{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:XLC3MSNBIR7K2NZRVMRGZQH6XS","short_pith_number":"pith:XLC3MSNB","schema_version":"1.0","canonical_sha256":"bac5b649a1447ead3731ab226cc0febca33d452e5e5089fcb84f2c09e6f28df7","source":{"kind":"arxiv","id":"2209.02744","version":2},"attestation_state":"computed","paper":{"title":"On the Morita invariance of Categorical Enumerative Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.SG"],"primary_cat":"math.AG","authors_text":"Junwu Tu, Lino Amorim","submitted_at":"2022-09-06T18:04:39Z","abstract_excerpt":"Categorical Enumerative Invariants (CEI) are invariants associated with a unital, cyclic, smooth $A_\\infty$-category and a splitting of its non-commutative Hodge filtration. In this paper, we extend the definition of CEI to Calabi-Yau $A_\\infty$-categories with a splitting. Moreover, we formulate and prove the Morita invariance of CEI. As part of our proof, we develop tools to construct unital and cyclic models for Calabi-Yau categories. In particular, we prove a unital version of Kontsevich-Soibelman's Darboux theorem. As an application, we compute CEI in some new examples. Also, when applied"},"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":"2209.02744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2022-09-06T18:04:39Z","cross_cats_sorted":["math.KT","math.SG"],"title_canon_sha256":"61ed2a4f6de2332963a5d79f04f7444e65428dd84dd22923f480d5e95a7bfcbf","abstract_canon_sha256":"a9fb7a4e1a1a9b9c2cf6ed581c7f4fe876153e80889fa838c0212cb92de1052d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:30.850129Z","signature_b64":"wPxUeKUA8fWUTELlLrx3VFmmeSXvExbBViLlZp41Ev2KHpWFBRkKjzvRnFLGY6ZqbvDXNv8pXyNDI+XzeMwoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bac5b649a1447ead3731ab226cc0febca33d452e5e5089fcb84f2c09e6f28df7","last_reissued_at":"2026-07-05T11:05:30.849614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:30.849614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Morita invariance of Categorical Enumerative Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.SG"],"primary_cat":"math.AG","authors_text":"Junwu Tu, Lino Amorim","submitted_at":"2022-09-06T18:04:39Z","abstract_excerpt":"Categorical Enumerative Invariants (CEI) are invariants associated with a unital, cyclic, smooth $A_\\infty$-category and a splitting of its non-commutative Hodge filtration. In this paper, we extend the definition of CEI to Calabi-Yau $A_\\infty$-categories with a splitting. Moreover, we formulate and prove the Morita invariance of CEI. As part of our proof, we develop tools to construct unital and cyclic models for Calabi-Yau categories. In particular, we prove a unital version of Kontsevich-Soibelman's Darboux theorem. As an application, we compute CEI in some new examples. Also, when applied"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02744","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/2209.02744/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":"2209.02744","created_at":"2026-07-05T11:05:30.849677+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.02744v2","created_at":"2026-07-05T11:05:30.849677+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02744","created_at":"2026-07-05T11:05:30.849677+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLC3MSNBIR7K","created_at":"2026-07-05T11:05:30.849677+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLC3MSNBIR7K2NZR","created_at":"2026-07-05T11:05:30.849677+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLC3MSNB","created_at":"2026-07-05T11:05:30.849677+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.07960","citing_title":"B-model Categorical Enumerative Invariants and holomorphic anomaly equations","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03521","citing_title":"Open-closed Deligne-Mumford field theories: construction","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS","json":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS.json","graph_json":"https://pith.science/api/pith-number/XLC3MSNBIR7K2NZRVMRGZQH6XS/graph.json","events_json":"https://pith.science/api/pith-number/XLC3MSNBIR7K2NZRVMRGZQH6XS/events.json","paper":"https://pith.science/paper/XLC3MSNB"},"agent_actions":{"view_html":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS","download_json":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS.json","view_paper":"https://pith.science/paper/XLC3MSNB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.02744&json=true","fetch_graph":"https://pith.science/api/pith-number/XLC3MSNBIR7K2NZRVMRGZQH6XS/graph.json","fetch_events":"https://pith.science/api/pith-number/XLC3MSNBIR7K2NZRVMRGZQH6XS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS/action/storage_attestation","attest_author":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS/action/author_attestation","sign_citation":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS/action/citation_signature","submit_replication":"https://pith.science/pith/XLC3MSNBIR7K2NZRVMRGZQH6XS/action/replication_record"}},"created_at":"2026-07-05T11:05:30.849677+00:00","updated_at":"2026-07-05T11:05:30.849677+00:00"}