{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7OB3WOHR5JD4ZZDIDEV4LYVYH2","short_pith_number":"pith:7OB3WOHR","schema_version":"1.0","canonical_sha256":"fb83bb38f1ea47cce468192bc5e2b83e8942a132f77cabba60c071b3c6565b7e","source":{"kind":"arxiv","id":"2309.05326","version":3},"attestation_state":"computed","paper":{"title":"Probing bad theories with the dualization algorithm I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chiung Hwang, Fabio Marino, Matteo Sacchi, Sara Pasquetti, Simone Giacomelli","submitted_at":"2023-09-11T09:19:15Z","abstract_excerpt":"Recently an algorithm to build $SL(2,\\mathbb{Z})$ duals, including mirror duals, of 3d $\\mathcal{N}=4$ quiver theories and their 4d $\\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with $U(N"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2309.05326","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-11T09:19:15Z","cross_cats_sorted":[],"title_canon_sha256":"366b72c1e42ac5a4dbcd459ad081ef24f86a6f975462daa68f9eca4f54d12296","abstract_canon_sha256":"0b1887f97fd3e415d4438994fbd3bede09f39a287e3e9f1ffe1be7773b8861b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:03:44.063163Z","signature_b64":"rlg+nNNwsMST+NNnBN9G8HILNG2f5RxzsDc9x73ipzTGFFahRzPVOmg6wab8RUOTV3vpl3aAjcdsflX9WwR5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb83bb38f1ea47cce468192bc5e2b83e8942a132f77cabba60c071b3c6565b7e","last_reissued_at":"2026-07-05T08:03:44.062770Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:03:44.062770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probing bad theories with the dualization algorithm I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chiung Hwang, Fabio Marino, Matteo Sacchi, Sara Pasquetti, Simone Giacomelli","submitted_at":"2023-09-11T09:19:15Z","abstract_excerpt":"Recently an algorithm to build $SL(2,\\mathbb{Z})$ duals, including mirror duals, of 3d $\\mathcal{N}=4$ quiver theories and their 4d $\\mathcal{N}=1$ uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with $U(N"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05326","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/2309.05326/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2309.05326","created_at":"2026-07-05T08:03:44.062824+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.05326v3","created_at":"2026-07-05T08:03:44.062824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.05326","created_at":"2026-07-05T08:03:44.062824+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OB3WOHR5JD4","created_at":"2026-07-05T08:03:44.062824+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OB3WOHR5JD4ZZDI","created_at":"2026-07-05T08:03:44.062824+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OB3WOHR","created_at":"2026-07-05T08:03:44.062824+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2607.01327","citing_title":"Algorithmic Dualization of Unitary Circular Quivers","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30731","citing_title":"Half-BPS Boundaries and the RG-Wall of $\\mathcal{N}=2$ $SU(N)$ SYM","ref_index":63,"is_internal_anchor":false},{"citing_arxiv_id":"2604.17449","citing_title":"Refined 3D index","ref_index":42,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2","json":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2.json","graph_json":"https://pith.science/api/pith-number/7OB3WOHR5JD4ZZDIDEV4LYVYH2/graph.json","events_json":"https://pith.science/api/pith-number/7OB3WOHR5JD4ZZDIDEV4LYVYH2/events.json","paper":"https://pith.science/paper/7OB3WOHR"},"agent_actions":{"view_html":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2","download_json":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2.json","view_paper":"https://pith.science/paper/7OB3WOHR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.05326&json=true","fetch_graph":"https://pith.science/api/pith-number/7OB3WOHR5JD4ZZDIDEV4LYVYH2/graph.json","fetch_events":"https://pith.science/api/pith-number/7OB3WOHR5JD4ZZDIDEV4LYVYH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2/action/storage_attestation","attest_author":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2/action/author_attestation","sign_citation":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2/action/citation_signature","submit_replication":"https://pith.science/pith/7OB3WOHR5JD4ZZDIDEV4LYVYH2/action/replication_record"}},"created_at":"2026-07-05T08:03:44.062824+00:00","updated_at":"2026-07-05T08:03:44.062824+00:00"}