{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QRTYHFJMEWT7KM774B5CJFIME4","short_pith_number":"pith:QRTYHFJM","schema_version":"1.0","canonical_sha256":"846783952c25a7f533ffe07a24950c273fe9a7a461f93c74c6998db9ad9139a6","source":{"kind":"arxiv","id":"2511.01504","version":3},"attestation_state":"computed","paper":{"title":"Central diagonal sections of Gaussian cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Bernardo Gonz\\'alez Merino, Ferenc Fodor","submitted_at":"2025-11-03T12:18:23Z","abstract_excerpt":"The investigation of the volume, surface area, and other geometric properties of sections of convex bodies, and in particular cubes, has a long history and a rich literature. However, much less is known when the cube has a volume distribution that is different from the Lebesgue measure; for example, a Gaussian density. We study the probability densities in the standard cube $B^n_\\infty=[-1,1]^n$ of $\\mathbb R^n$ generated by $e^{-b\\|x\\|^2}$, $b> 0$. We prove that the limit of the induced Gaussian-type volume of hyperplane sections of $B^n_\\infty$ through the origin and orthogonal to a main dia"},"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":"2511.01504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2025-11-03T12:18:23Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"7ffd7a53524edad876f9c45c3b1bd2d099ee8671e12fd25998601323554be4ce","abstract_canon_sha256":"f104b81f371b1aaf4817ce10a468eedfa3bebbcf1d933028b9d162d7d55d4bf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:14:30.516229Z","signature_b64":"b6dbKKcJn7u/WPdtgjMedZEGujrEGV6XOOP6elwaes0Y3lyVIX9Wp1oibEn+35L8Q8I74h4yDNjZzLV0vtNVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"846783952c25a7f533ffe07a24950c273fe9a7a461f93c74c6998db9ad9139a6","last_reissued_at":"2026-06-05T01:14:30.515678Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:14:30.515678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central diagonal sections of Gaussian cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Bernardo Gonz\\'alez Merino, Ferenc Fodor","submitted_at":"2025-11-03T12:18:23Z","abstract_excerpt":"The investigation of the volume, surface area, and other geometric properties of sections of convex bodies, and in particular cubes, has a long history and a rich literature. However, much less is known when the cube has a volume distribution that is different from the Lebesgue measure; for example, a Gaussian density. We study the probability densities in the standard cube $B^n_\\infty=[-1,1]^n$ of $\\mathbb R^n$ generated by $e^{-b\\|x\\|^2}$, $b> 0$. We prove that the limit of the induced Gaussian-type volume of hyperplane sections of $B^n_\\infty$ through the origin and orthogonal to a main dia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.01504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.01504/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":"2511.01504","created_at":"2026-06-05T01:14:30.515746+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.01504v3","created_at":"2026-06-05T01:14:30.515746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.01504","created_at":"2026-06-05T01:14:30.515746+00:00"},{"alias_kind":"pith_short_12","alias_value":"QRTYHFJMEWT7","created_at":"2026-06-05T01:14:30.515746+00:00"},{"alias_kind":"pith_short_16","alias_value":"QRTYHFJMEWT7KM77","created_at":"2026-06-05T01:14:30.515746+00:00"},{"alias_kind":"pith_short_8","alias_value":"QRTYHFJM","created_at":"2026-06-05T01:14:30.515746+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/QRTYHFJMEWT7KM774B5CJFIME4","json":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4.json","graph_json":"https://pith.science/api/pith-number/QRTYHFJMEWT7KM774B5CJFIME4/graph.json","events_json":"https://pith.science/api/pith-number/QRTYHFJMEWT7KM774B5CJFIME4/events.json","paper":"https://pith.science/paper/QRTYHFJM"},"agent_actions":{"view_html":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4","download_json":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4.json","view_paper":"https://pith.science/paper/QRTYHFJM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.01504&json=true","fetch_graph":"https://pith.science/api/pith-number/QRTYHFJMEWT7KM774B5CJFIME4/graph.json","fetch_events":"https://pith.science/api/pith-number/QRTYHFJMEWT7KM774B5CJFIME4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4/action/storage_attestation","attest_author":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4/action/author_attestation","sign_citation":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4/action/citation_signature","submit_replication":"https://pith.science/pith/QRTYHFJMEWT7KM774B5CJFIME4/action/replication_record"}},"created_at":"2026-06-05T01:14:30.515746+00:00","updated_at":"2026-06-05T01:14:30.515746+00:00"}