{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:S2SOUXGIL3C3YHHFOSOIPEV4IQ","short_pith_number":"pith:S2SOUXGI","schema_version":"1.0","canonical_sha256":"96a4ea5cc85ec5bc1ce5749c8792bc4424233d123f05b7bd2b6fee83c1d719eb","source":{"kind":"arxiv","id":"1302.6093","version":1},"attestation_state":"computed","paper":{"title":"On the analogue of the concavity of entropy power in the Brunn-Minkowski theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MG"],"primary_cat":"math.FA","authors_text":"Arnaud Marsiglietti, Matthieu Fradelizi","submitted_at":"2013-02-25T14:08:15Z","abstract_excerpt":"Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in {\\it On the similarity of the entropy power inequality and the Brunn-Minkowski inequality} (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the $\\frac{1}{n}$-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities."},"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":"1302.6093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-25T14:08:15Z","cross_cats_sorted":["cs.IT","math.IT","math.MG"],"title_canon_sha256":"cdb510859ad22c17d37c0f0e9dc4d0f57dd827b2bf705bf8970abf7bc128621c","abstract_canon_sha256":"4a0a543e7dbb12e24a67e96fd6d70f911d5d05332f74047d258aaf655a73958a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:32.587743Z","signature_b64":"rCcchSjWZA6QtfZ+YaKcipbxFVBhtynTJfALEoignlngyWTCzSb9YiyCS8xFIXdEK0GBZnu1XTWp+dACRF/3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a4ea5cc85ec5bc1ce5749c8792bc4424233d123f05b7bd2b6fee83c1d719eb","last_reissued_at":"2026-05-18T03:32:32.587043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:32.587043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the analogue of the concavity of entropy power in the Brunn-Minkowski theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MG"],"primary_cat":"math.FA","authors_text":"Arnaud Marsiglietti, Matthieu Fradelizi","submitted_at":"2013-02-25T14:08:15Z","abstract_excerpt":"Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in {\\it On the similarity of the entropy power inequality and the Brunn-Minkowski inequality} (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the $\\frac{1}{n}$-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6093","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":""},"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":"1302.6093","created_at":"2026-05-18T03:32:32.587143+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.6093v1","created_at":"2026-05-18T03:32:32.587143+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6093","created_at":"2026-05-18T03:32:32.587143+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2SOUXGIL3C3","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2SOUXGIL3C3YHHF","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2SOUXGI","created_at":"2026-05-18T12:27:59.945178+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/S2SOUXGIL3C3YHHFOSOIPEV4IQ","json":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ.json","graph_json":"https://pith.science/api/pith-number/S2SOUXGIL3C3YHHFOSOIPEV4IQ/graph.json","events_json":"https://pith.science/api/pith-number/S2SOUXGIL3C3YHHFOSOIPEV4IQ/events.json","paper":"https://pith.science/paper/S2SOUXGI"},"agent_actions":{"view_html":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ","download_json":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ.json","view_paper":"https://pith.science/paper/S2SOUXGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.6093&json=true","fetch_graph":"https://pith.science/api/pith-number/S2SOUXGIL3C3YHHFOSOIPEV4IQ/graph.json","fetch_events":"https://pith.science/api/pith-number/S2SOUXGIL3C3YHHFOSOIPEV4IQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ/action/storage_attestation","attest_author":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ/action/author_attestation","sign_citation":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ/action/citation_signature","submit_replication":"https://pith.science/pith/S2SOUXGIL3C3YHHFOSOIPEV4IQ/action/replication_record"}},"created_at":"2026-05-18T03:32:32.587143+00:00","updated_at":"2026-05-18T03:32:32.587143+00:00"}