{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:QMDEXECYAMUHA376Z55VUIPK5Z","short_pith_number":"pith:QMDEXECY","schema_version":"1.0","canonical_sha256":"83064b90580328706ffecf7b5a21eaee7f1869ccbd00a76ed793b1d68340f6b4","source":{"kind":"arxiv","id":"math/0010321","version":2},"attestation_state":"computed","paper":{"title":"A proof of the Tsygan formality conjecture for chains","license":"","headline":"","cross_cats":["hep-th","math.AC","math.KT"],"primary_cat":"math.QA","authors_text":"Boris Shoikhet (ETH-Zentrum & IPDE)","submitted_at":"2000-10-31T18:51:45Z","abstract_excerpt":"We extend the Kontsevich formality $L_\\infty$-morphism $\\U\\colon T^\\ndot_\\poly(\\R^d)\\to\\D^\\ndot_\\poly(\\R^d)$ to an $L_\\infty$-morphism of an $L_\\infty$-modules over $T^\\ndot_\\poly(\\R^d)$, $\\hat \\U\\colon C_\\ndot(A,A)\\to\\Omega^\\ndot(\\R^d)$, $A=C^\\infty(\\R^d)$. The construction of the map $\\hat \\U$ is given in Kontsevich-type integrals. The conjecture that such an $L_\\infty$-morphism exists is due to Boris Tsygan \\cite{Ts}. As an application, we obtain an explicit formula for isomorphism $A_*/[A_*,A_*]\\simto A/\\{A,A\\}$ ($A_*$ is the Kontsevich deformation quantization of the algebra $A$ by a Pois"},"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":"math/0010321","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2000-10-31T18:51:45Z","cross_cats_sorted":["hep-th","math.AC","math.KT"],"title_canon_sha256":"5ba84d6a7b11584a3265e18ea2816b591652d1a3e9f235b49f7378bbbefa170b","abstract_canon_sha256":"fb0be7fb056e93e15a63cac4d8cc27cf7a335394a179abcece1cf38e0eddeb60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:53.991637Z","signature_b64":"jxWBe2s/CfqkppgkgqcAcpNZZGTr/ojMJhqKbdsNXX6LELBHZ6yT4FlifM7G3q6E2SxEUIdk/syIRObFe4vqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83064b90580328706ffecf7b5a21eaee7f1869ccbd00a76ed793b1d68340f6b4","last_reissued_at":"2026-07-04T14:34:53.991282Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:53.991282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A proof of the Tsygan formality conjecture for chains","license":"","headline":"","cross_cats":["hep-th","math.AC","math.KT"],"primary_cat":"math.QA","authors_text":"Boris Shoikhet (ETH-Zentrum & IPDE)","submitted_at":"2000-10-31T18:51:45Z","abstract_excerpt":"We extend the Kontsevich formality $L_\\infty$-morphism $\\U\\colon T^\\ndot_\\poly(\\R^d)\\to\\D^\\ndot_\\poly(\\R^d)$ to an $L_\\infty$-morphism of an $L_\\infty$-modules over $T^\\ndot_\\poly(\\R^d)$, $\\hat \\U\\colon C_\\ndot(A,A)\\to\\Omega^\\ndot(\\R^d)$, $A=C^\\infty(\\R^d)$. The construction of the map $\\hat \\U$ is given in Kontsevich-type integrals. The conjecture that such an $L_\\infty$-morphism exists is due to Boris Tsygan \\cite{Ts}. As an application, we obtain an explicit formula for isomorphism $A_*/[A_*,A_*]\\simto A/\\{A,A\\}$ ($A_*$ is the Kontsevich deformation quantization of the algebra $A$ by a Pois"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0010321","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/math/0010321/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":"math/0010321","created_at":"2026-07-04T14:34:53.991342+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0010321v2","created_at":"2026-07-04T14:34:53.991342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0010321","created_at":"2026-07-04T14:34:53.991342+00:00"},{"alias_kind":"pith_short_12","alias_value":"QMDEXECYAMUH","created_at":"2026-07-04T14:34:53.991342+00:00"},{"alias_kind":"pith_short_16","alias_value":"QMDEXECYAMUHA376","created_at":"2026-07-04T14:34:53.991342+00:00"},{"alias_kind":"pith_short_8","alias_value":"QMDEXECY","created_at":"2026-07-04T14:34:53.991342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.20459","citing_title":"Scalar Field on a higher-spin Background via Fedosov quantization","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z","json":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z.json","graph_json":"https://pith.science/api/pith-number/QMDEXECYAMUHA376Z55VUIPK5Z/graph.json","events_json":"https://pith.science/api/pith-number/QMDEXECYAMUHA376Z55VUIPK5Z/events.json","paper":"https://pith.science/paper/QMDEXECY"},"agent_actions":{"view_html":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z","download_json":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z.json","view_paper":"https://pith.science/paper/QMDEXECY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0010321&json=true","fetch_graph":"https://pith.science/api/pith-number/QMDEXECYAMUHA376Z55VUIPK5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/QMDEXECYAMUHA376Z55VUIPK5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z/action/storage_attestation","attest_author":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z/action/author_attestation","sign_citation":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z/action/citation_signature","submit_replication":"https://pith.science/pith/QMDEXECYAMUHA376Z55VUIPK5Z/action/replication_record"}},"created_at":"2026-07-04T14:34:53.991342+00:00","updated_at":"2026-07-04T14:34:53.991342+00:00"}