{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UL4FRJFKDYCUJFAUPAEFZPOPQV","short_pith_number":"pith:UL4FRJFK","canonical_record":{"source":{"id":"1807.02784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-07-08T09:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"38c309045efe7addb534243df60285fef03c0c3f8c5bc16c6fce804e6bf1e47b","abstract_canon_sha256":"99357c79fccd34ef5fc48c4430418475b6b0c48f068acfec7841c3cbb4897331"},"schema_version":"1.0"},"canonical_sha256":"a2f858a4aa1e0544941478085cbdcf85491558b738955af76571bd856e079429","source":{"kind":"arxiv","id":"1807.02784","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02784","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02784v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02784","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"UL4FRJFKDYCU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UL4FRJFKDYCUJFAU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UL4FRJFK","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UL4FRJFKDYCUJFAUPAEFZPOPQV","target":"record","payload":{"canonical_record":{"source":{"id":"1807.02784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-07-08T09:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"38c309045efe7addb534243df60285fef03c0c3f8c5bc16c6fce804e6bf1e47b","abstract_canon_sha256":"99357c79fccd34ef5fc48c4430418475b6b0c48f068acfec7841c3cbb4897331"},"schema_version":"1.0"},"canonical_sha256":"a2f858a4aa1e0544941478085cbdcf85491558b738955af76571bd856e079429","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:17.242564Z","signature_b64":"NGVAAPm0SvS2o2AAc7hRE3CW69m4EFnIe3Dhi1tcozyVGxptuEzO+C6A32AvyfuRv5S56nD1/FKQnPAE6YMjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2f858a4aa1e0544941478085cbdcf85491558b738955af76571bd856e079429","last_reissued_at":"2026-05-18T00:07:17.241881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:17.241881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.02784","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":"2026-05-18T00:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZ23/zn+kVSIDUeHdO5w4WB3WIN+y/856EfnH5vkbLW1R71LI8tvP+FKGP7KxLqcDLKGF5oqXS/xd5GedtofAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:43:06.648491Z"},"content_sha256":"e525c3e1668de9ae7804a60ac7f022a8d9f96520d826befa303b3d111ed306b1","schema_version":"1.0","event_id":"sha256:e525c3e1668de9ae7804a60ac7f022a8d9f96520d826befa303b3d111ed306b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UL4FRJFKDYCUJFAUPAEFZPOPQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Amihay Hanany, Marcus Sperling","submitted_at":"2018-07-08T09:03:37Z","abstract_excerpt":"The study of Coulomb branches of 3-dimensional N=4 gauge theories via the associated Hilbert series, the so-called monopole formula, has been proven useful not only for 3-dimensional theories, but also for Higgs branches of 5 and 6-dimensional gauge theories with 8 supercharges. Recently, a conjecture connected different phases of 6-dimensional Higgs branches via gauging of a discrete global $S_n$ symmetry. On the corresponding 3-dimensional Coulomb branch, this amounts to a geometric $S_n$-quotient. In this note, we prove the conjecture on Coulomb branches with unitary nodes and, moreover, ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02784","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":"2026-05-18T00:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HW3PGM04m+9SIMX7zxgemNork/PLoK9Xdy+YF/8gO7iLah6zE9KCpDL1eULcQ1uRQtfL7uX/+sGe2Akox1rAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:43:06.649145Z"},"content_sha256":"0d0c103737c3448480337c2c3936223d46df45bff5a5e60f0e7ed9d59d3a2856","schema_version":"1.0","event_id":"sha256:0d0c103737c3448480337c2c3936223d46df45bff5a5e60f0e7ed9d59d3a2856"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV/bundle.json","state_url":"https://pith.science/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV/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":"2026-06-05T19:43:06Z","links":{"resolver":"https://pith.science/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV","bundle":"https://pith.science/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV/bundle.json","state":"https://pith.science/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UL4FRJFKDYCUJFAUPAEFZPOPQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UL4FRJFKDYCUJFAUPAEFZPOPQV","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":"99357c79fccd34ef5fc48c4430418475b6b0c48f068acfec7841c3cbb4897331","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-07-08T09:03:37Z","title_canon_sha256":"38c309045efe7addb534243df60285fef03c0c3f8c5bc16c6fce804e6bf1e47b"},"schema_version":"1.0","source":{"id":"1807.02784","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.02784","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1807.02784v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.02784","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"UL4FRJFKDYCU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UL4FRJFKDYCUJFAU","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UL4FRJFK","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:0d0c103737c3448480337c2c3936223d46df45bff5a5e60f0e7ed9d59d3a2856","target":"graph","created_at":"2026-05-18T00:07:17Z","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":"The study of Coulomb branches of 3-dimensional N=4 gauge theories via the associated Hilbert series, the so-called monopole formula, has been proven useful not only for 3-dimensional theories, but also for Higgs branches of 5 and 6-dimensional gauge theories with 8 supercharges. Recently, a conjecture connected different phases of 6-dimensional Higgs branches via gauging of a discrete global $S_n$ symmetry. On the corresponding 3-dimensional Coulomb branch, this amounts to a geometric $S_n$-quotient. In this note, we prove the conjecture on Coulomb branches with unitary nodes and, moreover, ex","authors_text":"Amihay Hanany, Marcus Sperling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-07-08T09:03:37Z","title":"Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02784","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:e525c3e1668de9ae7804a60ac7f022a8d9f96520d826befa303b3d111ed306b1","target":"record","created_at":"2026-05-18T00:07:17Z","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":"99357c79fccd34ef5fc48c4430418475b6b0c48f068acfec7841c3cbb4897331","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-07-08T09:03:37Z","title_canon_sha256":"38c309045efe7addb534243df60285fef03c0c3f8c5bc16c6fce804e6bf1e47b"},"schema_version":"1.0","source":{"id":"1807.02784","kind":"arxiv","version":2}},"canonical_sha256":"a2f858a4aa1e0544941478085cbdcf85491558b738955af76571bd856e079429","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2f858a4aa1e0544941478085cbdcf85491558b738955af76571bd856e079429","first_computed_at":"2026-05-18T00:07:17.241881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:17.241881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGVAAPm0SvS2o2AAc7hRE3CW69m4EFnIe3Dhi1tcozyVGxptuEzO+C6A32AvyfuRv5S56nD1/FKQnPAE6YMjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:17.242564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.02784","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e525c3e1668de9ae7804a60ac7f022a8d9f96520d826befa303b3d111ed306b1","sha256:0d0c103737c3448480337c2c3936223d46df45bff5a5e60f0e7ed9d59d3a2856"],"state_sha256":"269fd4ebb4a227a0da89ac94920ea5151acde0907f49f7ea45b558432de9f02f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Z35BCL08+hDC1Fq+yO/kTrlVBIaR7QX+Slq+h+96kPAAvTKLtiGpdffQ7GGfGy2UpI7a4AbkwvA6kxsUSbZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:43:06.652474Z","bundle_sha256":"bfe873ff39eb6894a7c7154f3a5336444425fbf4c6f9d04038e57febf85e61b5"}}