{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KIHZIOUFFNJJSQLKVFFA2NGAEO","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":"5ec15b1a4ca28f4c879171f3a126766a7d86792d9d3336f6c40d46af627b24de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-09T00:39:54Z","title_canon_sha256":"de2c13db10e2132fb9d804d0685ed36d6c7a7552a3d9cb5f9cb92cbf034e7a27"},"schema_version":"1.0","source":{"id":"1401.1866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1866","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1866v2","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1866","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"pith_short_12","alias_value":"KIHZIOUFFNJJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KIHZIOUFFNJJSQLK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KIHZIOUF","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:561fe626e022d8b450550321cd08dede3556752541807f7e523611aa7326dc8f","target":"graph","created_at":"2026-05-18T02:44:31Z","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":"We study dilated holomorphic $L^p$ space of Gaussian measures over $\\mathbb{C}^n$, denoted $\\mathcal{H}_{p,\\alpha}^n$ with variance scaling parameter $\\alpha>0$. The duality relations $(\\mathcal{H}_{p,\\alpha}^n)^\\ast \\cong \\mathcal{H}_{p',\\alpha}$ hold with $\\frac{1}{p}+\\frac{1}{p'}=1$, but not isometrically. We identify the sharp lower constant comparing the norms on $\\mathcal{H}_{p',\\alpha}$ and $(\\mathcal{H}_{p,\\alpha}^n)^\\ast$, and provide upper and lower bounds on the sharp upper constant. We prove several suggestive partial results on the sharpness of the upper constant. One of these par","authors_text":"Todd Kemp, William E. Gryc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-09T00:39:54Z","title":"On Sharp Constants for Dual Segal--Bargmann $L^p$ Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1866","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:cd34c3453b3c847ebfbbefbec0ad6f32d91d3d409a44b0c8a16dda2775b0ba6b","target":"record","created_at":"2026-05-18T02:44:31Z","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":"5ec15b1a4ca28f4c879171f3a126766a7d86792d9d3336f6c40d46af627b24de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-09T00:39:54Z","title_canon_sha256":"de2c13db10e2132fb9d804d0685ed36d6c7a7552a3d9cb5f9cb92cbf034e7a27"},"schema_version":"1.0","source":{"id":"1401.1866","kind":"arxiv","version":2}},"canonical_sha256":"520f943a852b5299416aa94a0d34c02385b0515c4594d21734b00ce36791c78d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"520f943a852b5299416aa94a0d34c02385b0515c4594d21734b00ce36791c78d","first_computed_at":"2026-05-18T02:44:31.473690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:31.473690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x9NOyJLotA/vwhFFFMO1lz30aLDhlseTQoVAVEcjEDlyLLplnMzHT5g7pNsEZzzG2jYWbIDkFM2qm/GWHX27Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:31.474292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd34c3453b3c847ebfbbefbec0ad6f32d91d3d409a44b0c8a16dda2775b0ba6b","sha256:561fe626e022d8b450550321cd08dede3556752541807f7e523611aa7326dc8f"],"state_sha256":"19c1e14368b5a6b322a557bcfeb32292a7bf9cdb71335ca3369e59b3373f3f3b"}