{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FBCR376YJJUNXS3ZPS3ZQRU2YR","short_pith_number":"pith:FBCR376Y","canonical_record":{"source":{"id":"1802.04919","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-02-14T01:38:40Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"f514dcb5782d22731b6e3a9922a252c096054044ffa1a46d22ee9eb8a233b569","abstract_canon_sha256":"c1eb599d3937ece3abe3dc4a229e2f031573e09e5f0e6cfe7b8e43deaef96a8e"},"schema_version":"1.0"},"canonical_sha256":"28451dffd84a68dbcb797cb798469ac44e6db05dfb66ecff8a84a99ec5fe517c","source":{"kind":"arxiv","id":"1802.04919","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04919","created_at":"2026-05-17T23:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04919v2","created_at":"2026-05-17T23:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04919","created_at":"2026-05-17T23:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"FBCR376YJJUN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FBCR376YJJUNXS3Z","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FBCR376Y","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FBCR376YJJUNXS3ZPS3ZQRU2YR","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04919","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-02-14T01:38:40Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"f514dcb5782d22731b6e3a9922a252c096054044ffa1a46d22ee9eb8a233b569","abstract_canon_sha256":"c1eb599d3937ece3abe3dc4a229e2f031573e09e5f0e6cfe7b8e43deaef96a8e"},"schema_version":"1.0"},"canonical_sha256":"28451dffd84a68dbcb797cb798469ac44e6db05dfb66ecff8a84a99ec5fe517c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:45.928307Z","signature_b64":"tvFz0k6cAXIajT69xErKbe6jabakCQvXzZb28DUpYmfNARNr4TZnit0EMK0Kpjw9Sv5mAdo2JntqhwbwRol0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28451dffd84a68dbcb797cb798469ac44e6db05dfb66ecff8a84a99ec5fe517c","last_reissued_at":"2026-05-17T23:48:45.927919Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:45.927919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04919","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rq81Gv91NyCsQ1jEVnp5ErCjQZRMbejmZe0Bn6MxzILhkP07y3bZ15xi48hUhGWrIsMmvsFydlu/zLGnuIQTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:56:14.167578Z"},"content_sha256":"76d4ab236e92d72e1dd15806b334c4e0ea2967f24e65388a80b8ca0aec12b060","schema_version":"1.0","event_id":"sha256:76d4ab236e92d72e1dd15806b334c4e0ea2967f24e65388a80b8ca0aec12b060"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FBCR376YJJUNXS3ZPS3ZQRU2YR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Universal Deformation Formulas for deformation quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Murray Gerstenhaber","submitted_at":"2018-02-14T01:38:40Z","abstract_excerpt":"Universal Deformation Formulas (UDFs) for the deformation of associative algebras play a key role in deformation quantization. Here we present examples for certain classes of infinitesimals. A basic representable 2-cocycle $F$ of an associative algebra $\\mathcal A$ is one for which there exist commuting derivations $D,\\dots, D_n$ of $\\mathcal A$ such that $F = \\sum_{ij}a_{ij}D_i \\smile D_j$, where the $a_{ij}$ are central elements of $\\mathcal A$. When $\\mathcal A$ is defined over the rationals, there is a natural definition of the exponential of such a cocycle. With this $\\exp \\hbar F$ define"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04919","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kzINNmB1gsjjNwnOHM+Sm4VbeiLm1ER4aTs/MY7yoLfBBomdHVF2OQvGJEDH7G+VEhKny4JYnrnv0m0D/9ANBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:56:14.168268Z"},"content_sha256":"7058ef91ea0d8ce6e46ee452c5520649b23449ff866a54aaa612c82d09874dbf","schema_version":"1.0","event_id":"sha256:7058ef91ea0d8ce6e46ee452c5520649b23449ff866a54aaa612c82d09874dbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR/bundle.json","state_url":"https://pith.science/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T21:56:14Z","links":{"resolver":"https://pith.science/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR","bundle":"https://pith.science/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR/bundle.json","state":"https://pith.science/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FBCR376YJJUNXS3ZPS3ZQRU2YR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FBCR376YJJUNXS3ZPS3ZQRU2YR","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":"c1eb599d3937ece3abe3dc4a229e2f031573e09e5f0e6cfe7b8e43deaef96a8e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-02-14T01:38:40Z","title_canon_sha256":"f514dcb5782d22731b6e3a9922a252c096054044ffa1a46d22ee9eb8a233b569"},"schema_version":"1.0","source":{"id":"1802.04919","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04919","created_at":"2026-05-17T23:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04919v2","created_at":"2026-05-17T23:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04919","created_at":"2026-05-17T23:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"FBCR376YJJUN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FBCR376YJJUNXS3Z","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FBCR376Y","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:7058ef91ea0d8ce6e46ee452c5520649b23449ff866a54aaa612c82d09874dbf","target":"graph","created_at":"2026-05-17T23:48:45Z","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"},"paper":{"abstract_excerpt":"Universal Deformation Formulas (UDFs) for the deformation of associative algebras play a key role in deformation quantization. Here we present examples for certain classes of infinitesimals. A basic representable 2-cocycle $F$ of an associative algebra $\\mathcal A$ is one for which there exist commuting derivations $D,\\dots, D_n$ of $\\mathcal A$ such that $F = \\sum_{ij}a_{ij}D_i \\smile D_j$, where the $a_{ij}$ are central elements of $\\mathcal A$. When $\\mathcal A$ is defined over the rationals, there is a natural definition of the exponential of such a cocycle. With this $\\exp \\hbar F$ define","authors_text":"Murray Gerstenhaber","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-02-14T01:38:40Z","title":"New Universal Deformation Formulas for deformation quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04919","kind":"arxiv","version":2},"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":"sha256:76d4ab236e92d72e1dd15806b334c4e0ea2967f24e65388a80b8ca0aec12b060","target":"record","created_at":"2026-05-17T23:48:45Z","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":"c1eb599d3937ece3abe3dc4a229e2f031573e09e5f0e6cfe7b8e43deaef96a8e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-02-14T01:38:40Z","title_canon_sha256":"f514dcb5782d22731b6e3a9922a252c096054044ffa1a46d22ee9eb8a233b569"},"schema_version":"1.0","source":{"id":"1802.04919","kind":"arxiv","version":2}},"canonical_sha256":"28451dffd84a68dbcb797cb798469ac44e6db05dfb66ecff8a84a99ec5fe517c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28451dffd84a68dbcb797cb798469ac44e6db05dfb66ecff8a84a99ec5fe517c","first_computed_at":"2026-05-17T23:48:45.927919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:45.927919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tvFz0k6cAXIajT69xErKbe6jabakCQvXzZb28DUpYmfNARNr4TZnit0EMK0Kpjw9Sv5mAdo2JntqhwbwRol0CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:45.928307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04919","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76d4ab236e92d72e1dd15806b334c4e0ea2967f24e65388a80b8ca0aec12b060","sha256:7058ef91ea0d8ce6e46ee452c5520649b23449ff866a54aaa612c82d09874dbf"],"state_sha256":"1428819a8a83ed19f9ffe20d04b09f011587e7d0bd8ae70f2cfe69fcb1898c83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h3hLmEBkPX7F9wY+MSxBBeSrAkXUi/rHAfQwmpkFr01+OEvDD4kybkYmZVplk32qGBCM40U2w6kBgVn5W62eCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:56:14.172650Z","bundle_sha256":"12cdeb7e01ab90a2e327beb744243dc47e9f9d0953cd818a3f54090e9cc052e8"}}