{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WVQIYUUOERSEUYJZF4SEHJDKAS","short_pith_number":"pith:WVQIYUUO","canonical_record":{"source":{"id":"1302.5498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-02-22T07:10:01Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"18d6e4cc6706fe156feb884e4cebd28ab8c25b6d38234d59feaccac5300e2022","abstract_canon_sha256":"0b4a61a6b7744c1fd9f809cccc61b69e5b3e983a6c17994ae79c10cf800cd70a"},"schema_version":"1.0"},"canonical_sha256":"b5608c528e24644a61392f2443a46a0494ea22293e669831dfc487b3a72a2fae","source":{"kind":"arxiv","id":"1302.5498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5498","created_at":"2026-05-18T01:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5498v2","created_at":"2026-05-18T01:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5498","created_at":"2026-05-18T01:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"WVQIYUUOERSE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WVQIYUUOERSEUYJZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WVQIYUUO","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WVQIYUUOERSEUYJZF4SEHJDKAS","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-02-22T07:10:01Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"18d6e4cc6706fe156feb884e4cebd28ab8c25b6d38234d59feaccac5300e2022","abstract_canon_sha256":"0b4a61a6b7744c1fd9f809cccc61b69e5b3e983a6c17994ae79c10cf800cd70a"},"schema_version":"1.0"},"canonical_sha256":"b5608c528e24644a61392f2443a46a0494ea22293e669831dfc487b3a72a2fae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:34.210492Z","signature_b64":"3u1fuPUekhOpVo4NjPJqpM7twqjaYoMUIKee2H2iZzZTenVVol8Huw6NOPNcGx9LXHs/U4geF/gcrTvN/F2BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5608c528e24644a61392f2443a46a0494ea22293e669831dfc487b3a72a2fae","last_reissued_at":"2026-05-18T01:51:34.210015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:34.210015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5498","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":"2026-05-18T01:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmvRj0XB/TlSh9yTDj43rXwlwWW5aa4k622nOKex1UvvwWJ8e7gzKYOefxXb8pFepHu91dhWD6iJyOSqhEbpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:21:32.428496Z"},"content_sha256":"45e9407ce71392a9e7568e315122d791c2f4b4996364a1524d44ac7a90906a21","schema_version":"1.0","event_id":"sha256:45e9407ce71392a9e7568e315122d791c2f4b4996364a1524d44ac7a90906a21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WVQIYUUOERSEUYJZF4SEHJDKAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"hep-th","authors_text":"Ashoke Sen, Boris Pioline, Jan Manschot","submitted_at":"2013-02-22T07:10:01Z","abstract_excerpt":"In previous work we have shown that the equivariant index of multi-centered N=2 black holes localizes on collinear configurations along a fixed axis. Here we provide a general algorithm for enumerating such collinear configurations and computing their contribution to the index. We apply this machinery to the case of black holes described by quiver quantum mechanics, and give a systematic prescription -- the Coulomb branch formula -- for computing the cohomology of the moduli space of quiver representations. For quivers without oriented loops, the Coulomb branch formula is shown to agree with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5498","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":""},"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":"2026-05-18T01:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHGGCs5YcANPGfPjw8eqeFCbBL+mvtYjnOuPoJTBnLMTSSACkDuQya1eNyw+3DXpczvS0equXWd7cDezZTgLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:21:32.429198Z"},"content_sha256":"d928280b146a2968e71479ced452300d9c9283bac6ee4acdd606decca1bd405e","schema_version":"1.0","event_id":"sha256:d928280b146a2968e71479ced452300d9c9283bac6ee4acdd606decca1bd405e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVQIYUUOERSEUYJZF4SEHJDKAS/bundle.json","state_url":"https://pith.science/pith/WVQIYUUOERSEUYJZF4SEHJDKAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVQIYUUOERSEUYJZF4SEHJDKAS/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":"2026-05-26T03:21:32Z","links":{"resolver":"https://pith.science/pith/WVQIYUUOERSEUYJZF4SEHJDKAS","bundle":"https://pith.science/pith/WVQIYUUOERSEUYJZF4SEHJDKAS/bundle.json","state":"https://pith.science/pith/WVQIYUUOERSEUYJZF4SEHJDKAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVQIYUUOERSEUYJZF4SEHJDKAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WVQIYUUOERSEUYJZF4SEHJDKAS","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":"0b4a61a6b7744c1fd9f809cccc61b69e5b3e983a6c17994ae79c10cf800cd70a","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-02-22T07:10:01Z","title_canon_sha256":"18d6e4cc6706fe156feb884e4cebd28ab8c25b6d38234d59feaccac5300e2022"},"schema_version":"1.0","source":{"id":"1302.5498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5498","created_at":"2026-05-18T01:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5498v2","created_at":"2026-05-18T01:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5498","created_at":"2026-05-18T01:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"WVQIYUUOERSE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WVQIYUUOERSEUYJZ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WVQIYUUO","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:d928280b146a2968e71479ced452300d9c9283bac6ee4acdd606decca1bd405e","target":"graph","created_at":"2026-05-18T01:51:34Z","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":"In previous work we have shown that the equivariant index of multi-centered N=2 black holes localizes on collinear configurations along a fixed axis. Here we provide a general algorithm for enumerating such collinear configurations and computing their contribution to the index. We apply this machinery to the case of black holes described by quiver quantum mechanics, and give a systematic prescription -- the Coulomb branch formula -- for computing the cohomology of the moduli space of quiver representations. For quivers without oriented loops, the Coulomb branch formula is shown to agree with t","authors_text":"Ashoke Sen, Boris Pioline, Jan Manschot","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-02-22T07:10:01Z","title":"On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5498","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":"sha256:45e9407ce71392a9e7568e315122d791c2f4b4996364a1524d44ac7a90906a21","target":"record","created_at":"2026-05-18T01:51:34Z","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":"0b4a61a6b7744c1fd9f809cccc61b69e5b3e983a6c17994ae79c10cf800cd70a","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-02-22T07:10:01Z","title_canon_sha256":"18d6e4cc6706fe156feb884e4cebd28ab8c25b6d38234d59feaccac5300e2022"},"schema_version":"1.0","source":{"id":"1302.5498","kind":"arxiv","version":2}},"canonical_sha256":"b5608c528e24644a61392f2443a46a0494ea22293e669831dfc487b3a72a2fae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5608c528e24644a61392f2443a46a0494ea22293e669831dfc487b3a72a2fae","first_computed_at":"2026-05-18T01:51:34.210015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:51:34.210015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3u1fuPUekhOpVo4NjPJqpM7twqjaYoMUIKee2H2iZzZTenVVol8Huw6NOPNcGx9LXHs/U4geF/gcrTvN/F2BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:51:34.210492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45e9407ce71392a9e7568e315122d791c2f4b4996364a1524d44ac7a90906a21","sha256:d928280b146a2968e71479ced452300d9c9283bac6ee4acdd606decca1bd405e"],"state_sha256":"4430c668827886d03fbf44de6994567cd2a3f00a185e94a7fdccfe22b7aaa9a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3Kjggd8lDFcTInDaG9F3emjGz5DsAL8VyByqNHCiqwxO47Iw4LRPihu98+FWRPBakKAR7JAnQn0NHp7JHA9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:21:32.432731Z","bundle_sha256":"cb98139c011645470197d6b06615865859f3f27d08f920742c6dd9d007d9321d"}}