{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NTJ3HCDNIZMH3O44ZGC4HZVDDD","short_pith_number":"pith:NTJ3HCDN","schema_version":"1.0","canonical_sha256":"6cd3b3886d46587dbb9cc985c3e6a318eaaabb9123aad3df39c410a0c394a601","source":{"kind":"arxiv","id":"2405.12269","version":2},"attestation_state":"computed","paper":{"title":"Decomposition squared","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Eric Sharpe, Hao Zhang","submitted_at":"2024-05-20T18:00:00Z","abstract_excerpt":"In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of parallel one-dimensional objects (such as Wilson lines) and dimensional reductions to two dimensions do decompose, sometimes in two independent ways. We apply this to extend conjectures for quantum K theory rings of gerbes (realized by three-dimensional gauge theories with one-form symmetries) via both orbifold partition functions and gauged linear sigma model"},"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":"2405.12269","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-05-20T18:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"1db2802c5bb7e2963f3219f37053d415ee47cc9ed33037f6cc08caa0d4f6e353","abstract_canon_sha256":"ae46667d6fb99f03414f29a8d060aadd73b1514128ce5914fb5d9e9e3c5189d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:24:58.107871Z","signature_b64":"U3SynP6Wu9XIBwV9jh4aGidRpM0OlBnDgHlkVL5iZIfcNmkWvWXql2qXvmFdOfZoQE8DImcdT1Lr+5UmjewxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cd3b3886d46587dbb9cc985c3e6a318eaaabb9123aad3df39c410a0c394a601","last_reissued_at":"2026-07-05T09:24:58.107401Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:24:58.107401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition squared","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Eric Sharpe, Hao Zhang","submitted_at":"2024-05-20T18:00:00Z","abstract_excerpt":"In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an application of decomposition to three-dimensional theories with one-form symmetries and to quantum K theory. The theories themselves do not decompose, but, OPEs of parallel one-dimensional objects (such as Wilson lines) and dimensional reductions to two dimensions do decompose, sometimes in two independent ways. We apply this to extend conjectures for quantum K theory rings of gerbes (realized by three-dimensional gauge theories with one-form symmetries) via both orbifold partition functions and gauged linear sigma model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12269","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/2405.12269/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":"2405.12269","created_at":"2026-07-05T09:24:58.107460+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.12269v2","created_at":"2026-07-05T09:24:58.107460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12269","created_at":"2026-07-05T09:24:58.107460+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTJ3HCDNIZMH","created_at":"2026-07-05T09:24:58.107460+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTJ3HCDNIZMH3O44","created_at":"2026-07-05T09:24:58.107460+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTJ3HCDN","created_at":"2026-07-05T09:24:58.107460+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.15261","citing_title":"On the Schubert calculus of the quantum K-theory for partial flag manifolds: a 3d A-model perspective","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2508.00050","citing_title":"Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries","ref_index":100,"is_internal_anchor":false},{"citing_arxiv_id":"2512.19802","citing_title":"Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2601.18881","citing_title":"Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials","ref_index":20,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD","json":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD.json","graph_json":"https://pith.science/api/pith-number/NTJ3HCDNIZMH3O44ZGC4HZVDDD/graph.json","events_json":"https://pith.science/api/pith-number/NTJ3HCDNIZMH3O44ZGC4HZVDDD/events.json","paper":"https://pith.science/paper/NTJ3HCDN"},"agent_actions":{"view_html":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD","download_json":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD.json","view_paper":"https://pith.science/paper/NTJ3HCDN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.12269&json=true","fetch_graph":"https://pith.science/api/pith-number/NTJ3HCDNIZMH3O44ZGC4HZVDDD/graph.json","fetch_events":"https://pith.science/api/pith-number/NTJ3HCDNIZMH3O44ZGC4HZVDDD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD/action/storage_attestation","attest_author":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD/action/author_attestation","sign_citation":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD/action/citation_signature","submit_replication":"https://pith.science/pith/NTJ3HCDNIZMH3O44ZGC4HZVDDD/action/replication_record"}},"created_at":"2026-07-05T09:24:58.107460+00:00","updated_at":"2026-07-05T09:24:58.107460+00:00"}