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We have a symmetrization map $I: \\oplus_k \\sss^k(L(\\dd^1(X))) \\rar \\dd^{\\bullet}(X)$. Theorem 1 of this paper measures how the map $I$ fails to commute with multiplication.\n  A consequence of Theorem 1 and Theorem 2 is Corollary 1, a result \"dual\" to Theorem 1 of Markarian [3] that m"},"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/0512104","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2005-12-05T17:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"f7326e4db093c5cd388578fefce585be70028b60b98deba08c410788ae64cb3d","abstract_canon_sha256":"ba058b7663198d3d84d3e35b9ff258b569150489562c8ebd012ae02370e662be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:13:01.943851Z","signature_b64":"ikjBQuc24L88T2pgIS8L3TC8UVXOHiXLkZLkmm3nWA75dLeyUCkjjcVPA9J+qS9alUA1M14hvXkrVWy6ACFnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f39acd318c0d8f13df2b258cd52b28adf8d0362f4213fcf4d10143ae53cca865","last_reissued_at":"2026-07-04T15:13:01.943431Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:13:01.943431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The big Chern classes and the Chern character","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ajay C. Ramadoss","submitted_at":"2005-12-05T17:14:59Z","abstract_excerpt":"Let $X$ be a smooth scheme over a field of characteristic 0. Let $\\dd^{\\bullet}(X)$ be the complex of polydifferential operators on $X$ equipped with Hochschild co-boundary. Let $L(\\dd^1(X))$ be the free Lie algebra generated over $\\strc$ by $\\dd^1(X)$ concentrated in degree 1 equipped with Hochschild co-boundary. We have a symmetrization map $I: \\oplus_k \\sss^k(L(\\dd^1(X))) \\rar \\dd^{\\bullet}(X)$. Theorem 1 of this paper measures how the map $I$ fails to commute with multiplication.\n  A consequence of Theorem 1 and Theorem 2 is Corollary 1, a result \"dual\" to Theorem 1 of Markarian [3] that m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512104","kind":"arxiv","version":5},"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/0512104/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/0512104","created_at":"2026-07-04T15:13:01.943486+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0512104v5","created_at":"2026-07-04T15:13:01.943486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512104","created_at":"2026-07-04T15:13:01.943486+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ONM2MMMBWHR","created_at":"2026-07-04T15:13:01.943486+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ONM2MMMBWHRHXZL","created_at":"2026-07-04T15:13:01.943486+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ONM2MMM","created_at":"2026-07-04T15:13:01.943486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX","json":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX.json","graph_json":"https://pith.science/api/pith-number/6ONM2MMMBWHRHXZLEWGNKKZIVX/graph.json","events_json":"https://pith.science/api/pith-number/6ONM2MMMBWHRHXZLEWGNKKZIVX/events.json","paper":"https://pith.science/paper/6ONM2MMM"},"agent_actions":{"view_html":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX","download_json":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX.json","view_paper":"https://pith.science/paper/6ONM2MMM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0512104&json=true","fetch_graph":"https://pith.science/api/pith-number/6ONM2MMMBWHRHXZLEWGNKKZIVX/graph.json","fetch_events":"https://pith.science/api/pith-number/6ONM2MMMBWHRHXZLEWGNKKZIVX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX/action/storage_attestation","attest_author":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX/action/author_attestation","sign_citation":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX/action/citation_signature","submit_replication":"https://pith.science/pith/6ONM2MMMBWHRHXZLEWGNKKZIVX/action/replication_record"}},"created_at":"2026-07-04T15:13:01.943486+00:00","updated_at":"2026-07-04T15:13:01.943486+00:00"}