{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7XUGDG2QYAWJFXS2KJ4UQCETAI","short_pith_number":"pith:7XUGDG2Q","canonical_record":{"source":{"id":"1703.05254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-15T16:55:22Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"387f8f369b962c4c79e9d3d780b06e0706952bca6e1cebae5246d9c595f1e1e9","abstract_canon_sha256":"440d037687a9c4f301f29b9d65855c19889bd83b9bc93fda95de8dc1cdce5a66"},"schema_version":"1.0"},"canonical_sha256":"fde8619b50c02c92de5a5279480893023c2f6248ffa14c098b016def56b938b8","source":{"kind":"arxiv","id":"1703.05254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05254","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05254v1","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05254","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"7XUGDG2QYAWJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7XUGDG2QYAWJFXS2","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7XUGDG2Q","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7XUGDG2QYAWJFXS2KJ4UQCETAI","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-15T16:55:22Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"387f8f369b962c4c79e9d3d780b06e0706952bca6e1cebae5246d9c595f1e1e9","abstract_canon_sha256":"440d037687a9c4f301f29b9d65855c19889bd83b9bc93fda95de8dc1cdce5a66"},"schema_version":"1.0"},"canonical_sha256":"fde8619b50c02c92de5a5279480893023c2f6248ffa14c098b016def56b938b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:34.679590Z","signature_b64":"kb4yC0hUG6q4XQKiyc1DkLoUVOOfqRvUDj/T0CEXEUwYazPBLfh4IoIw4O/cpTQ+TtLrqCqAOkW8NIStGOM8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fde8619b50c02c92de5a5279480893023c2f6248ffa14c098b016def56b938b8","last_reissued_at":"2026-05-18T00:48:34.678925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:34.678925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05254","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":"2026-05-18T00:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"65qfhpuco+O0QAiKJGy4Hs+KjLwjIlyOuIriIWqODPTNCoaUFwz5D9FeuLMmIxZEGg4Xeeyh8hxTu0qjQWMiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:20:44.696233Z"},"content_sha256":"2647e189076bad3899b948e0e79794bf3a5f294b223c76859cbcd8b0b19d27bc","schema_version":"1.0","event_id":"sha256:2647e189076bad3899b948e0e79794bf3a5f294b223c76859cbcd8b0b19d27bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7XUGDG2QYAWJFXS2KJ4UQCETAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Plurisubharmonic envelopes and supersolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Ahmed Zeriahi, Chinh H. Lu, Vincent Guedj","submitted_at":"2017-03-15T16:55:22Z","abstract_excerpt":"We make a systematic study of (quasi-)plurisubharmonic envelopes on compact K\\\"ahler manifolds, as well as on domains of $\\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Amp\\`ere equation. We use these ideas to solve complex Monge-Amp\\`ere equations by taking lower envelopes of super-solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05254","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":"2026-05-18T00:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eW7+tFqSjZYTpDnawB2UQnm7RC6DRM2CAkbDlQWUUWkpU1apS7sd0M6BArHG6y6wii6BX/E68oP9pREieB+XDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:20:44.696938Z"},"content_sha256":"fcce14b92db6a0faed034e2e4c2632773f6836fac98351837b000271ca3ef328","schema_version":"1.0","event_id":"sha256:fcce14b92db6a0faed034e2e4c2632773f6836fac98351837b000271ca3ef328"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI/bundle.json","state_url":"https://pith.science/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI/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":"2026-05-26T08:20:44Z","links":{"resolver":"https://pith.science/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI","bundle":"https://pith.science/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI/bundle.json","state":"https://pith.science/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XUGDG2QYAWJFXS2KJ4UQCETAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7XUGDG2QYAWJFXS2KJ4UQCETAI","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":"440d037687a9c4f301f29b9d65855c19889bd83b9bc93fda95de8dc1cdce5a66","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-15T16:55:22Z","title_canon_sha256":"387f8f369b962c4c79e9d3d780b06e0706952bca6e1cebae5246d9c595f1e1e9"},"schema_version":"1.0","source":{"id":"1703.05254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05254","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05254v1","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05254","created_at":"2026-05-18T00:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"7XUGDG2QYAWJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7XUGDG2QYAWJFXS2","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7XUGDG2Q","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:fcce14b92db6a0faed034e2e4c2632773f6836fac98351837b000271ca3ef328","target":"graph","created_at":"2026-05-18T00:48:34Z","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"},"paper":{"abstract_excerpt":"We make a systematic study of (quasi-)plurisubharmonic envelopes on compact K\\\"ahler manifolds, as well as on domains of $\\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Amp\\`ere equation. We use these ideas to solve complex Monge-Amp\\`ere equations by taking lower envelopes of super-solutions.","authors_text":"Ahmed Zeriahi, Chinh H. Lu, Vincent Guedj","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-15T16:55:22Z","title":"Plurisubharmonic envelopes and supersolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05254","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":"sha256:2647e189076bad3899b948e0e79794bf3a5f294b223c76859cbcd8b0b19d27bc","target":"record","created_at":"2026-05-18T00:48:34Z","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":"440d037687a9c4f301f29b9d65855c19889bd83b9bc93fda95de8dc1cdce5a66","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-15T16:55:22Z","title_canon_sha256":"387f8f369b962c4c79e9d3d780b06e0706952bca6e1cebae5246d9c595f1e1e9"},"schema_version":"1.0","source":{"id":"1703.05254","kind":"arxiv","version":1}},"canonical_sha256":"fde8619b50c02c92de5a5279480893023c2f6248ffa14c098b016def56b938b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fde8619b50c02c92de5a5279480893023c2f6248ffa14c098b016def56b938b8","first_computed_at":"2026-05-18T00:48:34.678925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:34.678925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kb4yC0hUG6q4XQKiyc1DkLoUVOOfqRvUDj/T0CEXEUwYazPBLfh4IoIw4O/cpTQ+TtLrqCqAOkW8NIStGOM8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:34.679590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2647e189076bad3899b948e0e79794bf3a5f294b223c76859cbcd8b0b19d27bc","sha256:fcce14b92db6a0faed034e2e4c2632773f6836fac98351837b000271ca3ef328"],"state_sha256":"616c6c3479e93d25eda794bba671ce190da90664676fdb49c8fb295b23058774"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aMm2lnRc8xUq7Fr+COJLhKccp8P4xDCwn6nQ5d/i1UyV+X1FrFtlnuWHuOaud8qZ8iCA05N5YgqaASs09kKQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:20:44.700680Z","bundle_sha256":"d01bf4beede2c0caed2343c65c5d30b73487e136c4af27dc78f4321115727772"}}