{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6I7LCRRXMGL4EEXT5XC7IHZU36","short_pith_number":"pith:6I7LCRRX","schema_version":"1.0","canonical_sha256":"f23eb146376197c212f3edc5f41f34df973b47c251b342d1b2d86d82018a9803","source":{"kind":"arxiv","id":"1503.04809","version":3},"attestation_state":"computed","paper":{"title":"A 3d-3d appetizer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Du Pei, Ke Ye","submitted_at":"2015-03-16T20:00:22Z","abstract_excerpt":"We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d ${\\cal N}=2$ \"Lens space theory\" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition function of Chern-Simons theory arises from the index of a free theory. For large $p$, we find that the index of $T[L(p,1)]$ becomes a constant independent of $p$. In addition, we study $T[L(p,1)]$ on the squashed three-sphere $S^3_b$. This enables us to see clearly, at the level of "},"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":"1503.04809","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-03-16T20:00:22Z","cross_cats_sorted":["math-ph","math.GT","math.MP","math.QA"],"title_canon_sha256":"b9ed9c4529845914786cca8cb0333d567d4c50284995ebd8f9782aa25c07b6dc","abstract_canon_sha256":"12313124195f85453e4fc349d6add33616447e2b01a9dba5ebcf503f60c8ffa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:32.094807Z","signature_b64":"If15YKlPbX69ugWYmeE2Ns1oxBavrWGVr57Dzyi++P/wuOVANWN196DIba6xMIIEELPcB8PjfkaV/ZZp+v5vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f23eb146376197c212f3edc5f41f34df973b47c251b342d1b2d86d82018a9803","last_reissued_at":"2026-05-18T00:57:32.094287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:32.094287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A 3d-3d appetizer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GT","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Du Pei, Ke Ye","submitted_at":"2015-03-16T20:00:22Z","abstract_excerpt":"We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d ${\\cal N}=2$ \"Lens space theory\" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition function of Chern-Simons theory arises from the index of a free theory. For large $p$, we find that the index of $T[L(p,1)]$ becomes a constant independent of $p$. In addition, we study $T[L(p,1)]$ on the squashed three-sphere $S^3_b$. This enables us to see clearly, at the level of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04809","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":""},"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":"1503.04809","created_at":"2026-05-18T00:57:32.094364+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.04809v3","created_at":"2026-05-18T00:57:32.094364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04809","created_at":"2026-05-18T00:57:32.094364+00:00"},{"alias_kind":"pith_short_12","alias_value":"6I7LCRRXMGL4","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6I7LCRRXMGL4EEXT","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6I7LCRRX","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.17449","citing_title":"Refined 3D index","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36","json":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36.json","graph_json":"https://pith.science/api/pith-number/6I7LCRRXMGL4EEXT5XC7IHZU36/graph.json","events_json":"https://pith.science/api/pith-number/6I7LCRRXMGL4EEXT5XC7IHZU36/events.json","paper":"https://pith.science/paper/6I7LCRRX"},"agent_actions":{"view_html":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36","download_json":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36.json","view_paper":"https://pith.science/paper/6I7LCRRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.04809&json=true","fetch_graph":"https://pith.science/api/pith-number/6I7LCRRXMGL4EEXT5XC7IHZU36/graph.json","fetch_events":"https://pith.science/api/pith-number/6I7LCRRXMGL4EEXT5XC7IHZU36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36/action/storage_attestation","attest_author":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36/action/author_attestation","sign_citation":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36/action/citation_signature","submit_replication":"https://pith.science/pith/6I7LCRRXMGL4EEXT5XC7IHZU36/action/replication_record"}},"created_at":"2026-05-18T00:57:32.094364+00:00","updated_at":"2026-05-18T00:57:32.094364+00:00"}