{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RG3D5WXU25Q3VMBXKAUEBZNYO7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f181db3c153d7a75b196d24b88e435c4a9fe8327bd02fc8079ed371c9e6eb861","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2008-07-31T17:28:19Z","title_canon_sha256":"d9f7f72bb1c884436803df870c3651fbc3d0226964082528ebf40549a98fcf51"},"schema_version":"1.0","source":{"id":"0807.5117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.5117","created_at":"2026-07-04T15:13:19Z"},{"alias_kind":"arxiv_version","alias_value":"0807.5117v1","created_at":"2026-07-04T15:13:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.5117","created_at":"2026-07-04T15:13:19Z"},{"alias_kind":"pith_short_12","alias_value":"RG3D5WXU25Q3","created_at":"2026-07-04T15:13:19Z"},{"alias_kind":"pith_short_16","alias_value":"RG3D5WXU25Q3VMBX","created_at":"2026-07-04T15:13:19Z"},{"alias_kind":"pith_short_8","alias_value":"RG3D5WXU","created_at":"2026-07-04T15:13:19Z"}],"graph_snapshots":[{"event_id":"sha256:5b6e54f02b49fde6fb1c17dacbe5a7530ad7c8efbe2ae1bf8763ac337e3a969a","target":"graph","created_at":"2026-07-04T15:13:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0807.5117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Kontsevich-Soibelman solution of the cyclic version of Deligne's conjecture and the formality of the operad of little discs on a cylinder provide us with a natural homotopy calculus structure on the pair (C^*(A), C_*(A)) ``Hochschild cochains + Hochschild chains'' of an associative algebra A. We show that for an arbitrary smooth algebraic variety X with the structure sheaf O_X the sheaf (C^*(O_X), C_*(O_X)) of homotopy calculi is formal. This result was announced in paper [29] by the second and the third author.","authors_text":"Boris Tsygan, Dmitry Tamarkin, Vasiliy Dolgushev","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2008-07-31T17:28:19Z","title":"Formality of the homotopy calculus algebra of Hochschild (co)chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.5117","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d8ea5cc158b6888626608cd8afa79c8a673575807b170e1c7fda518ba487f3d","target":"record","created_at":"2026-07-04T15:13:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f181db3c153d7a75b196d24b88e435c4a9fe8327bd02fc8079ed371c9e6eb861","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2008-07-31T17:28:19Z","title_canon_sha256":"d9f7f72bb1c884436803df870c3651fbc3d0226964082528ebf40549a98fcf51"},"schema_version":"1.0","source":{"id":"0807.5117","kind":"arxiv","version":1}},"canonical_sha256":"89b63edaf4d761bab037502840e5b877cc1126f3fa208096667874e9d373a714","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89b63edaf4d761bab037502840e5b877cc1126f3fa208096667874e9d373a714","first_computed_at":"2026-07-04T15:13:19.271938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:13:19.271938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oNb2VIoAy7lyfmqGAH9iNkPkNA7Q9AY/fluP4yOH1ur/viTYh8MXENi2n9oqLLRiCCLMxKAnWPrDrlbVdaVPCw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:13:19.272324Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.5117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d8ea5cc158b6888626608cd8afa79c8a673575807b170e1c7fda518ba487f3d","sha256:5b6e54f02b49fde6fb1c17dacbe5a7530ad7c8efbe2ae1bf8763ac337e3a969a"],"state_sha256":"1937aec13c9948cbbf54b41110e8abc7609566fe6177d367146a9f40d954d310"}