{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EKM53FRXXG2CSYOT6UUNHALHMV","short_pith_number":"pith:EKM53FRX","canonical_record":{"source":{"id":"1502.02185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-07T21:13:38Z","cross_cats_sorted":[],"title_canon_sha256":"bc0794c0ed76a0255257eaf256976443e467674806e7796d83b99a1fc02e6d27","abstract_canon_sha256":"02d5ecb6755d0b0a190c7c95b742d22db07a3fbbf2dd7620f7ff1e9eb4b0f342"},"schema_version":"1.0"},"canonical_sha256":"2299dd9637b9b42961d3f528d381676572694884df94a359b338fda9d7a3429d","source":{"kind":"arxiv","id":"1502.02185","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02185","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02185v2","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02185","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"EKM53FRXXG2C","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EKM53FRXXG2CSYOT","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EKM53FRX","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EKM53FRXXG2CSYOT6UUNHALHMV","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-07T21:13:38Z","cross_cats_sorted":[],"title_canon_sha256":"bc0794c0ed76a0255257eaf256976443e467674806e7796d83b99a1fc02e6d27","abstract_canon_sha256":"02d5ecb6755d0b0a190c7c95b742d22db07a3fbbf2dd7620f7ff1e9eb4b0f342"},"schema_version":"1.0"},"canonical_sha256":"2299dd9637b9b42961d3f528d381676572694884df94a359b338fda9d7a3429d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:32.242048Z","signature_b64":"2gXcnGfWL7yxRNwwH6DRwi/FXpwL/kf11ug9koAmcf/kDooGomyyziYNjV3moYFWbz2TtN32jP40AZ3uEHNZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2299dd9637b9b42961d3f528d381676572694884df94a359b338fda9d7a3429d","last_reissued_at":"2026-05-18T00:46:32.241534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:32.241534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02185","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ha6ylWsGSN7JC8EWNiZ8bfGnm9Pduc2nAsLw4zltZt6vn+LFXEf64DdbCYtUVELJ5CThEScz73rcuuiE6DgTCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:44:58.635910Z"},"content_sha256":"aa259df0fd6d7d52fbc76d6289355eabae4a6dcaf9088aac763baaa9b9cd21b9","schema_version":"1.0","event_id":"sha256:aa259df0fd6d7d52fbc76d6289355eabae4a6dcaf9088aac763baaa9b9cd21b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EKM53FRXXG2CSYOT6UUNHALHMV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity formula for complete hypersurfaces in the Hyperbolic space and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Greg\\'orio Silva Neto, Hil\\'ario Alencar","submitted_at":"2015-02-07T21:13:38Z","abstract_excerpt":"In this paper we prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a lower bound for the integral of the mean curvature and that the integral of the mean curvature is infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02185","kind":"arxiv","version":2},"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":"2026-05-18T00:46:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2gAq36rk0ko1xE+iW9IrN6deMpoaueUWlyAHgJZIuDeuG5M3te0CxPUowSJLNMSoqNtqPacOaWGkHO9WXxaTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:44:58.636261Z"},"content_sha256":"93e4e9946f122733f119dae5f5e035cfb9b51bdeca8af2b3754b82ce18e54655","schema_version":"1.0","event_id":"sha256:93e4e9946f122733f119dae5f5e035cfb9b51bdeca8af2b3754b82ce18e54655"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKM53FRXXG2CSYOT6UUNHALHMV/bundle.json","state_url":"https://pith.science/pith/EKM53FRXXG2CSYOT6UUNHALHMV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKM53FRXXG2CSYOT6UUNHALHMV/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":"2026-06-02T21:44:58Z","links":{"resolver":"https://pith.science/pith/EKM53FRXXG2CSYOT6UUNHALHMV","bundle":"https://pith.science/pith/EKM53FRXXG2CSYOT6UUNHALHMV/bundle.json","state":"https://pith.science/pith/EKM53FRXXG2CSYOT6UUNHALHMV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKM53FRXXG2CSYOT6UUNHALHMV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EKM53FRXXG2CSYOT6UUNHALHMV","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":"02d5ecb6755d0b0a190c7c95b742d22db07a3fbbf2dd7620f7ff1e9eb4b0f342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-07T21:13:38Z","title_canon_sha256":"bc0794c0ed76a0255257eaf256976443e467674806e7796d83b99a1fc02e6d27"},"schema_version":"1.0","source":{"id":"1502.02185","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02185","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02185v2","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02185","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"EKM53FRXXG2C","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EKM53FRXXG2CSYOT","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EKM53FRX","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:93e4e9946f122733f119dae5f5e035cfb9b51bdeca8af2b3754b82ce18e54655","target":"graph","created_at":"2026-05-18T00:46:32Z","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 prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a lower bound for the integral of the mean curvature and that the integral of the mean curvature is infinity.","authors_text":"Greg\\'orio Silva Neto, Hil\\'ario Alencar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-07T21:13:38Z","title":"Monotonicity formula for complete hypersurfaces in the Hyperbolic space and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02185","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:aa259df0fd6d7d52fbc76d6289355eabae4a6dcaf9088aac763baaa9b9cd21b9","target":"record","created_at":"2026-05-18T00:46:32Z","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":"02d5ecb6755d0b0a190c7c95b742d22db07a3fbbf2dd7620f7ff1e9eb4b0f342","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-07T21:13:38Z","title_canon_sha256":"bc0794c0ed76a0255257eaf256976443e467674806e7796d83b99a1fc02e6d27"},"schema_version":"1.0","source":{"id":"1502.02185","kind":"arxiv","version":2}},"canonical_sha256":"2299dd9637b9b42961d3f528d381676572694884df94a359b338fda9d7a3429d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2299dd9637b9b42961d3f528d381676572694884df94a359b338fda9d7a3429d","first_computed_at":"2026-05-18T00:46:32.241534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:32.241534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2gXcnGfWL7yxRNwwH6DRwi/FXpwL/kf11ug9koAmcf/kDooGomyyziYNjV3moYFWbz2TtN32jP40AZ3uEHNZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:32.242048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02185","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa259df0fd6d7d52fbc76d6289355eabae4a6dcaf9088aac763baaa9b9cd21b9","sha256:93e4e9946f122733f119dae5f5e035cfb9b51bdeca8af2b3754b82ce18e54655"],"state_sha256":"06049d7a2cd48d22feb8993590e3ca0d04fec4dfc9484c963b39c29f18aa6e5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e6ydHatsty0+v+lC+YQYYD8JKB+5Ie6tJWsSEF2I0/kLhkdM/dMcyEqlLhXx/mVb6/YO+i6I37v4te4SfHW5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:44:58.638288Z","bundle_sha256":"af37970eead34de6e6a9230e23dd106677adc8f2518a41e34cd05d7d5e8f9ec1"}}