{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YDIQM2DJKV4VXY3UW3SWVMQWNE","short_pith_number":"pith:YDIQM2DJ","schema_version":"1.0","canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","source":{"kind":"arxiv","id":"2608.13443","version":1},"attestation_state":"computed","paper":{"title":"Fundamental Gaps for the Dirichlet \\(p\\)-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Hauer, Rui Chen","submitted_at":"2026-08-13T16:29:36Z","abstract_excerpt":"We study fundamental gaps for the Dirichlet \\(p\\)-Laplacian on bounded convex domains with convex potentials. We prove log-concavity of the positive first eigenfunction by a regularization and two-point maximum principle. For \\(N\\geq2\\), we identify a sharp transition at \\(p=2\\) through collapsing smooth convex domains: the gap vanishes for \\(1<p<2\\), remains of order \\(D^{-2}\\) for \\(p=2\\), and diverges for \\(p>2\\). For \\(p\\geq2\\) and convex potentials, we first establish a degenerate weighted Poincar\\'e inequality, which yields quantitative stability estimates for the \\(L^p\\)-Poincar\\'e ineq"},"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":"2608.13443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-13T16:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"f62ac9a5fa475b7d2b29ad2d486066a051f4327ed5894cc49a969aad05067402","abstract_canon_sha256":"b328bee107e813623433ad4cb5608ad7c11988391018d4608829c8cdac62b84e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T01:04:27.205185Z","signature_b64":"Lz3lWQD+CI6X+s9r3fsvHkR5SmoccfDYTeMIy8jmdpC6UMVix4eQkRPa9qAS8s90LGkqsiqAyuFCv7IkYZWtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0d106686955795be374b6e56ab2166917f0878d9851ec34c9d7cc7a172f2f96","last_reissued_at":"2026-08-14T01:04:27.203469Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T01:04:27.203469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fundamental Gaps for the Dirichlet \\(p\\)-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Hauer, Rui Chen","submitted_at":"2026-08-13T16:29:36Z","abstract_excerpt":"We study fundamental gaps for the Dirichlet \\(p\\)-Laplacian on bounded convex domains with convex potentials. We prove log-concavity of the positive first eigenfunction by a regularization and two-point maximum principle. For \\(N\\geq2\\), we identify a sharp transition at \\(p=2\\) through collapsing smooth convex domains: the gap vanishes for \\(1<p<2\\), remains of order \\(D^{-2}\\) for \\(p=2\\), and diverges for \\(p>2\\). For \\(p\\geq2\\) and convex potentials, we first establish a degenerate weighted Poincar\\'e inequality, which yields quantitative stability estimates for the \\(L^p\\)-Poincar\\'e ineq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13443","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.13443/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.13443","created_at":"2026-08-14T01:04:27.204393+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.13443v1","created_at":"2026-08-14T01:04:27.204393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13443","created_at":"2026-08-14T01:04:27.204393+00:00"},{"alias_kind":"pith_short_12","alias_value":"YDIQM2DJKV4V","created_at":"2026-08-14T01:04:27.204393+00:00"},{"alias_kind":"pith_short_16","alias_value":"YDIQM2DJKV4VXY3U","created_at":"2026-08-14T01:04:27.204393+00:00"},{"alias_kind":"pith_short_8","alias_value":"YDIQM2DJ","created_at":"2026-08-14T01:04:27.204393+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/YDIQM2DJKV4VXY3UW3SWVMQWNE","json":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE.json","graph_json":"https://pith.science/api/pith-number/YDIQM2DJKV4VXY3UW3SWVMQWNE/graph.json","events_json":"https://pith.science/api/pith-number/YDIQM2DJKV4VXY3UW3SWVMQWNE/events.json","paper":"https://pith.science/paper/YDIQM2DJ"},"agent_actions":{"view_html":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE","download_json":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE.json","view_paper":"https://pith.science/paper/YDIQM2DJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.13443&json=true","fetch_graph":"https://pith.science/api/pith-number/YDIQM2DJKV4VXY3UW3SWVMQWNE/graph.json","fetch_events":"https://pith.science/api/pith-number/YDIQM2DJKV4VXY3UW3SWVMQWNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/action/storage_attestation","attest_author":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/action/author_attestation","sign_citation":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/action/citation_signature","submit_replication":"https://pith.science/pith/YDIQM2DJKV4VXY3UW3SWVMQWNE/action/replication_record"}},"created_at":"2026-08-14T01:04:27.204393+00:00","updated_at":"2026-08-14T01:04:27.204393+00:00"}