{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:NWWXKKRVK5IC226B4ABS3O4CHI","short_pith_number":"pith:NWWXKKRV","schema_version":"1.0","canonical_sha256":"6dad752a3557502d6bc1e0032dbb823a3b7a15596372b0a7008f8b065bde230a","source":{"kind":"arxiv","id":"math-ph/0610059","version":2},"attestation_state":"computed","paper":{"title":"Differential operators on supercircle: conformally equivariant quantization and symbol calculus","license":"","headline":"","cross_cats":["math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Hichem Gargoubi (IPEIT), Najla Mellouli (ICJ), Valentin Ovsienko (ICJ)","submitted_at":"2006-10-24T08:38:15Z","abstract_excerpt":"We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\\\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist."},"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-ph/0610059","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2006-10-24T08:38:15Z","cross_cats_sorted":["math.MP","math.RT"],"title_canon_sha256":"3e5823264c06ded59622c81b2740a5a797f5ae2edca94283ecceb11e15eb9ea3","abstract_canon_sha256":"6632e6ca9c908cf0361a66d293ca2374a26590351b72dd6ca9527720ea387eed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:32.593134Z","signature_b64":"n2x1/qrmBXfaTlDLJ2tTTZ9G0/cc76J4tHYFVaPpdU698LR16AMuN1JV1II4TQICgS8AcaRXEm5dio8ye+q/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dad752a3557502d6bc1e0032dbb823a3b7a15596372b0a7008f8b065bde230a","last_reissued_at":"2026-05-18T01:38:32.592623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:32.592623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential operators on supercircle: conformally equivariant quantization and symbol calculus","license":"","headline":"","cross_cats":["math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Hichem Gargoubi (IPEIT), Najla Mellouli (ICJ), Valentin Ovsienko (ICJ)","submitted_at":"2006-10-24T08:38:15Z","abstract_excerpt":"We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\\\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0610059","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0610059","created_at":"2026-05-18T01:38:32.592706+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0610059v2","created_at":"2026-05-18T01:38:32.592706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0610059","created_at":"2026-05-18T01:38:32.592706+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWWXKKRVK5IC","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWWXKKRVK5IC226B","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWWXKKRV","created_at":"2026-05-18T12:25:54.717736+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/NWWXKKRVK5IC226B4ABS3O4CHI","json":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI.json","graph_json":"https://pith.science/api/pith-number/NWWXKKRVK5IC226B4ABS3O4CHI/graph.json","events_json":"https://pith.science/api/pith-number/NWWXKKRVK5IC226B4ABS3O4CHI/events.json","paper":"https://pith.science/paper/NWWXKKRV"},"agent_actions":{"view_html":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI","download_json":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI.json","view_paper":"https://pith.science/paper/NWWXKKRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0610059&json=true","fetch_graph":"https://pith.science/api/pith-number/NWWXKKRVK5IC226B4ABS3O4CHI/graph.json","fetch_events":"https://pith.science/api/pith-number/NWWXKKRVK5IC226B4ABS3O4CHI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI/action/storage_attestation","attest_author":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI/action/author_attestation","sign_citation":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI/action/citation_signature","submit_replication":"https://pith.science/pith/NWWXKKRVK5IC226B4ABS3O4CHI/action/replication_record"}},"created_at":"2026-05-18T01:38:32.592706+00:00","updated_at":"2026-05-18T01:38:32.592706+00:00"}