{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:MEKW6IVU2VO2S2TTOW64GXEKM4","short_pith_number":"pith:MEKW6IVU","canonical_record":{"source":{"id":"2012.11711","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2020-12-21T22:16:08Z","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"title_canon_sha256":"f27c7305e7651fca53420b27e3d041d2b7bdae278c657ce98f0487d620a47995","abstract_canon_sha256":"7b537caf24748cfa0cd259923e5d15a7d7c8a8a114f2087c0929bb0ce81d7625"},"schema_version":"1.0"},"canonical_sha256":"61156f22b4d55da96a7375bdc35c8a67068404de225a979a0045fc2b15484a3b","source":{"kind":"arxiv","id":"2012.11711","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.11711","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"arxiv_version","alias_value":"2012.11711v3","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11711","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"pith_short_12","alias_value":"MEKW6IVU2VO2","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"pith_short_16","alias_value":"MEKW6IVU2VO2S2TT","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"pith_short_8","alias_value":"MEKW6IVU","created_at":"2026-07-05T02:56:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:MEKW6IVU2VO2S2TTOW64GXEKM4","target":"record","payload":{"canonical_record":{"source":{"id":"2012.11711","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2020-12-21T22:16:08Z","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"title_canon_sha256":"f27c7305e7651fca53420b27e3d041d2b7bdae278c657ce98f0487d620a47995","abstract_canon_sha256":"7b537caf24748cfa0cd259923e5d15a7d7c8a8a114f2087c0929bb0ce81d7625"},"schema_version":"1.0"},"canonical_sha256":"61156f22b4d55da96a7375bdc35c8a67068404de225a979a0045fc2b15484a3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:13.988157Z","signature_b64":"N19N1jy8cj+5GpQfAMD9FFAcyzQIwBmoE4PjtDK6UiXuqv3I9kDFj/bYR/kZ9EidR19lzi1qb/lZ4+Mjp/8JBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61156f22b4d55da96a7375bdc35c8a67068404de225a979a0045fc2b15484a3b","last_reissued_at":"2026-07-05T02:56:13.987802Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:13.987802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.11711","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:56:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6EOeo3JMgpbAKF5IRS5xM0u20/kn4SRoTdQMBYFusjWB2a3ZHbyvqRBDPhla7IhTNzgxHDpT1awgWbQrmiDPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T11:35:04.848527Z"},"content_sha256":"bc136f75c367f7b0cf04ccd4506221ab60a8c1231abf5e73796d595a69265e06","schema_version":"1.0","event_id":"sha256:bc136f75c367f7b0cf04ccd4506221ab60a8c1231abf5e73796d595a69265e06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:MEKW6IVU2VO2S2TTOW64GXEKM4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Instanton Counting, Quantum Geometry and Algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"Taro Kimura","submitted_at":"2020-12-21T22:16:08Z","abstract_excerpt":"The aim of this memoir for \"Habilitation \\`a Diriger des Recherches\" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by instantons. We start with a brief summary of the equivariant localization of the instanton moduli space, and show how to obtain the instanton partition function and its generalization to quiver gauge theory and supergroup gauge theory in three ways: the equivariant index formula, the contour integral formula, and the combinatorial formula. We then explore the geomet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11711","kind":"arxiv","version":3},"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/2012.11711/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":"2026-07-05T02:56:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KtUhxPNph1bSh8qOwk6dByZOPTcJJxcsuduJKuDauMX/oDnPXxeNFmrgQLrFhINBJ30k8TPtaI46m9b6Ah9dDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T11:35:04.850412Z"},"content_sha256":"e3a2387635b6f068483200b720654220e49301650845325a10e83246509995a4","schema_version":"1.0","event_id":"sha256:e3a2387635b6f068483200b720654220e49301650845325a10e83246509995a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEKW6IVU2VO2S2TTOW64GXEKM4/bundle.json","state_url":"https://pith.science/pith/MEKW6IVU2VO2S2TTOW64GXEKM4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEKW6IVU2VO2S2TTOW64GXEKM4/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":"2026-08-12T11:35:04Z","links":{"resolver":"https://pith.science/pith/MEKW6IVU2VO2S2TTOW64GXEKM4","bundle":"https://pith.science/pith/MEKW6IVU2VO2S2TTOW64GXEKM4/bundle.json","state":"https://pith.science/pith/MEKW6IVU2VO2S2TTOW64GXEKM4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEKW6IVU2VO2S2TTOW64GXEKM4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MEKW6IVU2VO2S2TTOW64GXEKM4","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":"7b537caf24748cfa0cd259923e5d15a7d7c8a8a114f2087c0929bb0ce81d7625","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2020-12-21T22:16:08Z","title_canon_sha256":"f27c7305e7651fca53420b27e3d041d2b7bdae278c657ce98f0487d620a47995"},"schema_version":"1.0","source":{"id":"2012.11711","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.11711","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"arxiv_version","alias_value":"2012.11711v3","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.11711","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"pith_short_12","alias_value":"MEKW6IVU2VO2","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"pith_short_16","alias_value":"MEKW6IVU2VO2S2TT","created_at":"2026-07-05T02:56:13Z"},{"alias_kind":"pith_short_8","alias_value":"MEKW6IVU","created_at":"2026-07-05T02:56:13Z"}],"graph_snapshots":[{"event_id":"sha256:e3a2387635b6f068483200b720654220e49301650845325a10e83246509995a4","target":"graph","created_at":"2026-07-05T02:56:13Z","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/2012.11711/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this memoir for \"Habilitation \\`a Diriger des Recherches\" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by instantons. We start with a brief summary of the equivariant localization of the instanton moduli space, and show how to obtain the instanton partition function and its generalization to quiver gauge theory and supergroup gauge theory in three ways: the equivariant index formula, the contour integral formula, and the combinatorial formula. We then explore the geomet","authors_text":"Taro Kimura","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2020-12-21T22:16:08Z","title":"Instanton Counting, Quantum Geometry and Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11711","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:bc136f75c367f7b0cf04ccd4506221ab60a8c1231abf5e73796d595a69265e06","target":"record","created_at":"2026-07-05T02:56:13Z","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":"7b537caf24748cfa0cd259923e5d15a7d7c8a8a114f2087c0929bb0ce81d7625","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2020-12-21T22:16:08Z","title_canon_sha256":"f27c7305e7651fca53420b27e3d041d2b7bdae278c657ce98f0487d620a47995"},"schema_version":"1.0","source":{"id":"2012.11711","kind":"arxiv","version":3}},"canonical_sha256":"61156f22b4d55da96a7375bdc35c8a67068404de225a979a0045fc2b15484a3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61156f22b4d55da96a7375bdc35c8a67068404de225a979a0045fc2b15484a3b","first_computed_at":"2026-07-05T02:56:13.987802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:56:13.987802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N19N1jy8cj+5GpQfAMD9FFAcyzQIwBmoE4PjtDK6UiXuqv3I9kDFj/bYR/kZ9EidR19lzi1qb/lZ4+Mjp/8JBw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:56:13.988157Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.11711","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc136f75c367f7b0cf04ccd4506221ab60a8c1231abf5e73796d595a69265e06","sha256:e3a2387635b6f068483200b720654220e49301650845325a10e83246509995a4"],"state_sha256":"bdba5304438632afb47da92bc4165f43c927574ae0cf4a786013bbc9c0d6c971"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jgXlNHS1SrlI8WKQKgruHfZ/TWuh033rrcoIfUMPSQD44ZzwTJ3JmvNRsOuNk2cRBpaOjSWrSjIA7HQM6fyGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T11:35:04.857513Z","bundle_sha256":"e59d3be84464aad00709e0a9dd06e02949598e7d159397b4625137f7a1588ae7"}}