{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NB6G6GJRPMAAX4HRZJOXFPBYQ2","short_pith_number":"pith:NB6G6GJR","canonical_record":{"source":{"id":"1309.1135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-04T18:51:59Z","cross_cats_sorted":[],"title_canon_sha256":"8ed6b989edc32562d5e19b89279fc7bb7f0f02f5ba90c2c884dd421bc58e6ee5","abstract_canon_sha256":"851410157e259ed4195eb1c996d374fa0a12ab7fc29e1d663bad137a263fb95e"},"schema_version":"1.0"},"canonical_sha256":"687c6f19317b000bf0f1ca5d72bc38868ba8873d8f03c712246177dec337607f","source":{"kind":"arxiv","id":"1309.1135","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1135","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1135v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1135","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"NB6G6GJRPMAA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NB6G6GJRPMAAX4HR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NB6G6GJR","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NB6G6GJRPMAAX4HRZJOXFPBYQ2","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-04T18:51:59Z","cross_cats_sorted":[],"title_canon_sha256":"8ed6b989edc32562d5e19b89279fc7bb7f0f02f5ba90c2c884dd421bc58e6ee5","abstract_canon_sha256":"851410157e259ed4195eb1c996d374fa0a12ab7fc29e1d663bad137a263fb95e"},"schema_version":"1.0"},"canonical_sha256":"687c6f19317b000bf0f1ca5d72bc38868ba8873d8f03c712246177dec337607f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:09.014647Z","signature_b64":"e4RoJozgOyaQ9PmBi0KTp1TMLSxIBHnO0Z5OQcusRPE1dbpkKxFgEt7z9P9nCx9U5O5WZw6UpxoJnvIftlSsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"687c6f19317b000bf0f1ca5d72bc38868ba8873d8f03c712246177dec337607f","last_reissued_at":"2026-05-18T03:14:09.014042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:09.014042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1135","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":"2026-05-18T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nuezhTbAWEu6REgZEhL/z1R5NMolWKgt8MC2O4w3LGtTzbEhQ8vRXI//274PsVlivECJ8tsiD0eyiFbwPRIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:57:07.240517Z"},"content_sha256":"0396a23e0a1ab470b64d9f69deecfc05a1dcd14aba29cb01932967f3f8a624bf","schema_version":"1.0","event_id":"sha256:0396a23e0a1ab470b64d9f69deecfc05a1dcd14aba29cb01932967f3f8a624bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NB6G6GJRPMAAX4HRZJOXFPBYQ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Harnack-Type Inequality for a Prescribing Curvature equation on a Domain with Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lei Zhang, Mathew Gluck, Ying Guo","submitted_at":"2013-09-04T18:51:59Z","abstract_excerpt":"In this paper we consider a class of prescribing curvature type equations on half Euclidean balls. Under suitable assumptions on the scalar curvature function and boundary mean curvature function we prove a min-max type inequality and the corresponding energy estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1135","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":"2026-05-18T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFYolXivsBP8efwNWFH4twvgBmOva0PetxDFsbttDgvec335KAwVGAeGddpBZUxwBQQY5KyC6OQvH/7KIZguAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:57:07.240864Z"},"content_sha256":"6d5ad61727bf77bfce35a38b21b1dcf13dd15777cabe570c92a95ebf45e5af85","schema_version":"1.0","event_id":"sha256:6d5ad61727bf77bfce35a38b21b1dcf13dd15777cabe570c92a95ebf45e5af85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2/bundle.json","state_url":"https://pith.science/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2/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":"2026-06-08T12:57:07Z","links":{"resolver":"https://pith.science/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2","bundle":"https://pith.science/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2/bundle.json","state":"https://pith.science/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NB6G6GJRPMAAX4HRZJOXFPBYQ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NB6G6GJRPMAAX4HRZJOXFPBYQ2","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":"851410157e259ed4195eb1c996d374fa0a12ab7fc29e1d663bad137a263fb95e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-04T18:51:59Z","title_canon_sha256":"8ed6b989edc32562d5e19b89279fc7bb7f0f02f5ba90c2c884dd421bc58e6ee5"},"schema_version":"1.0","source":{"id":"1309.1135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1135","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1135v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1135","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"NB6G6GJRPMAA","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NB6G6GJRPMAAX4HR","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NB6G6GJR","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:6d5ad61727bf77bfce35a38b21b1dcf13dd15777cabe570c92a95ebf45e5af85","target":"graph","created_at":"2026-05-18T03:14:09Z","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 consider a class of prescribing curvature type equations on half Euclidean balls. Under suitable assumptions on the scalar curvature function and boundary mean curvature function we prove a min-max type inequality and the corresponding energy estimates.","authors_text":"Lei Zhang, Mathew Gluck, Ying Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-04T18:51:59Z","title":"A Harnack-Type Inequality for a Prescribing Curvature equation on a Domain with Boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1135","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":"sha256:0396a23e0a1ab470b64d9f69deecfc05a1dcd14aba29cb01932967f3f8a624bf","target":"record","created_at":"2026-05-18T03:14:09Z","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":"851410157e259ed4195eb1c996d374fa0a12ab7fc29e1d663bad137a263fb95e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-04T18:51:59Z","title_canon_sha256":"8ed6b989edc32562d5e19b89279fc7bb7f0f02f5ba90c2c884dd421bc58e6ee5"},"schema_version":"1.0","source":{"id":"1309.1135","kind":"arxiv","version":1}},"canonical_sha256":"687c6f19317b000bf0f1ca5d72bc38868ba8873d8f03c712246177dec337607f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"687c6f19317b000bf0f1ca5d72bc38868ba8873d8f03c712246177dec337607f","first_computed_at":"2026-05-18T03:14:09.014042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:09.014042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4RoJozgOyaQ9PmBi0KTp1TMLSxIBHnO0Z5OQcusRPE1dbpkKxFgEt7z9P9nCx9U5O5WZw6UpxoJnvIftlSsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:09.014647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0396a23e0a1ab470b64d9f69deecfc05a1dcd14aba29cb01932967f3f8a624bf","sha256:6d5ad61727bf77bfce35a38b21b1dcf13dd15777cabe570c92a95ebf45e5af85"],"state_sha256":"ea4fd6bb602c00ff7949db86fe2912ebad542798f946502a93a79a0e7d853941"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rRDB7BMAVQMAErBuu/krwu4Qy68htX7IRBo5y4XHenNWFsyX1likLKTnVGbnbUJrBhiwgQ4JS89ALaLfKttwCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:57:07.242732Z","bundle_sha256":"e716036f06773a0055536da011bd16423624319eade8e166293d1a480ea0e169"}}