803caec01775a93594a322044bcd2762420644ec7cd5954b1c564619d8310"},"schema_version":"1.0","source":{"id":"1912.01896","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.01896","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"arxiv_version","alias_value":"1912.01896v4","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.01896","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"pith_short_12","alias_value":"PLKAWJMHSON2","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"pith_short_16","alias_value":"PLKAWJMHSON2Y6MS","created_at":"2026-07-05T01:13:56Z"},{"alias_kind":"pith_short_8","alias_value":"PLKAWJMH","created_at":"2026-07-05T01:13:56Z"}],"graph_snapshots":[{"event_id":"sha256:dd40184216142ca3e9cc2e721f4be1f04f9fb2bf5aa3f6d1687fe0f789a6345f","target":"graph","created_at":"2026-07-05T01:13:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.01896/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We interpret aspects of the Schur indices, that were identified with characters of highest weight modules in Virasoro $(p,p')=(2,2k+3)$ minimal models for $k=1,2,\\dots$, in terms of paths that first appeared in exact solutions in statistical mechanics. From that, we propose closed-form fermionic sum expressions, that is, $q, t$-series with manifestly non-negative coefficients, for two infinite-series of Macdonald indices of $(A_1,A_{2k})$ Argyres-Douglas theories that correspond to $t$-refinements of Virasoro $(p,p')=(2,2k+3)$ minimal model characters, and two rank-2 Macdonald indices that cor","authors_text":"Omar Foda, Rui-Dong Zhu","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:12:37Z","title":"Closed form fermionic expressions for the Macdonald index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.01896","kind":"arxiv","version":4},"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":"sha256:0b3108b67529d6f59659396b4a01ddda89d89e493b7ec0d53b000eaebb514b7b","target":"record","created_at":"2026-07-05T01:13:56Z","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":"ff611e0412cd978797dde684a2a2ef9cf2851a9ada2ff2ee22799926a3d6c7fd","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-04T11:12:37Z","title_canon_sha256":"186803caec01775a93594a322044bcd2762420644ec7cd5954b1c564619d8310"},"schema_version":"1.0","source":{"id":"1912.01896","kind":"arxiv","version":4}},"canonical_sha256":"7ad40b2587939bac7992c369421450fd8ca6438103f825bea17cb405e526f411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ad40b2587939bac7992c369421450fd8ca6438103f825bea17cb405e526f411","first_computed_at":"2026-07-05T01:13:56.486850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:13:56.486850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R85OkjPA0Cn5t/r0P9QeJMgc9cfsBa5OtgqjhSPUiF8VC/R/zKSUgKmY4bQYf/PyAAhgGhCwayTgQIlOt1I7CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:13:56.487240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.01896","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b3108b67529d6f59659396b4a01ddda89d89e493b7ec0d53b000eaebb514b7b","sha256:dd40184216142ca3e9cc2e721f4be1f04f9fb2bf5aa3f6d1687fe0f789a6345f"],"state_sha256":"a3324a837b3ab5fc4ae5db0b32bef684969b137c5d67005df41e962527d1fb5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0O4PH2UDPzk1h6416oOU8bzyHqoWgGsjZq5FIHZBAY74mFvD/xnftgKxeZ8kdsFMR3cJBTmP7sbaTcFfrJE0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T19:25:37.213707Z","bundle_sha256":"2de0743bae496e158752cdee143d8e51c5759fc2efbdc6b1929f2741e85785eb"}}