{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:B6D7DPTGG4YXAZOQJUYPB7EG3I","short_pith_number":"pith:B6D7DPTG","schema_version":"1.0","canonical_sha256":"0f87f1be6637317065d04d30f0fc86da272c7631636158c91a8deb0e3d19d11a","source":{"kind":"arxiv","id":"1301.0177","version":3},"attestation_state":"computed","paper":{"title":"The log-Sobolev inequality for the ground state of a Schr\\\"odinger operator on bounded convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dejun Luo, Huaiqian Li","submitted_at":"2013-01-02T07:07:48Z","abstract_excerpt":"We consider the ground state $\\phi_0$ of the Schr\\\"odinger operator $L=-\\Delta+V$ on the bounded convex domain $\\Omega\\subset\\R^n$, satisfying the Dirichlet boundary condition. Assume that $V\\in C^1(\\Omega)$ and it admits an even function $\\tilde V\\in C^1([-D/2,D/2])$ as its modulus of convexity, where $D$ is the diameter of $\\Omega$. If the first Dirichlet eigenvalue $\\tilde\\lambda_0$ of $-\\frac{\\d^2}{\\d t^2}+\\tilde V$ on the interval $[-D/2,D/2]$ satisfies $\\tilde\\lambda_0>\\tilde V(0)$, then the measure $\\d\\mu=\\phi_0 \\d x$ satisfies the log-Sobolev inequality on $\\Omega$ with the constant $\\"},"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":"1301.0177","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-02T07:07:48Z","cross_cats_sorted":[],"title_canon_sha256":"175896333d58f992f4ca531bbe02525da08dcb9f9f09fc20df792c68c774ef3c","abstract_canon_sha256":"53d76eb05d5c8cf81a0fb9797342e1a10de776f28e1b0ec92f3612508a2e6ee7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:20.491479Z","signature_b64":"5BZqA5D/b0Tzj5+i2tz7zVIdgglbf59p4WdATKtcTZ7XgO0A1X8QgvbTwKJw5NFon8pKoi/byI1ZIxz9oIdIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f87f1be6637317065d04d30f0fc86da272c7631636158c91a8deb0e3d19d11a","last_reissued_at":"2026-05-18T03:31:20.490731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:20.490731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The log-Sobolev inequality for the ground state of a Schr\\\"odinger operator on bounded convex domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dejun Luo, Huaiqian Li","submitted_at":"2013-01-02T07:07:48Z","abstract_excerpt":"We consider the ground state $\\phi_0$ of the Schr\\\"odinger operator $L=-\\Delta+V$ on the bounded convex domain $\\Omega\\subset\\R^n$, satisfying the Dirichlet boundary condition. Assume that $V\\in C^1(\\Omega)$ and it admits an even function $\\tilde V\\in C^1([-D/2,D/2])$ as its modulus of convexity, where $D$ is the diameter of $\\Omega$. If the first Dirichlet eigenvalue $\\tilde\\lambda_0$ of $-\\frac{\\d^2}{\\d t^2}+\\tilde V$ on the interval $[-D/2,D/2]$ satisfies $\\tilde\\lambda_0>\\tilde V(0)$, then the measure $\\d\\mu=\\phi_0 \\d x$ satisfies the log-Sobolev inequality on $\\Omega$ with the constant $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0177","kind":"arxiv","version":3},"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":"1301.0177","created_at":"2026-05-18T03:31:20.490866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0177v3","created_at":"2026-05-18T03:31:20.490866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0177","created_at":"2026-05-18T03:31:20.490866+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6D7DPTGG4YX","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6D7DPTGG4YXAZOQ","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6D7DPTG","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/B6D7DPTGG4YXAZOQJUYPB7EG3I","json":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I.json","graph_json":"https://pith.science/api/pith-number/B6D7DPTGG4YXAZOQJUYPB7EG3I/graph.json","events_json":"https://pith.science/api/pith-number/B6D7DPTGG4YXAZOQJUYPB7EG3I/events.json","paper":"https://pith.science/paper/B6D7DPTG"},"agent_actions":{"view_html":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I","download_json":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I.json","view_paper":"https://pith.science/paper/B6D7DPTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0177&json=true","fetch_graph":"https://pith.science/api/pith-number/B6D7DPTGG4YXAZOQJUYPB7EG3I/graph.json","fetch_events":"https://pith.science/api/pith-number/B6D7DPTGG4YXAZOQJUYPB7EG3I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I/action/storage_attestation","attest_author":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I/action/author_attestation","sign_citation":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I/action/citation_signature","submit_replication":"https://pith.science/pith/B6D7DPTGG4YXAZOQJUYPB7EG3I/action/replication_record"}},"created_at":"2026-05-18T03:31:20.490866+00:00","updated_at":"2026-05-18T03:31:20.490866+00:00"}