{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EJTZSIGSQKO27LGDGM34KWDIUV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"779baa474c39fe37d3158b17d1db4925deac6ef999d28403991b23f813a9b018","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-18T11:06:11Z","title_canon_sha256":"307a7da5ad7d977143b0976495645e52f79cb319c2b1b82c5f4e7d8054c3b527"},"schema_version":"1.0","source":{"id":"1707.05559","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05559","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05559v2","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05559","created_at":"2026-05-17T23:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"EJTZSIGSQKO2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EJTZSIGSQKO27LGD","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EJTZSIGS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:1c4772f5bcfb7e8869852b7c359d89a60045190ea419cbaff16c8981bbe4a633","target":"graph","created_at":"2026-05-17T23:58:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we give a relation between the volume of sublevel sets and the area of level sets using a Gelfand-Leray form. As a consequence, we give an estimation of the volume of sublevel sets. In particular we give a proof of the known fact that the derivative of the volume of a $n$-dimensional ball with respect to the radius equals the area of the sphere which bounds the $n$-dimensional ball.","authors_text":"Trinh Duc Tai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-18T11:06:11Z","title":"Volume of sublevel sets versus area of level sets via Gelfand-Leray form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05559","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4c6b6388e96da7a5d6149638970b94e0f91471bd6cdf47c6680499cf93688f2c","target":"record","created_at":"2026-05-17T23:58:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"779baa474c39fe37d3158b17d1db4925deac6ef999d28403991b23f813a9b018","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-07-18T11:06:11Z","title_canon_sha256":"307a7da5ad7d977143b0976495645e52f79cb319c2b1b82c5f4e7d8054c3b527"},"schema_version":"1.0","source":{"id":"1707.05559","kind":"arxiv","version":2}},"canonical_sha256":"22679920d2829dafacc33337c55868a56b7969ef8122275b486cf7ac28eb0efe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22679920d2829dafacc33337c55868a56b7969ef8122275b486cf7ac28eb0efe","first_computed_at":"2026-05-17T23:58:23.293098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:23.293098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jP++1JWqQxUfZxqVYRzRIwSn0fF+/ax/jopFTgdsp7FRWL5DfZmITg1sElCHnMvoU0A1HteGaLradeCVrj74Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:23.293797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05559","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c6b6388e96da7a5d6149638970b94e0f91471bd6cdf47c6680499cf93688f2c","sha256:1c4772f5bcfb7e8869852b7c359d89a60045190ea419cbaff16c8981bbe4a633"],"state_sha256":"f7049aee625f8508b40fce3fc611c31f6cb651d0e7e523af9fc6919f1068dc1f"}