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Denote by $\\times$ the commutative associative multiplication in the Poisson algebra $\\boldsymbol{\\mathcal{A}}$ of local functionals $\\Gamma(\\pi)\\to\\Bbbk$ that take field configurations to numbers. By applying the techniques from geometry of iterated variations, we make well defined the deformation quantization map ${\\times}\\mapsto{\\star}={\\times}+\\hbar\\,\\{{\\cdot},{\\cdot}\\}_{\\boldsymbol{\\mathcal{P}}}+\\bar{o}(\\hbar)$ that produces a"},"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":"1705.01777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-05-04T10:16:30Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"810e5c8e1755b6667178017651cf089e6c53f85de6d87cf2902c532959c8c69a","abstract_canon_sha256":"d25e08a1db6379561028a3c38b83dd79a767798b875cc204b842345f83deb671"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:36.072130Z","signature_b64":"tKkOmYAn7XRMmKwlxMIg4c+pNb+5c5tFdy494PXr+971PiGYZI0lYwWPjF9mxnQXtxxl/8AE5njWNdSUEVrhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a45de82de79172eaf06cad2e81a4889c39859b302acd5662c6864bf07d018ab","last_reissued_at":"2026-05-18T00:24:36.071710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:36.071710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The deformation quantization mapping of Poisson- to associative structures in field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.QA","authors_text":"Arthemy V. 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By applying the techniques from geometry of iterated variations, we make well defined the deformation quantization map ${\\times}\\mapsto{\\star}={\\times}+\\hbar\\,\\{{\\cdot},{\\cdot}\\}_{\\boldsymbol{\\mathcal{P}}}+\\bar{o}(\\hbar)$ that produces a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01777","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.01777","created_at":"2026-05-18T00:24:36.071771+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01777v1","created_at":"2026-05-18T00:24:36.071771+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01777","created_at":"2026-05-18T00:24:36.071771+00:00"},{"alias_kind":"pith_short_12","alias_value":"DJC55AW6PELS","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"DJC55AW6PELS5LYG","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"DJC55AW6","created_at":"2026-05-18T12:31:10.602751+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/DJC55AW6PELS5LYGZLJOQGSIRH","json":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH.json","graph_json":"https://pith.science/api/pith-number/DJC55AW6PELS5LYGZLJOQGSIRH/graph.json","events_json":"https://pith.science/api/pith-number/DJC55AW6PELS5LYGZLJOQGSIRH/events.json","paper":"https://pith.science/paper/DJC55AW6"},"agent_actions":{"view_html":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH","download_json":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH.json","view_paper":"https://pith.science/paper/DJC55AW6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01777&json=true","fetch_graph":"https://pith.science/api/pith-number/DJC55AW6PELS5LYGZLJOQGSIRH/graph.json","fetch_events":"https://pith.science/api/pith-number/DJC55AW6PELS5LYGZLJOQGSIRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH/action/storage_attestation","attest_author":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH/action/author_attestation","sign_citation":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH/action/citation_signature","submit_replication":"https://pith.science/pith/DJC55AW6PELS5LYGZLJOQGSIRH/action/replication_record"}},"created_at":"2026-05-18T00:24:36.071771+00:00","updated_at":"2026-05-18T00:24:36.071771+00:00"}