{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:FFK66JTFMB47IV7SLUISOSRYTB","short_pith_number":"pith:FFK66JTF","canonical_record":{"source":{"id":"2103.03205","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-03-04T18:15:12Z","cross_cats_sorted":[],"title_canon_sha256":"9035742f1fce46c1d47ccef4624d56c33df21543ba6f46007915374f36f5864d","abstract_canon_sha256":"a0bf7435ab9ceb4705b30b517abf6f7076e8c257d9f84636ae6415de56567858"},"schema_version":"1.0"},"canonical_sha256":"2955ef26656079f457f25d11274a389868fcd94c6b5875855ab6f1092d825a5c","source":{"kind":"arxiv","id":"2103.03205","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.03205","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2103.03205v2","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.03205","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"FFK66JTFMB47","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"FFK66JTFMB47IV7S","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"FFK66JTF","created_at":"2026-07-05T03:04:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:FFK66JTFMB47IV7SLUISOSRYTB","target":"record","payload":{"canonical_record":{"source":{"id":"2103.03205","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-03-04T18:15:12Z","cross_cats_sorted":[],"title_canon_sha256":"9035742f1fce46c1d47ccef4624d56c33df21543ba6f46007915374f36f5864d","abstract_canon_sha256":"a0bf7435ab9ceb4705b30b517abf6f7076e8c257d9f84636ae6415de56567858"},"schema_version":"1.0"},"canonical_sha256":"2955ef26656079f457f25d11274a389868fcd94c6b5875855ab6f1092d825a5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:04:47.156957Z","signature_b64":"5+4otHspX6QwAY+xN82BV1vR6vphTW8G+keFuF+Oagz/OMAY9SRkTvjo63S4eZWyEiwcTZNa9QqGBVngKWp2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2955ef26656079f457f25d11274a389868fcd94c6b5875855ab6f1092d825a5c","last_reissued_at":"2026-07-05T03:04:47.156568Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:04:47.156568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.03205","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0JJGTGNTUsVK3CCD50LD1LDYc5cY4pEy0O5QgeMQ30Mm5rrO5FZDAqFxDDKKNJzT3qJqDytwcuWGGfI+jANFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T06:32:48.539408Z"},"content_sha256":"42cd31c8d3e75de90e88011788eeaa7febb5ad149ff34cddff883ec2314c0eb6","schema_version":"1.0","event_id":"sha256:42cd31c8d3e75de90e88011788eeaa7febb5ad149ff34cddff883ec2314c0eb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:FFK66JTFMB47IV7SLUISOSRYTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-centered black holes, scaling solutions and pure-Higgs indices from localization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Boris Pioline, Guillaume Beaujard, Swapnamay Mondal","submitted_at":"2021-03-04T18:15:12Z","abstract_excerpt":"The Coulomb Branch Formula conjecturally expresses the refined Witten index for $N=4$ Quiver Quantum Mechanics as a sum over multi-centered collinear black hole solutions, weighted by so-called `single-centered' or `pure-Higgs' indices, and suitably modified when the quiver has oriented cycles. On the other hand, localization expresses the same index as an integral over the complexified Cartan torus and auxiliary fields, which by Stokes' theorem leads to the famous Jeffrey-Kirwan residue formula. Here, by evaluating the same integral using steepest descent methods, we show the index is in fact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.03205","kind":"arxiv","version":2},"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/2103.03205/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":"2026-07-05T03:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJ2mYI46uwL7csKSo052vmdoXGBdczgj9YWzcR7xUDSGdmK/IAuOzxPFpeFRxKreRuPKa1NF94ZIJyYiutRnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T06:32:48.539966Z"},"content_sha256":"af6edebd85775a5abd3c1adf095855d286ffeaa101f1b6f9f7ba778fad8a9903","schema_version":"1.0","event_id":"sha256:af6edebd85775a5abd3c1adf095855d286ffeaa101f1b6f9f7ba778fad8a9903"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFK66JTFMB47IV7SLUISOSRYTB/bundle.json","state_url":"https://pith.science/pith/FFK66JTFMB47IV7SLUISOSRYTