{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XNE5IYEEOKZHGE3S52CV4IFDZA","short_pith_number":"pith:XNE5IYEE","canonical_record":{"source":{"id":"1410.5749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T17:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"7a636ac474cdebea803340071aa890ba79c396be746c182a82c36e73bc47f1d1","abstract_canon_sha256":"1744ddb3dc5160a9ef1f45876d4b20aaf4797ac48483bbd1c7d12bc521f87bfc"},"schema_version":"1.0"},"canonical_sha256":"bb49d4608472b2731372ee855e20a3c839ce440759d5165d87a16ebbfe83e170","source":{"kind":"arxiv","id":"1410.5749","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5749","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5749v1","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5749","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"XNE5IYEEOKZH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XNE5IYEEOKZHGE3S","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XNE5IYEE","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XNE5IYEEOKZHGE3S52CV4IFDZA","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T17:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"7a636ac474cdebea803340071aa890ba79c396be746c182a82c36e73bc47f1d1","abstract_canon_sha256":"1744ddb3dc5160a9ef1f45876d4b20aaf4797ac48483bbd1c7d12bc521f87bfc"},"schema_version":"1.0"},"canonical_sha256":"bb49d4608472b2731372ee855e20a3c839ce440759d5165d87a16ebbfe83e170","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:41.424088Z","signature_b64":"8u4Lka3zhgh7oY0kKMBaFdUWmbY2WEScLvxEIrH4jckXUfSCC//jSR3yjzObeR5Kv7vhq9Qv5D/3WNq5n+woCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb49d4608472b2731372ee855e20a3c839ce440759d5165d87a16ebbfe83e170","last_reissued_at":"2026-05-18T01:41:41.423592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:41.423592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5749","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":"2026-05-18T01:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q+OTHvoc+ROEUp4ejGte9WDw7yWf4Iix7mC+8q0HNKmIM69fVmXY5xG7M84GLgV3L3qXFKJDyiXOCyswB6KFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:37:31.222796Z"},"content_sha256":"51f815ae89613b21fbe504006e4ec76adf2e46279150eacca067d24b9d3c249c","schema_version":"1.0","event_id":"sha256:51f815ae89613b21fbe504006e4ec76adf2e46279150eacca067d24b9d3c249c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XNE5IYEEOKZHGE3S52CV4IFDZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Capillary surfaces in a cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Juncheol Pyo, Rafael L\\'opez","submitted_at":"2014-10-21T17:29:48Z","abstract_excerpt":"We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and the boundary of surface meets the boundary of the cone with a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing toward the domain bounded by the surface and the boundary of the cone. In the particular case that the cone is circular, we prove that the surface is a spherical cap or a planar disc. The proofs are based on an extension of the Alexandrov reflection method by using inversions about spheres."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5749","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":"2026-05-18T01:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjK3s47OpeS1gwUz5+tPUvR+U2tJbSj2BM1zl7N6SDBoPY23Jjzw+6LM/dNqpo+4E0HoaquGS1KIjIYYxvcfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:37:31.223132Z"},"content_sha256":"a10402119268f9fba0974b210ff73af43310bf2428a0681616401d4cf3922314","schema_version":"1.0","event_id":"sha256:a10402119268f9fba0974b210ff73af43310bf2428a0681616401d4cf3922314"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNE5IYEEOKZHGE3S52CV4IFDZA/bundle.json","state_url":"https://pith.science/pith/XNE5IYEEOKZHGE3S52CV4IFDZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNE5IYEEOKZHGE3S52CV4IFDZA/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":"2026-06-01T08:37:31Z","links":{"resolver":"https://pith.science/pith/XNE5IYEEOKZHGE3S52CV4IFDZA","bundle":"https://pith.science/pith/XNE5IYEEOKZHGE3S52CV4IFDZA/bundle.json","state":"https://pith.science/pith/XNE5IYEEOKZHGE3S52CV4IFDZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNE5IYEEOKZHGE3S52CV4IFDZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XNE5IYEEOKZHGE3S52CV4IFDZA","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":"1744ddb3dc5160a9ef1f45876d4b20aaf4797ac48483bbd1c7d12bc521f87bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T17:29:48Z","title_canon_sha256":"7a636ac474cdebea803340071aa890ba79c396be746c182a82c36e73bc47f1d1"},"schema_version":"1.0","source":{"id":"1410.5749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5749","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5749v1","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5749","created_at":"2026-05-18T01:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"XNE5IYEEOKZH","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XNE5IYEEOKZHGE3S","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XNE5IYEE","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:a10402119268f9fba0974b210ff73af43310bf2428a0681616401d4cf3922314","target":"graph","created_at":"2026-05-18T01:41:41Z","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 show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and the boundary of surface meets the boundary of the cone with a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing toward the domain bounded by the surface and the boundary of the cone. In the particular case that the cone is circular, we prove that the surface is a spherical cap or a planar disc. The proofs are based on an extension of the Alexandrov reflection method by using inversions about spheres.","authors_text":"Juncheol Pyo, Rafael L\\'opez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T17:29:48Z","title":"Capillary surfaces in a cone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5749","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":"sha256:51f815ae89613b21fbe504006e4ec76adf2e46279150eacca067d24b9d3c249c","target":"record","created_at":"2026-05-18T01:41:41Z","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":"1744ddb3dc5160a9ef1f45876d4b20aaf4797ac48483bbd1c7d12bc521f87bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-21T17:29:48Z","title_canon_sha256":"7a636ac474cdebea803340071aa890ba79c396be746c182a82c36e73bc47f1d1"},"schema_version":"1.0","source":{"id":"1410.5749","kind":"arxiv","version":1}},"canonical_sha256":"bb49d4608472b2731372ee855e20a3c839ce440759d5165d87a16ebbfe83e170","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb49d4608472b2731372ee855e20a3c839ce440759d5165d87a16ebbfe83e170","first_computed_at":"2026-05-18T01:41:41.423592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:41.423592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8u4Lka3zhgh7oY0kKMBaFdUWmbY2WEScLvxEIrH4jckXUfSCC//jSR3yjzObeR5Kv7vhq9Qv5D/3WNq5n+woCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:41.424088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51f815ae89613b21fbe504006e4ec76adf2e46279150eacca067d24b9d3c249c","sha256:a10402119268f9fba0974b210ff73af43310bf2428a0681616401d4cf3922314"],"state_sha256":"ef691081272af502206b505f9a69ae71df72e998ee882eddc05f4234a274fc8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/7b0rsDyDNRTZcNYaQoOYUCFq0IOt4GmaPLE3C8r0XNDBXFLJWb3Ds/w0IN3hIYBdOvwNaCjWE2bunRzA37DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:37:31.224935Z","bundle_sha256":"d5b1bd59f4b0f21bf51a108501b30cb5b4e2d92826432b7fa28b3728111b01a2"}}