{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7VX64PISF4RHEYBRNQOXFQOW36","short_pith_number":"pith:7VX64PIS","schema_version":"1.0","canonical_sha256":"fd6fee3d122f227260316c1d72c1d6df9d5c30ec56c7bae967bdbfa4a70971fa","source":{"kind":"arxiv","id":"1309.6760","version":5},"attestation_state":"computed","paper":{"title":"Geometric quantization and families of inner products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.OA","math.SG"],"primary_cat":"math.DG","authors_text":"Peter Hochs, Varghese Mathai","submitted_at":"2013-09-26T09:00:17Z","abstract_excerpt":"We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and the zero set of a deformation vector field, associated to the momentum map and an equivariant family of inner products on the Lie algebra $\\mathfrak{g}$ of $G$, is $G$-cocompact. The central result establishes an asymptotic version of this quantization commutes with reduction principle. Using an equivariant family of inner products on $\\mathfrak{g}$ instead "},"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":"1309.6760","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-26T09:00:17Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.OA","math.SG"],"title_canon_sha256":"82d1627db5bb8d15a951f3f31d0b05a8b639dbc018a39f5690da798dc2315ea8","abstract_canon_sha256":"f0f8da3b7a2a489838a96c8cb96d27c560ff5ac263aee9aa4bbd0226e4896bf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.014932Z","signature_b64":"tvdy7Sm+pnG3dRjGgiectiTiG7CcUTb2/U4hjCNaZzphEAO4BaznIeFP9daBGgCiejS03szWcd38XzebS0okCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd6fee3d122f227260316c1d72c1d6df9d5c30ec56c7bae967bdbfa4a70971fa","last_reissued_at":"2026-05-18T01:36:21.014436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.014436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric quantization and families of inner products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.OA","math.SG"],"primary_cat":"math.DG","authors_text":"Peter Hochs, Varghese Mathai","submitted_at":"2013-09-26T09:00:17Z","abstract_excerpt":"We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and the zero set of a deformation vector field, associated to the momentum map and an equivariant family of inner products on the Lie algebra $\\mathfrak{g}$ of $G$, is $G$-cocompact. The central result establishes an asymptotic version of this quantization commutes with reduction principle. Using an equivariant family of inner products on $\\mathfrak{g}$ instead "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6760","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":""},"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":"1309.6760","created_at":"2026-05-18T01:36:21.014500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6760v5","created_at":"2026-05-18T01:36:21.014500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6760","created_at":"2026-05-18T01:36:21.014500+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VX64PISF4RH","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VX64PISF4RHEYBR","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VX64PIS","created_at":"2026-05-18T12:27:38.830355+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/7VX64PISF4RHEYBRNQOXFQOW36","json":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36.json","graph_json":"https://pith.science/api/pith-number/7VX64PISF4RHEYBRNQOXFQOW36/graph.json","events_json":"https://pith.science/api/pith-number/7VX64PISF4RHEYBRNQOXFQOW36/events.json","paper":"https://pith.science/paper/7VX64PIS"},"agent_actions":{"view_html":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36","download_json":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36.json","view_paper":"https://pith.science/paper/7VX64PIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6760&json=true","fetch_graph":"https://pith.science/api/pith-number/7VX64PISF4RHEYBRNQOXFQOW36/graph.json","fetch_events":"https://pith.science/api/pith-number/7VX64PISF4RHEYBRNQOXFQOW36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36/action/storage_attestation","attest_author":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36/action/author_attestation","sign_citation":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36/action/citation_signature","submit_replication":"https://pith.science/pith/7VX64PISF4RHEYBRNQOXFQOW36/action/replication_record"}},"created_at":"2026-05-18T01:36:21.014500+00:00","updated_at":"2026-05-18T01:36:21.014500+00:00"}