{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DS4ZWSLMYQADEGO6KM3PQTTCJ2","short_pith_number":"pith:DS4ZWSLM","canonical_record":{"source":{"id":"1601.02552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-11T18:36:26Z","cross_cats_sorted":[],"title_canon_sha256":"6b376bcfeb9c0d6dc1e970f565fd6c1523cf02feffa10cad1b9062fd3e12831f","abstract_canon_sha256":"87bb53477be4840074fa3f0d76398c2292575d832ce9cbbdefcc4fa64969a6b2"},"schema_version":"1.0"},"canonical_sha256":"1cb99b496cc4003219de5336f84e624ea8acda5ee1de7f4376413358e1aba08c","source":{"kind":"arxiv","id":"1601.02552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02552","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02552v1","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02552","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"DS4ZWSLMYQAD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS4ZWSLMYQADEGO6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS4ZWSLM","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DS4ZWSLMYQADEGO6KM3PQTTCJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-11T18:36:26Z","cross_cats_sorted":[],"title_canon_sha256":"6b376bcfeb9c0d6dc1e970f565fd6c1523cf02feffa10cad1b9062fd3e12831f","abstract_canon_sha256":"87bb53477be4840074fa3f0d76398c2292575d832ce9cbbdefcc4fa64969a6b2"},"schema_version":"1.0"},"canonical_sha256":"1cb99b496cc4003219de5336f84e624ea8acda5ee1de7f4376413358e1aba08c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:04.854108Z","signature_b64":"l1/qKLLr/yKJ22ZSc4KlM1BNC1uTleXoc5YiUBxtKKPIzRReitBJB6DjsmR3wHft3N5j77Fdc05A7y0f1n2yCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb99b496cc4003219de5336f84e624ea8acda5ee1de7f4376413358e1aba08c","last_reissued_at":"2026-05-18T01:23:04.853555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:04.853555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02552","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":"2026-05-18T01:23:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IoByJ5lLXWNxsls2qNwSgAL1JP/jd3LiPnsXtnC3+ZxEwMqyWt1Yld0JbFs3LVFvT5SqLO2QNqh2UPzwl7UkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:02:06.934607Z"},"content_sha256":"381fb2f77b8335c0ee6487163fd7699b6d8424708a9d598345b313f5e7519457","schema_version":"1.0","event_id":"sha256:381fb2f77b8335c0ee6487163fd7699b6d8424708a9d598345b313f5e7519457"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DS4ZWSLMYQADEGO6KM3PQTTCJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a variational problem related to NLS on Hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chenjie Fan, Peter Kleinhenz","submitted_at":"2016-01-11T18:36:26Z","abstract_excerpt":"Motivated by NLS, We study a variational problem on hyperbolic space. In particular, we compute its minimum value and we show the minimizer does not exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02552","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":"2026-05-18T01:23:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OI8uIVoVLBWxAsBJ5YVXWUEP7Zv+/B4dLX73R/bogo6iOHZR6IqCv3XjYtPXWLmNVZibjPvoXo6+1OmZ9xXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:02:06.935242Z"},"content_sha256":"4631480b4593fe3f55ad6d8c9f1bdce91d7d060a621d5d431b47bee6f3283b92","schema_version":"1.0","event_id":"sha256:4631480b4593fe3f55ad6d8c9f1bdce91d7d060a621d5d431b47bee6f3283b92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2/bundle.json","state_url":"https://pith.science/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2/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":"2026-06-08T17:02:06Z","links":{"resolver":"https://pith.science/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2","bundle":"https://pith.science/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2/bundle.json","state":"https://pith.science/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS4ZWSLMYQADEGO6KM3PQTTCJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DS4ZWSLMYQADEGO6KM3PQTTCJ2","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":"87bb53477be4840074fa3f0d76398c2292575d832ce9cbbdefcc4fa64969a6b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-11T18:36:26Z","title_canon_sha256":"6b376bcfeb9c0d6dc1e970f565fd6c1523cf02feffa10cad1b9062fd3e12831f"},"schema_version":"1.0","source":{"id":"1601.02552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02552","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02552v1","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02552","created_at":"2026-05-18T01:23:04Z"},{"alias_kind":"pith_short_12","alias_value":"DS4ZWSLMYQAD","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DS4ZWSLMYQADEGO6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DS4ZWSLM","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:4631480b4593fe3f55ad6d8c9f1bdce91d7d060a621d5d431b47bee6f3283b92","target":"graph","created_at":"2026-05-18T01:23:04Z","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":"Motivated by NLS, We study a variational problem on hyperbolic space. In particular, we compute its minimum value and we show the minimizer does not exist","authors_text":"Chenjie Fan, Peter Kleinhenz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-11T18:36:26Z","title":"On a variational problem related to NLS on Hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02552","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":"sha256:381fb2f77b8335c0ee6487163fd7699b6d8424708a9d598345b313f5e7519457","target":"record","created_at":"2026-05-18T01:23:04Z","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":"87bb53477be4840074fa3f0d76398c2292575d832ce9cbbdefcc4fa64969a6b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-11T18:36:26Z","title_canon_sha256":"6b376bcfeb9c0d6dc1e970f565fd6c1523cf02feffa10cad1b9062fd3e12831f"},"schema_version":"1.0","source":{"id":"1601.02552","kind":"arxiv","version":1}},"canonical_sha256":"1cb99b496cc4003219de5336f84e624ea8acda5ee1de7f4376413358e1aba08c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cb99b496cc4003219de5336f84e624ea8acda5ee1de7f4376413358e1aba08c","first_computed_at":"2026-05-18T01:23:04.853555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:04.853555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l1/qKLLr/yKJ22ZSc4KlM1BNC1uTleXoc5YiUBxtKKPIzRReitBJB6DjsmR3wHft3N5j77Fdc05A7y0f1n2yCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:04.854108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:381fb2f77b8335c0ee6487163fd7699b6d8424708a9d598345b313f5e7519457","sha256:4631480b4593fe3f55ad6d8c9f1bdce91d7d060a621d5d431b47bee6f3283b92"],"state_sha256":"bd4809968095a9c97b2bb6b53296543f07651a398858b1052a6459a6be5d1f98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4/7TznF+h2nPRjyo6I2TF7LWzH93WHD+OsQ8mqeI8GR+b513DJwhxQtDuxkw2GWlkRb+6oLTef3fxxvs5HaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:02:06.939243Z","bundle_sha256":"d55143643c81a59b906551b84d98edfd448cb3cd55271258c52b51e0a3a4155f"}}