{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2CPE4JV4I2CMU4DLI6BNRVSJPP","short_pith_number":"pith:2CPE4JV4","schema_version":"1.0","canonical_sha256":"d09e4e26bc4684ca706b4782d8d6497bd8369a0896ed7e65f562327f898f78c5","source":{"kind":"arxiv","id":"1605.04840","version":2},"attestation_state":"computed","paper":{"title":"Boundary value problem and the Ehrhard inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paata Ivanisvili","submitted_at":"2016-05-16T17:06:58Z","abstract_excerpt":"Let $I, J\\subset \\mathbb{R}$ be closed intervals, and let $H$ be $C^{3}$ smooth real valued function on $I\\times J$ with nonvanishing $H_{x}$ and $H_{y}$. Take any fixed positive numbers $a,b$, and let $d\\mu$ be a probability measure with finite moments and absolutely continuous with respect to Lebesgue measure. We show that for the inequality $$ \\int_{\\mathbb{R}^{n}} \\mathrm{ess\\,sup}_{y \\in \\mathbb{R}^{n}}\\; H\\left( f\\left(\\frac{x-y}{a}\\right),g\\left(\\frac{y}{b}\\right)\\right)d\\mu (x) \\geq H\\left(\\int_{\\mathbb{R}^{n}}fd\\mu, \\int_{\\mathbb{R}^{n}}gd\\mu \\right) $$ to hold for all Borel functions"},"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":"1605.04840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-16T17:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"e02053f74541cbc6d5993dd05ff4dca17ac127182225e22f2c7059e7fdfaca0c","abstract_canon_sha256":"401902423b2acc73bef19848779bc0cb65fc8af373c7e4cb6fda2c0645136f80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:58.412299Z","signature_b64":"RCmU/1cgM3iVdWyT9aTZU65Kb9YPZxwm0BQC4S/RWktE31GfhBPEWJsMq+HTwzomnbTjpOvBo6nvnuyP/oWdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d09e4e26bc4684ca706b4782d8d6497bd8369a0896ed7e65f562327f898f78c5","last_reissued_at":"2026-05-18T00:41:58.411830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:58.411830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundary value problem and the Ehrhard inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Paata Ivanisvili","submitted_at":"2016-05-16T17:06:58Z","abstract_excerpt":"Let $I, J\\subset \\mathbb{R}$ be closed intervals, and let $H$ be $C^{3}$ smooth real valued function on $I\\times J$ with nonvanishing $H_{x}$ and $H_{y}$. Take any fixed positive numbers $a,b$, and let $d\\mu$ be a probability measure with finite moments and absolutely continuous with respect to Lebesgue measure. We show that for the inequality $$ \\int_{\\mathbb{R}^{n}} \\mathrm{ess\\,sup}_{y \\in \\mathbb{R}^{n}}\\; H\\left( f\\left(\\frac{x-y}{a}\\right),g\\left(\\frac{y}{b}\\right)\\right)d\\mu (x) \\geq H\\left(\\int_{\\mathbb{R}^{n}}fd\\mu, \\int_{\\mathbb{R}^{n}}gd\\mu \\right) $$ to hold for all Borel functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04840","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":"1605.04840","created_at":"2026-05-18T00:41:58.411904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.04840v2","created_at":"2026-05-18T00:41:58.411904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04840","created_at":"2026-05-18T00:41:58.411904+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CPE4JV4I2CM","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CPE4JV4I2CMU4DL","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CPE4JV4","created_at":"2026-05-18T12:29:52.810259+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/2CPE4JV4I2CMU4DLI6BNRVSJPP","json":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP.json","graph_json":"https://pith.science/api/pith-number/2CPE4JV4I2CMU4DLI6BNRVSJPP/graph.json","events_json":"https://pith.science/api/pith-number/2CPE4JV4I2CMU4DLI6BNRVSJPP/events.json","paper":"https://pith.science/paper/2CPE4JV4"},"agent_actions":{"view_html":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP","download_json":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP.json","view_paper":"https://pith.science/paper/2CPE4JV4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.04840&json=true","fetch_graph":"https://pith.science/api/pith-number/2CPE4JV4I2CMU4DLI6BNRVSJPP/graph.json","fetch_events":"https://pith.science/api/pith-number/2CPE4JV4I2CMU4DLI6BNRVSJPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP/action/storage_attestation","attest_author":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP/action/author_attestation","sign_citation":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP/action/citation_signature","submit_replication":"https://pith.science/pith/2CPE4JV4I2CMU4DLI6BNRVSJPP/action/replication_record"}},"created_at":"2026-05-18T00:41:58.411904+00:00","updated_at":"2026-05-18T00:41:58.411904+00:00"}