{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5GZKTMLBLZ3GKJVVLSQQEBNMJH","short_pith_number":"pith:5GZKTMLB","canonical_record":{"source":{"id":"1505.04152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T18:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"2d934491414075cdef6b095c795cda4ab6e1051a1771992f912bf20abb0e7668","abstract_canon_sha256":"b5c170c6c05dc44b29524d8a8d8bd6cb4b5a5ab3db144b43e8b2667cb6a6cdcc"},"schema_version":"1.0"},"canonical_sha256":"e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f","source":{"kind":"arxiv","id":"1505.04152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04152","created_at":"2026-05-18T02:09:39Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04152v1","created_at":"2026-05-18T02:09:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04152","created_at":"2026-05-18T02:09:39Z"},{"alias_kind":"pith_short_12","alias_value":"5GZKTMLBLZ3G","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GZKTMLBLZ3GKJVV","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GZKTMLB","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5GZKTMLBLZ3GKJVVLSQQEBNMJH","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T18:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"2d934491414075cdef6b095c795cda4ab6e1051a1771992f912bf20abb0e7668","abstract_canon_sha256":"b5c170c6c05dc44b29524d8a8d8bd6cb4b5a5ab3db144b43e8b2667cb6a6cdcc"},"schema_version":"1.0"},"canonical_sha256":"e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:39.924545Z","signature_b64":"m3NZUAnWYjS+WxH8OatnFSPY5BHabSGey7qQ3hHhfV0E7hXpFc4yI6aI0iwE0Csrjn1RpIJbCP2J3g2adJNpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f","last_reissued_at":"2026-05-18T02:09:39.923954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:39.923954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04152","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":"2026-05-18T02:09:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sAoUpwMl9nwjSkMPazoPUU00sajQ+CuBm5iJrDsiN0JL+PVTnZa8PxvvyY1UVeMDdLjJzKI6VUs4hSZ7mpTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:16:53.122162Z"},"content_sha256":"3b63486c23e5e7f4ae4488d716030947160c418787ef034718732b32aba0b8a9","schema_version":"1.0","event_id":"sha256:3b63486c23e5e7f4ae4488d716030947160c418787ef034718732b32aba0b8a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5GZKTMLBLZ3GKJVVLSQQEBNMJH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Micah Warren","submitted_at":"2015-05-15T18:42:51Z","abstract_excerpt":"Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary, we find that any entire solution of the fourth order Hamiltonian stationary equation with Lagrangian phase angle uniformly larger than the critical angle must be a quadratic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04152","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":"2026-05-18T02:09:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ErnC8GRynHBhhnDOex1dEmj2YQHbU81GwvJkH657Kn4UcMmHJLa99Tay/mtCKcXiyDTJWyTqBY9IOPtoKPs2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:16:53.122650Z"},"content_sha256":"07de68b2a675f5ca83849645cf5540357320e172070502e85a7d965da4c9a478","schema_version":"1.0","event_id":"sha256:07de68b2a675f5ca83849645cf5540357320e172070502e85a7d965da4c9a478"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH/bundle.json","state_url":"https://pith.science/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH/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":"2026-06-25T13:16:53Z","links":{"resolver":"https://pith.science/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH","bundle":"https://pith.science/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH/bundle.json","state":"https://pith.science/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GZKTMLBLZ3GKJVVLSQQEBNMJH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5GZKTMLBLZ3GKJVVLSQQEBNMJH","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":"b5c170c6c05dc44b29524d8a8d8bd6cb4b5a5ab3db144b43e8b2667cb6a6cdcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T18:42:51Z","title_canon_sha256":"2d934491414075cdef6b095c795cda4ab6e1051a1771992f912bf20abb0e7668"},"schema_version":"1.0","source":{"id":"1505.04152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04152","created_at":"2026-05-18T02:09:39Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04152v1","created_at":"2026-05-18T02:09:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04152","created_at":"2026-05-18T02:09:39Z"},{"alias_kind":"pith_short_12","alias_value":"5GZKTMLBLZ3G","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GZKTMLBLZ3GKJVV","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GZKTMLB","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:07de68b2a675f5ca83849645cf5540357320e172070502e85a7d965da4c9a478","target":"graph","created_at":"2026-05-18T02:09:39Z","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":"Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary, we find that any entire solution of the fourth order Hamiltonian stationary equation with Lagrangian phase angle uniformly larger than the critical angle must be a quadratic.","authors_text":"Micah Warren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T18:42:51Z","title":"A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04152","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":"sha256:3b63486c23e5e7f4ae4488d716030947160c418787ef034718732b32aba0b8a9","target":"record","created_at":"2026-05-18T02:09:39Z","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":"b5c170c6c05dc44b29524d8a8d8bd6cb4b5a5ab3db144b43e8b2667cb6a6cdcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-15T18:42:51Z","title_canon_sha256":"2d934491414075cdef6b095c795cda4ab6e1051a1771992f912bf20abb0e7668"},"schema_version":"1.0","source":{"id":"1505.04152","kind":"arxiv","version":1}},"canonical_sha256":"e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f","first_computed_at":"2026-05-18T02:09:39.923954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:39.923954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3NZUAnWYjS+WxH8OatnFSPY5BHabSGey7qQ3hHhfV0E7hXpFc4yI6aI0iwE0Csrjn1RpIJbCP2J3g2adJNpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:39.924545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b63486c23e5e7f4ae4488d716030947160c418787ef034718732b32aba0b8a9","sha256:07de68b2a675f5ca83849645cf5540357320e172070502e85a7d965da4c9a478"],"state_sha256":"30c45dea720d8549978bf1fd980eadbf4928762a4ee6c4baddeec93cd371c7f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lz/1q/KCT9VDUEugsv9komAvXVQDC8ttADVZAivba5YYKhnDCroy1Fat+XtIq2wMiKptDBcu1jEwAXV/aMh5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:16:53.125326Z","bundle_sha256":"f7529cbab38ff6a9fa6c1f0d4a2acf6267c888e76dc7780c0a0e1c9cc403d537"}}