{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NMJ6EOPTQSDTZIB3T4WSCBAPBV","short_pith_number":"pith:NMJ6EOPT","canonical_record":{"source":{"id":"1609.05806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-19T16:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"adc5e52d131954743ccfd33c153426a7067d1b695f6e4bbeee916aaab080cf62","abstract_canon_sha256":"79de5bc0836b936467aed730902a2861b54e991285a6dc18435d6255a5077a56"},"schema_version":"1.0"},"canonical_sha256":"6b13e239f384873ca03b9f2d21040f0d5eab2b7e01b40096e61f5d5d08f55e27","source":{"kind":"arxiv","id":"1609.05806","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NMJ6EOPTQSDTZIB3T4WSCBAPBV","target":"record","payload":{"canonical_record":{"source":{"id":"1609.05806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-19T16:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"adc5e52d131954743ccfd33c153426a7067d1b695f6e4bbeee916aaab080cf62","abstract_canon_sha256":"79de5bc0836b936467aed730902a2861b54e991285a6dc18435d6255a5077a56"},"schema_version":"1.0"},"canonical_sha256":"6b13e239f384873ca03b9f2d21040f0d5eab2b7e01b40096e61f5d5d08f55e27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:25.255557Z","signature_b64":"4oSD4vvwIcqgfhYgs/D7LyKPG4+WPOHi5IiWLxt8/Q4rTRA+piX9kSzqdMLbLDZIOLh7M5z47T+dsemwmB6bAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b13e239f384873ca03b9f2d21040f0d5eab2b7e01b40096e61f5d5d08f55e27","last_reissued_at":"2026-05-18T01:04:25.254778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:25.254778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.05806","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QDreZLlrHuAycaKU55OwA5WyFGMZZAjZO31dgOv+mhdbfy6CPdlT2sRfcQhDjb820PYgGjYrpH3XNvmtINA5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:30:31.039759Z"},"content_sha256":"2f91806d33ae7f463af04caf0c4e864dd14ee88bae081df4f3391af52d04cf2e","schema_version":"1.0","event_id":"sha256:2f91806d33ae7f463af04caf0c4e864dd14ee88bae081df4f3391af52d04cf2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NMJ6EOPTQSDTZIB3T4WSCBAPBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Alexandrov-Fenchel-type inequality for hypersurfaces in the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Frederico Gir\\~ao, Neilha M. Pinheiro","submitted_at":"2016-09-19T16:05:12Z","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, $n \\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05806","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YGl02tTp0BUlFxnQmjV4yVQVgK1tzbv3PwNw9hCDh3McJEiQMGWS4AOdzuDT+Zv0pT+CqMoL6VmI2451kG8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:30:31.040443Z"},"content_sha256":"8392a8b43507cf01196ee66bcd1666cc480f9417be7afcd122091d1efabdd4bd","schema_version":"1.0","event_id":"sha256:8392a8b43507cf01196ee66bcd1666cc480f9417be7afcd122091d1efabdd4bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV/bundle.json","state_url":"https://pith.science/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T19:30:31Z","links":{"resolver":"https://pith.science/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV","bundle":"https://pith.science/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV/bundle.json","state":"https://pith.science/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMJ6EOPTQSDTZIB3T4WSCBAPBV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jb6PCQ/1BjMbtj2tLsy1zP5b7mroStoKf/uhoAj+x2KWVcmMTpUyfgnJ0R/Y/AH2Hd89u5/AcG7UZekiqJYFBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:30:31.043780Z","bundle_sha256":"ba4ee89c62062a4fe82646f4fb19de1732e8d37f4d355b0ea1a80485087a4393"}}