{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NMJ6EOPTQSDTZIB3T4WSCBAPBV","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":"79de5bc0836b936467aed730902a2861b54e991285a6dc18435d6255a5077a56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-19T16:05:12Z","title_canon_sha256":"adc5e52d131954743ccfd33c153426a7067d1b695f6e4bbeee916aaab080cf62"},"schema_version":"1.0","source":{"id":"1609.05806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05806","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05806v1","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05806","created_at":"2026-05-18T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"NMJ6EOPTQSDT","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NMJ6EOPTQSDTZIB3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NMJ6EOPT","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:8392a8b43507cf01196ee66bcd1666cc480f9417be7afcd122091d1efabdd4bd","target":"graph","created_at":"2026-05-18T01:04:25Z","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":"We find a monotone quantity along the inverse mean curvature flow and use it to prove an Alexandrov-Fenchel-type inequality for strictly convex hypersurfaces in the $n$-dimensional sphere, $n \\geq 3$.","authors_text":"Frederico Gir\\~ao, Neilha M. Pinheiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-19T16:05:12Z","title":"An Alexandrov-Fenchel-type inequality for hypersurfaces in the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05806","kind":"arxiv","version":1},"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":"sha256:2f91806d33ae7f463af04caf0c4e864dd14ee88bae081df4f3391af52d04cf2e","target":"record","created_at":"2026-05-18T01:04:25Z","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":"79de5bc0836b936467aed730902a2861b54e991285a6dc18435d6255a5077a56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-19T16:05:12Z","title_canon_sha256":"adc5e52d131954743ccfd33c153426a7067d1b695f6e4bbeee916aaab080cf62"},"schema_version":"1.0","source":{"id":"1609.05806","kind":"arxiv","version":1}},"canonical_sha256":"6b13e239f384873ca03b9f2d21040f0d5eab2b7e01b40096e61f5d5d08f55e27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b13e239f384873ca03b9f2d21040f0d5eab2b7e01b40096e61f5d5d08f55e27","first_computed_at":"2026-05-18T01:04:25.254778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:25.254778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4oSD4vvwIcqgfhYgs/D7LyKPG4+WPOHi5IiWLxt8/Q4rTRA+piX9kSzqdMLbLDZIOLh7M5z47T+dsemwmB6bAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:25.255557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f91806d33ae7f463af04caf0c4e864dd14ee88bae081df4f3391af52d04cf2e","sha256:8392a8b43507cf01196ee66bcd1666cc480f9417be7afcd122091d1efabdd4bd"],"state_sha256":"f025b4ab9c713c5e5f4bdcf44ac07520d1ee6c772d8ecdd2b3a84467e49136a7"}