{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YD6PWUO4I7MWN2WUYZRDYQEVFD","short_pith_number":"pith:YD6PWUO4","schema_version":"1.0","canonical_sha256":"c0fcfb51dc47d966ead4c6623c409528dc3daf7e7ba75f2c25f8a3292ab785c7","source":{"kind":"arxiv","id":"1310.8424","version":3},"attestation_state":"computed","paper":{"title":"On the concavity of the arithmetic volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hideaki Ikoma","submitted_at":"2013-10-31T08:44:01Z","abstract_excerpt":"In this note, we study the differentiability of the arithmetic volumes along arithmetic R-divisors, and give some equality conditions for the Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big arithmetic R-divisors."},"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":"1310.8424","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-31T08:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"ff4c7f9c0b270d01a25308efbd3d00b59f07d5f27cf2b2b3c2e23b4a92c60b2c","abstract_canon_sha256":"ced8b5bf43fca1396ef09e712675b2732b414a8c1c50ea6343bb0118dc9aa7c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:14.449824Z","signature_b64":"az39uaXDLXWLREwG1808UeGgomz2vGifeMtofanu37MJFOLc52d2qpEQauHFHZzQM2hFa289Y71EkJcWS5BUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0fcfb51dc47d966ead4c6623c409528dc3daf7e7ba75f2c25f8a3292ab785c7","last_reissued_at":"2026-05-18T02:45:14.449164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:14.449164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the concavity of the arithmetic volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hideaki Ikoma","submitted_at":"2013-10-31T08:44:01Z","abstract_excerpt":"In this note, we study the differentiability of the arithmetic volumes along arithmetic R-divisors, and give some equality conditions for the Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big arithmetic R-divisors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8424","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":"1310.8424","created_at":"2026-05-18T02:45:14.449274+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.8424v3","created_at":"2026-05-18T02:45:14.449274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8424","created_at":"2026-05-18T02:45:14.449274+00:00"},{"alias_kind":"pith_short_12","alias_value":"YD6PWUO4I7MW","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YD6PWUO4I7MWN2WU","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YD6PWUO4","created_at":"2026-05-18T12:28:06.772260+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/YD6PWUO4I7MWN2WUYZRDYQEVFD","json":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD.json","graph_json":"https://pith.science/api/pith-number/YD6PWUO4I7MWN2WUYZRDYQEVFD/graph.json","events_json":"https://pith.science/api/pith-number/YD6PWUO4I7MWN2WUYZRDYQEVFD/events.json","paper":"https://pith.science/paper/YD6PWUO4"},"agent_actions":{"view_html":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD","download_json":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD.json","view_paper":"https://pith.science/paper/YD6PWUO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.8424&json=true","fetch_graph":"https://pith.science/api/pith-number/YD6PWUO4I7MWN2WUYZRDYQEVFD/graph.json","fetch_events":"https://pith.science/api/pith-number/YD6PWUO4I7MWN2WUYZRDYQEVFD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD/action/storage_attestation","attest_author":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD/action/author_attestation","sign_citation":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD/action/citation_signature","submit_replication":"https://pith.science/pith/YD6PWUO4I7MWN2WUYZRDYQEVFD/action/replication_record"}},"created_at":"2026-05-18T02:45:14.449274+00:00","updated_at":"2026-05-18T02:45:14.449274+00:00"}