{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5FE532V7JDZR63BR3SE6KW4HUX","short_pith_number":"pith:5FE532V7","canonical_record":{"source":{"id":"1210.5699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T07:10:38Z","cross_cats_sorted":[],"title_canon_sha256":"d832b0ba5f3e445923e280e81cd0824ed18c9cf58e5657a33f91e66fd237d398","abstract_canon_sha256":"785a97365f4ebf307915bd1dbcda371b7f4b157b572b8b46dda8215522660fbb"},"schema_version":"1.0"},"canonical_sha256":"e949ddeabf48f31f6c31dc89e55b87a5fec54e1a711bd04a9c2cefaba2b6f86c","source":{"kind":"arxiv","id":"1210.5699","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5699","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5699v1","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5699","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"5FE532V7JDZR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5FE532V7JDZR63BR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5FE532V7","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5FE532V7JDZR63BR3SE6KW4HUX","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T07:10:38Z","cross_cats_sorted":[],"title_canon_sha256":"d832b0ba5f3e445923e280e81cd0824ed18c9cf58e5657a33f91e66fd237d398","abstract_canon_sha256":"785a97365f4ebf307915bd1dbcda371b7f4b157b572b8b46dda8215522660fbb"},"schema_version":"1.0"},"canonical_sha256":"e949ddeabf48f31f6c31dc89e55b87a5fec54e1a711bd04a9c2cefaba2b6f86c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.510535Z","signature_b64":"NZFdWxyfN2CTQ8wIQzRZZzfRGSGvnsdujIhPx0nzMEU+WYzt0t3Hu7s/oFS33Ngiaejo0FdZRe1GTofBiRqfBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e949ddeabf48f31f6c31dc89e55b87a5fec54e1a711bd04a9c2cefaba2b6f86c","last_reissued_at":"2026-05-18T00:45:35.509823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:35.509823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5699","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V89N55M+ALRTapycvAsYRtVDt7go7wqzkGYzWVvCSCE9MT7kivPAl48kXOPezYi4BkZQmB6/dWskBKx4iUfkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:30:59.806136Z"},"content_sha256":"d561d93e10a2921fbbb8378116494b5e8dc06bce62271f0a9c31c40dd2093630","schema_version":"1.0","event_id":"sha256:d561d93e10a2921fbbb8378116494b5e8dc06bce62271f0a9c31c40dd2093630"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5FE532V7JDZR63BR3SE6KW4HUX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on Brendle-Eichmair's paper \"Isoperimetric and Weingarten surfaces in the Schwarchild manifold\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Changwei Xiong, Haizhong Li, Yong Wei","submitted_at":"2012-10-21T07:10:38Z","abstract_excerpt":"In this short note, we show that the assumption \"convex\" in Theorem 7 of Brendle-Eichmair's paper \\cite{BE} is unnecessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5699","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92/3lyKu0avQnF7i9ftCmBZAXnsJMiwjs2P5MwC+YRdeSkV3t7yXO4bGpRi+PPrR2gm+3OaQsIyZkggRtaucCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:30:59.806792Z"},"content_sha256":"2edfe0f30c89c553532f6c0921033a1c42cacf2371c0b0a452ba6ef03d3bd9b8","schema_version":"1.0","event_id":"sha256:2edfe0f30c89c553532f6c0921033a1c42cacf2371c0b0a452ba6ef03d3bd9b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FE532V7JDZR63BR3SE6KW4HUX/bundle.json","state_url":"https://pith.science/pith/5FE532V7JDZR63BR3SE6KW4HUX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FE532V7JDZR63BR3SE6KW4HUX/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":"2026-05-27T18:30:59Z","links":{"resolver":"https://pith.science/pith/5FE532V7JDZR63BR3SE6KW4HUX","bundle":"https://pith.science/pith/5FE532V7JDZR63BR3SE6KW4HUX/bundle.json","state":"https://pith.science/pith/5FE532V7JDZR63BR3SE6KW4HUX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FE532V7JDZR63BR3SE6KW4HUX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5FE532V7JDZR63BR3SE6KW4HUX","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":"785a97365f4ebf307915bd1dbcda371b7f4b157b572b8b46dda8215522660fbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T07:10:38Z","title_canon_sha256":"d832b0ba5f3e445923e280e81cd0824ed18c9cf58e5657a33f91e66fd237d398"},"schema_version":"1.0","source":{"id":"1210.5699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5699","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5699v1","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5699","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"5FE532V7JDZR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5FE532V7JDZR63BR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5FE532V7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:2edfe0f30c89c553532f6c0921033a1c42cacf2371c0b0a452ba6ef03d3bd9b8","target":"graph","created_at":"2026-05-18T00:45:35Z","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 short note, we show that the assumption \"convex\" in Theorem 7 of Brendle-Eichmair's paper \\cite{BE} is unnecessary.","authors_text":"Changwei Xiong, Haizhong Li, Yong Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T07:10:38Z","title":"Note on Brendle-Eichmair's paper \"Isoperimetric and Weingarten surfaces in the Schwarchild manifold\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5699","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:d561d93e10a2921fbbb8378116494b5e8dc06bce62271f0a9c31c40dd2093630","target":"record","created_at":"2026-05-18T00:45:35Z","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":"785a97365f4ebf307915bd1dbcda371b7f4b157b572b8b46dda8215522660fbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T07:10:38Z","title_canon_sha256":"d832b0ba5f3e445923e280e81cd0824ed18c9cf58e5657a33f91e66fd237d398"},"schema_version":"1.0","source":{"id":"1210.5699","kind":"arxiv","version":1}},"canonical_sha256":"e949ddeabf48f31f6c31dc89e55b87a5fec54e1a711bd04a9c2cefaba2b6f86c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e949ddeabf48f31f6c31dc89e55b87a5fec54e1a711bd04a9c2cefaba2b6f86c","first_computed_at":"2026-05-18T00:45:35.509823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:35.509823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NZFdWxyfN2CTQ8wIQzRZZzfRGSGvnsdujIhPx0nzMEU+WYzt0t3Hu7s/oFS33Ngiaejo0FdZRe1GTofBiRqfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:35.510535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d561d93e10a2921fbbb8378116494b5e8dc06bce62271f0a9c31c40dd2093630","sha256:2edfe0f30c89c553532f6c0921033a1c42cacf2371c0b0a452ba6ef03d3bd9b8"],"state_sha256":"a19a76baf053d338c5b830859f93e7e85cb4c562389318ef03ec47b13ac11628"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5eI9ifL7EBOBOE8US5Mtgogm+zo7rMy4r2E9nJU5c1z3B0/gg903TdNfuUiKxCMGtO5KUTMBcr0lstyMj8UCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:30:59.809406Z","bundle_sha256":"25d6be0efb2c75c4fca3d69261a87aea88bfdbfe96fc75d87b87da69e73566b2"}}