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFK66JTFMB47IV7SLUISOSRYTB/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":"2026-08-03T06:32:48Z","links":{"resolver":"https://pith.science/pith/FFK66JTFMB47IV7SLUISOSRYTB","bundle":"https://pith.science/pith/FFK66JTFMB47IV7SLUISOSRYTB/bundle.json","state":"https://pith.science/pith/FFK66JTFMB47IV7SLUISOSRYTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFK66JTFMB47IV7SLUISOSRYTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FFK66JTFMB47IV7SLUISOSRYTB","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":"a0bf7435ab9ceb4705b30b517abf6f7076e8c257d9f84636ae6415de56567858","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-03-04T18:15:12Z","title_canon_sha256":"9035742f1fce46c1d47ccef4624d56c33df21543ba6f46007915374f36f5864d"},"schema_version":"1.0","source":{"id":"2103.03205","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.03205","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2103.03205v2","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.03205","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"FFK66JTFMB47","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"FFK66JTFMB47IV7S","created_at":"2026-07-05T03:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"FFK66JTF","created_at":"2026-07-05T03:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:af6edebd85775a5abd3c1adf095855d286ffeaa101f1b6f9f7ba778fad8a9903","target":"graph","created_at":"2026-07-05T03:04:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.03205/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Coulomb Branch Formula conjecturally expresses the refined Witten index for $N=4$ Quiver Quantum Mechanics as a sum over multi-centered collinear black hole solutions, weighted by so-called `single-centered' or `pure-Higgs' indices, and suitably modified when the quiver has oriented cycles. On the other hand, localization expresses the same index as an integral over the complexified Cartan torus and auxiliary fields, which by Stokes' theorem leads to the famous Jeffrey-Kirwan residue formula. Here, by evaluating the same integral using steepest descent methods, we show the index is in fact","authors_text":"Boris Pioline, Guillaume Beaujard, Swapnamay Mondal","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-03-04T18:15:12Z","title":"Multi-centered black holes, scaling solutions and pure-Higgs indices from localization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.03205","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":"sha256:42cd31c8d3e75de90e88011788eeaa7febb5ad149ff34cddff883ec2314c0eb6","target":"record","created_at":"2026-07-05T03:04:47Z","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":"a0bf7435ab9ceb4705b30b517abf6f7076e8c257d9f84636ae6415de56567858","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-03-04T18:15:12Z","title_canon_sha256":"9035742f1fce46c1d47ccef4624d56c33df21543ba6f46007915374f36f5864d"},"schema_version":"1.0","source":{"id":"2103.03205","kind":"arxiv","version":2}},"canonical_sha256":"2955ef26656079f457f25d11274a389868fcd94c6b5875855ab6f1092d825a5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2955ef26656079f457f25d11274a389868fcd94c6b5875855ab6f1092d825a5c","first_computed_at":"2026-07-05T03:04:47.156568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:04:47.156568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+4otHspX6QwAY+xN82BV1vR6vphTW8G+keFuF+Oagz/OMAY9SRkTvjo63S4eZWyEiwcTZNa9QqGBVngKWp2Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T03:04:47.156957Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.03205","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42cd31c8d3e75de90e88011788eeaa7febb5ad149ff34cddff883ec2314c0eb6","sha256:af6edebd85775a5abd3c1adf095855d286ffeaa101f1b6f9f7ba778fad8a9903"],"state_sha256":"27183da17ed76c02fe61b9b83a4cdab3bd41b5f09efd291845ae8a3c598971bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S54ABrPWjTQYgPsjRb43ZqWbT0Z2ABcuj7iVRggEnp/qFFqZJtd+9XpcyVEnqTtCXkYuPxdned2mtwi3tW4+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T06:32:48.544464Z","bundle_sha256":"21fe8fc8ef87903c18e02923a66c16e215210f6f399587d5bcedb59a5ce02020"}}