{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:V7EQF6PJFBFCPD7SNUF5LOY4YJ","short_pith_number":"pith:V7EQF6PJ","canonical_record":{"source":{"id":"2001.11840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-01-30T14:20:51Z","cross_cats_sorted":[],"title_canon_sha256":"08dd5af71ad1dedb135f6b588fa5fff56faf3dc7d42642988f9453c8be0a54a2","abstract_canon_sha256":"7dfa708d4577939564cda9a16fa317dd54008b1257de88f0f54a7f9935ed2402"},"schema_version":"1.0"},"canonical_sha256":"afc902f9e9284a278ff26d0bd5bb1cc273cc14748c683e05504ab594f16a5711","source":{"kind":"arxiv","id":"2001.11840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11840","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11840v1","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11840","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"pith_short_12","alias_value":"V7EQF6PJFBFC","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"pith_short_16","alias_value":"V7EQF6PJFBFCPD7S","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"pith_short_8","alias_value":"V7EQF6PJ","created_at":"2026-07-05T00:37:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:V7EQF6PJFBFCPD7SNUF5LOY4YJ","target":"record","payload":{"canonical_record":{"source":{"id":"2001.11840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-01-30T14:20:51Z","cross_cats_sorted":[],"title_canon_sha256":"08dd5af71ad1dedb135f6b588fa5fff56faf3dc7d42642988f9453c8be0a54a2","abstract_canon_sha256":"7dfa708d4577939564cda9a16fa317dd54008b1257de88f0f54a7f9935ed2402"},"schema_version":"1.0"},"canonical_sha256":"afc902f9e9284a278ff26d0bd5bb1cc273cc14748c683e05504ab594f16a5711","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:37:34.279725Z","signature_b64":"Nmvt+8H9uUAfDaGDnJvw6NsJnDKgtkIyMevPD97sFL+NNnw6HYoNTmQVCexhzUZ2e3dIUzsclHfHHKCmOkbFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc902f9e9284a278ff26d0bd5bb1cc273cc14748c683e05504ab594f16a5711","last_reissued_at":"2026-07-05T00:37:34.279295Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:37:34.279295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.11840","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":"2026-07-05T00:37:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lelT2MyYOLnJhykXE8QXbA40donl9lk/B4wW4dIH8SzbADIk/yaZ3iTa7bZoKerBMsnHyFZ5AGIn18fSB9HzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:50:26.822642Z"},"content_sha256":"f3a2601cd1ebc8d10b79ec694bc4c2a6882686f2d588860f25bba66f7e4d62a2","schema_version":"1.0","event_id":"sha256:f3a2601cd1ebc8d10b79ec694bc4c2a6882686f2d588860f25bba66f7e4d62a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:V7EQF6PJFBFCPD7SNUF5LOY4YJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^{n}\\times\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chun-Lan Song, Jing Mao, Ya Gao","submitted_at":"2020-01-30T14:20:51Z","abstract_excerpt":"In this paper, we can prove the existence and uniqueness of solutions to the constant mean curvature (CMC for short) equation with nonzero Neumann boundary data in product manifold $M^{n}\\times\\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\\mathbb{R}$ is the Euclidean $1$-space. Equivalently, this conclusion gives the existence of CMC graphic hypersurfaces defined over a compact strictly convex domain $\\Omega\\subset M^{n}$ and having arbitrary contact angle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11840","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.11840/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:37:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5nXYWDhabmRZyzY2puUffBSi73z8mgovW/MnBXgXjzonwPxk89vYmPPY9tOaKbx8dlE4e3b2cHy40/dj/Q5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:50:26.823011Z"},"content_sha256":"37704359bfdc32b9359026455de7539cd381c18e458b3b281a80d66341fe8519","schema_version":"1.0","event_id":"sha256:37704359bfdc32b9359026455de7539cd381c18e458b3b281a80d66341fe8519"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ/bundle.json","state_url":"https://pith.science/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ/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":"2026-07-07T14:50:26Z","links":{"resolver":"https://pith.science/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ","bundle":"https://pith.science/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ/bundle.json","state":"https://pith.science/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7EQF6PJFBFCPD7SNUF5LOY4YJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:V7EQF6PJFBFCPD7SNUF5LOY4YJ","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":"7dfa708d4577939564cda9a16fa317dd54008b1257de88f0f54a7f9935ed2402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-01-30T14:20:51Z","title_canon_sha256":"08dd5af71ad1dedb135f6b588fa5fff56faf3dc7d42642988f9453c8be0a54a2"},"schema_version":"1.0","source":{"id":"2001.11840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11840","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11840v1","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11840","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"pith_short_12","alias_value":"V7EQF6PJFBFC","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"pith_short_16","alias_value":"V7EQF6PJFBFCPD7S","created_at":"2026-07-05T00:37:34Z"},{"alias_kind":"pith_short_8","alias_value":"V7EQF6PJ","created_at":"2026-07-05T00:37:34Z"}],"graph_snapshots":[{"event_id":"sha256:37704359bfdc32b9359026455de7539cd381c18e458b3b281a80d66341fe8519","target":"graph","created_at":"2026-07-05T00:37:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2001.11840/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we can prove the existence and uniqueness of solutions to the constant mean curvature (CMC for short) equation with nonzero Neumann boundary data in product manifold $M^{n}\\times\\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\\mathbb{R}$ is the Euclidean $1$-space. Equivalently, this conclusion gives the existence of CMC graphic hypersurfaces defined over a compact strictly convex domain $\\Omega\\subset M^{n}$ and having arbitrary contact angle.","authors_text":"Chun-Lan Song, Jing Mao, Ya Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-01-30T14:20:51Z","title":"Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^{n}\\times\\mathbb{R}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11840","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:f3a2601cd1ebc8d10b79ec694bc4c2a6882686f2d588860f25bba66f7e4d62a2","target":"record","created_at":"2026-07-05T00:37:34Z","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":"7dfa708d4577939564cda9a16fa317dd54008b1257de88f0f54a7f9935ed2402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-01-30T14:20:51Z","title_canon_sha256":"08dd5af71ad1dedb135f6b588fa5fff56faf3dc7d42642988f9453c8be0a54a2"},"schema_version":"1.0","source":{"id":"2001.11840","kind":"arxiv","version":1}},"canonical_sha256":"afc902f9e9284a278ff26d0bd5bb1cc273cc14748c683e05504ab594f16a5711","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afc902f9e9284a278ff26d0bd5bb1cc273cc14748c683e05504ab594f16a5711","first_computed_at":"2026-07-05T00:37:34.279295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:34.279295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nmvt+8H9uUAfDaGDnJvw6NsJnDKgtkIyMevPD97sFL+NNnw6HYoNTmQVCexhzUZ2e3dIUzsclHfHHKCmOkbFBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:34.279725Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.11840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a2601cd1ebc8d10b79ec694bc4c2a6882686f2d588860f25bba66f7e4d62a2","sha256:37704359bfdc32b9359026455de7539cd381c18e458b3b281a80d66341fe8519"],"state_sha256":"ac9be9b1f18bbb9a711648196827ef6c7609eb4dfc6f4bcc19e4aea99af9a146"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NOZOkaDXUlCyGwVBbH/YwgZJnUu9OCeXyCVDgZWA1ncPU6L+ZRlqmgp53nkr8pVTP1ImLiILHerbpyS5KpkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:50:26.824909Z","bundle_sha256":"53c7fd94226eb252d980387bcf7afe788b1191244a5e722d9e27519f0f1ba12f"}}