{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VCBQCXCKKWANE72HADIBIMOQJQ","short_pith_number":"pith:VCBQCXCK","canonical_record":{"source":{"id":"1709.06550","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T17:53:42Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"1fa1d802102f14d4ea0b2e61527d2b55576a076669f6f381a13d367bec16057b","abstract_canon_sha256":"e1d9a339388546008f59f7c4fc0cfc18b2e870b7c6abfe984c9d6d0d800f01d7"},"schema_version":"1.0"},"canonical_sha256":"a883015c4a5580d27f4700d01431d04c2b6279c0c4ebd140f6909461764d808b","source":{"kind":"arxiv","id":"1709.06550","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06550","created_at":"2026-05-18T00:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06550v4","created_at":"2026-05-18T00:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06550","created_at":"2026-05-18T00:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"VCBQCXCKKWAN","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VCBQCXCKKWANE72H","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VCBQCXCK","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VCBQCXCKKWANE72HADIBIMOQJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06550","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T17:53:42Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"1fa1d802102f14d4ea0b2e61527d2b55576a076669f6f381a13d367bec16057b","abstract_canon_sha256":"e1d9a339388546008f59f7c4fc0cfc18b2e870b7c6abfe984c9d6d0d800f01d7"},"schema_version":"1.0"},"canonical_sha256":"a883015c4a5580d27f4700d01431d04c2b6279c0c4ebd140f6909461764d808b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:14.185630Z","signature_b64":"no9mw/n1SJ2cc2NdOAYCdiIKNpY+sdK9Ks0hasGsWTEqbx+1luiL94RpFpAax7/Ugppqi2jKJ0s8NMqkc5oBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a883015c4a5580d27f4700d01431d04c2b6279c0c4ebd140f6909461764d808b","last_reissued_at":"2026-05-18T00:12:14.185081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:14.185081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06550","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7waCdn19ytQmmxPr/3Vj29PdGNf0uiRSxz9bqc+DH1bSrTg2rSanyJFLnze2a859D5wYggF+ELb/e3muODxrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:10:14.545682Z"},"content_sha256":"35a819cc64e97a85a0a8b5ecdea5f50109d5c627774ae5bf03d0f522939b09cf","schema_version":"1.0","event_id":"sha256:35a819cc64e97a85a0a8b5ecdea5f50109d5c627774ae5bf03d0f522939b09cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VCBQCXCKKWANE72HADIBIMOQJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Minkowski-like inequality for asymptotically flat static manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Stephen McCormick","submitted_at":"2017-09-19T17:53:42Z","abstract_excerpt":"The Minkowski inequality is a classical inequality in differential geometry, giving a bound from below, on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than R^n; for example, such an inequality holds for surfaces in spatial Schwarzschild and AdS-Schwarzschild manifolds. In this note, we adapt a recent analysis of Y. Wei to prove a Minkowski-like inequality for general static asymptotically flat manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06550","kind":"arxiv","version":4},"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":"2026-05-18T00:12:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uu6eCLrgXwQdvi9YxV0r+NMe9hMOMtt9lM3xkmR9ldsM/+mw5ZGHD6Wgha8mTts+IxVb9DZhE0Whu/UTRNyQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:10:14.546011Z"},"content_sha256":"a4926c812c2823cdfc95a611b6056da5f551ab9c72eae9ff6e4b5f82286509c9","schema_version":"1.0","event_id":"sha256:a4926c812c2823cdfc95a611b6056da5f551ab9c72eae9ff6e4b5f82286509c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCBQCXCKKWANE72HADIBIMOQJQ/bundle.json","state_url":"https://pith.science/pith/VCBQCXCKKWANE72HADIBIMOQJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCBQCXCKKWANE72HADIBIMOQJQ/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":"2026-06-02T13:10:14Z","links":{"resolver":"https://pith.science/pith/VCBQCXCKKWANE72HADIBIMOQJQ","bundle":"https://pith.science/pith/VCBQCXCKKWANE72HADIBIMOQJQ/bundle.json","state":"https://pith.science/pith/VCBQCXCKKWANE72HADIBIMOQJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCBQCXCKKWANE72HADIBIMOQJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VCBQCXCKKWANE72HADIBIMOQJQ","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":"e1d9a339388546008f59f7c4fc0cfc18b2e870b7c6abfe984c9d6d0d800f01d7","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T17:53:42Z","title_canon_sha256":"1fa1d802102f14d4ea0b2e61527d2b55576a076669f6f381a13d367bec16057b"},"schema_version":"1.0","source":{"id":"1709.06550","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06550","created_at":"2026-05-18T00:12:14Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06550v4","created_at":"2026-05-18T00:12:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06550","created_at":"2026-05-18T00:12:14Z"},{"alias_kind":"pith_short_12","alias_value":"VCBQCXCKKWAN","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VCBQCXCKKWANE72H","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VCBQCXCK","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:a4926c812c2823cdfc95a611b6056da5f551ab9c72eae9ff6e4b5f82286509c9","target":"graph","created_at":"2026-05-18T00:12:14Z","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":"The Minkowski inequality is a classical inequality in differential geometry, giving a bound from below, on the total mean curvature of a convex surface in Euclidean space, in terms of its area. Recently there has been interest in proving versions of this inequality for manifolds other than R^n; for example, such an inequality holds for surfaces in spatial Schwarzschild and AdS-Schwarzschild manifolds. In this note, we adapt a recent analysis of Y. Wei to prove a Minkowski-like inequality for general static asymptotically flat manifolds.","authors_text":"Stephen McCormick","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T17:53:42Z","title":"On a Minkowski-like inequality for asymptotically flat static manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06550","kind":"arxiv","version":4},"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":"sha256:35a819cc64e97a85a0a8b5ecdea5f50109d5c627774ae5bf03d0f522939b09cf","target":"record","created_at":"2026-05-18T00:12:14Z","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":"e1d9a339388546008f59f7c4fc0cfc18b2e870b7c6abfe984c9d6d0d800f01d7","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T17:53:42Z","title_canon_sha256":"1fa1d802102f14d4ea0b2e61527d2b55576a076669f6f381a13d367bec16057b"},"schema_version":"1.0","source":{"id":"1709.06550","kind":"arxiv","version":4}},"canonical_sha256":"a883015c4a5580d27f4700d01431d04c2b6279c0c4ebd140f6909461764d808b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a883015c4a5580d27f4700d01431d04c2b6279c0c4ebd140f6909461764d808b","first_computed_at":"2026-05-18T00:12:14.185081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:14.185081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"no9mw/n1SJ2cc2NdOAYCdiIKNpY+sdK9Ks0hasGsWTEqbx+1luiL94RpFpAax7/Ugppqi2jKJ0s8NMqkc5oBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:14.185630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06550","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a819cc64e97a85a0a8b5ecdea5f50109d5c627774ae5bf03d0f522939b09cf","sha256:a4926c812c2823cdfc95a611b6056da5f551ab9c72eae9ff6e4b5f82286509c9"],"state_sha256":"d989fb02b2444a005dfc7e1911aa41f95006e902b80e180d97cb076e9a0ed5d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"khFrF6Nd0T4sKqVzyfBIuFpmD1Euj6MOdqdpARcmfYRNb7GNtSj3bd01vblZejJtNFVfmUgnoJun1bTYRNA+Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:10:14.547837Z","bundle_sha256":"11fec157e556b304482a3a70745167ddf4f6e3927ae4326b69d5090ece443c99"}}