{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:T4BTBXHYO6DGQQNUAPDN5ONEEW","short_pith_number":"pith:T4BTBXHY","schema_version":"1.0","canonical_sha256":"9f0330dcf877866841b403c6deb9a4259d206c48123ede494c226e7f3ee8bba2","source":{"kind":"arxiv","id":"2406.07406","version":1},"attestation_state":"computed","paper":{"title":"Entropy, slicing problem and functional Mahler's conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Francisco Mar\\'in Sola, Matthieu Fradelizi","submitted_at":"2024-06-11T16:11:32Z","abstract_excerpt":"In a recent work, Bo'az Klartag showed that, given a convex body with minimal volume product, its isotropic constant is related to its volume product. As a consequence, he obtained that a strong version of the slicing conjecture implies Mahler's conjecture. In this work, we extend these geometrical results to the realm of log-concave functions. In this regard, the functional analogues of the projective perturbations of the body are the log-Laplace perturbations of the function. The differentiation along these transformations is simplified thanks to the known properties of the log-Laplace trans"},"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":"2406.07406","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2024-06-11T16:11:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"883fd74cf34457d6f88c290bc17eab987b19005cf83249f4150ca8a747c58e8f","abstract_canon_sha256":"84afd9ae2a603ea59b478e5b21350488cffbd6ad684b11d27adc9caf84496a2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:30:23.044219Z","signature_b64":"PPtOjTx/xY8/wT15oV1Tm8zYpT7aL97TEruH6667+4rqsMSLugwS2l9Z05kf9CFccNUqlppo+i1dP1TAq7+lCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f0330dcf877866841b403c6deb9a4259d206c48123ede494c226e7f3ee8bba2","last_reissued_at":"2026-07-05T08:30:23.043739Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:30:23.043739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy, slicing problem and functional Mahler's conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Francisco Mar\\'in Sola, Matthieu Fradelizi","submitted_at":"2024-06-11T16:11:32Z","abstract_excerpt":"In a recent work, Bo'az Klartag showed that, given a convex body with minimal volume product, its isotropic constant is related to its volume product. As a consequence, he obtained that a strong version of the slicing conjecture implies Mahler's conjecture. In this work, we extend these geometrical results to the realm of log-concave functions. In this regard, the functional analogues of the projective perturbations of the body are the log-Laplace perturbations of the function. The differentiation along these transformations is simplified thanks to the known properties of the log-Laplace trans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07406","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/2406.07406/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":"2406.07406","created_at":"2026-07-05T08:30:23.043801+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.07406v1","created_at":"2026-07-05T08:30:23.043801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07406","created_at":"2026-07-05T08:30:23.043801+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4BTBXHYO6DG","created_at":"2026-07-05T08:30:23.043801+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4BTBXHYO6DGQQNU","created_at":"2026-07-05T08:30:23.043801+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4BTBXHY","created_at":"2026-07-05T08:30:23.043801+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/T4BTBXHYO6DGQQNUAPDN5ONEEW","json":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW.json","graph_json":"https://pith.science/api/pith-number/T4BTBXHYO6DGQQNUAPDN5ONEEW/graph.json","events_json":"https://pith.science/api/pith-number/T4BTBXHYO6DGQQNUAPDN5ONEEW/events.json","paper":"https://pith.science/paper/T4BTBXHY"},"agent_actions":{"view_html":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW","download_json":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW.json","view_paper":"https://pith.science/paper/T4BTBXHY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.07406&json=true","fetch_graph":"https://pith.science/api/pith-number/T4BTBXHYO6DGQQNUAPDN5ONEEW/graph.json","fetch_events":"https://pith.science/api/pith-number/T4BTBXHYO6DGQQNUAPDN5ONEEW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW/action/storage_attestation","attest_author":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW/action/author_attestation","sign_citation":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW/action/citation_signature","submit_replication":"https://pith.science/pith/T4BTBXHYO6DGQQNUAPDN5ONEEW/action/replication_record"}},"created_at":"2026-07-05T08:30:23.043801+00:00","updated_at":"2026-07-05T08:30:23.043801+00:00"}