{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UUNRIXGDBDJLYJZBLXXLSVS7P5","short_pith_number":"pith:UUNRIXGD","canonical_record":{"source":{"id":"1805.05028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-14T07:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"5ae801902d2f5ef131b60dd1b24f77ace4afbbf6178226da8503a7a575ca3184","abstract_canon_sha256":"9c0b053a0172e12a3da5f255cdff746bb0393d5fef9f48f6df86d4f7cb4aa069"},"schema_version":"1.0"},"canonical_sha256":"a51b145cc308d2bc27215deeb9565f7f5f709f289fed56b4578a6c872318e1b5","source":{"kind":"arxiv","id":"1805.05028","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05028","created_at":"2026-05-18T00:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05028v1","created_at":"2026-05-18T00:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05028","created_at":"2026-05-18T00:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"UUNRIXGDBDJL","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUNRIXGDBDJLYJZB","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUNRIXGD","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UUNRIXGDBDJLYJZBLXXLSVS7P5","target":"record","payload":{"canonical_record":{"source":{"id":"1805.05028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-14T07:06:58Z","cross_cats_sorted":[],"title_canon_sha256":"5ae801902d2f5ef131b60dd1b24f77ace4afbbf6178226da8503a7a575ca3184","abstract_canon_sha256":"9c0b053a0172e12a3da5f255cdff746bb0393d5fef9f48f6df86d4f7cb4aa069"},"schema_version":"1.0"},"canonical_sha256":"a51b145cc308d2bc27215deeb9565f7f5f709f289fed56b4578a6c872318e1b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:04.029485Z","signature_b64":"h5JILn70OqN6Wnf+9kThYcdIJ+RTn5Ue+dxvdnzk5FJoAmSzA0hiWzt8moCdZ/sb/i+nkds7NHznAxjCZp/pCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a51b145cc308d2bc27215deeb9565f7f5f709f289fed56b4578a6c872318e1b5","last_reissued_at":"2026-05-18T00:16:04.029057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:04.029057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.05028","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":"2026-05-18T00:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAZDxgGS2zvz2E3fCMRcp+UqpOV86Grw0drG2V0/+xiReder/pvpVtueov4B9YxLlb2k/b0u2nwwxq/jt2QmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:26:38.471191Z"},"content_sha256":"ac36d790c2cf500e11c87e1f35af44a68a2c41da6eca991ffed4848c82dae879","schema_version":"1.0","event_id":"sha256:ac36d790c2cf500e11c87e1f35af44a68a2c41da6eca991ffed4848c82dae879"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UUNRIXGDBDJLYJZBLXXLSVS7P5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Monge-Amp\\`ere equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli","submitted_at":"2018-05-14T07:06:58Z","abstract_excerpt":"This text contains the material discussed by the author in the Bourbaki seminar of June 2018, on the recent developments in the theory of the Monge-Amp\\`ere equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05028","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":"2026-05-18T00:16:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vQ8mpugMa436CZ6S7tjbVgihKG4FnMTESO5xBKVvCsBJRB8KZuwdkNvQyQZHZi6QLga45AujpTA2FHShmeYcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:26:38.471557Z"},"content_sha256":"da45367ff6ccb65ab357558e1fabb6803c65f6ca0824b8c81548b9cab10e4a22","schema_version":"1.0","event_id":"sha256:da45367ff6ccb65ab357558e1fabb6803c65f6ca0824b8c81548b9cab10e4a22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5/bundle.json","state_url":"https://pith.science/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5/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":"2026-06-05T09:26:38Z","links":{"resolver":"https://pith.science/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5","bundle":"https://pith.science/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5/bundle.json","state":"https://pith.science/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UUNRIXGDBDJLYJZBLXXLSVS7P5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UUNRIXGDBDJLYJZBLXXLSVS7P5","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":"9c0b053a0172e12a3da5f255cdff746bb0393d5fef9f48f6df86d4f7cb4aa069","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-14T07:06:58Z","title_canon_sha256":"5ae801902d2f5ef131b60dd1b24f77ace4afbbf6178226da8503a7a575ca3184"},"schema_version":"1.0","source":{"id":"1805.05028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05028","created_at":"2026-05-18T00:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05028v1","created_at":"2026-05-18T00:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05028","created_at":"2026-05-18T00:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"UUNRIXGDBDJL","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUNRIXGDBDJLYJZB","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUNRIXGD","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:da45367ff6ccb65ab357558e1fabb6803c65f6ca0824b8c81548b9cab10e4a22","target":"graph","created_at":"2026-05-18T00:16:04Z","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":"This text contains the material discussed by the author in the Bourbaki seminar of June 2018, on the recent developments in the theory of the Monge-Amp\\`ere equation.","authors_text":"Alessio Figalli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-14T07:06:58Z","title":"On the Monge-Amp\\`ere equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05028","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:ac36d790c2cf500e11c87e1f35af44a68a2c41da6eca991ffed4848c82dae879","target":"record","created_at":"2026-05-18T00:16:04Z","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":"9c0b053a0172e12a3da5f255cdff746bb0393d5fef9f48f6df86d4f7cb4aa069","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-14T07:06:58Z","title_canon_sha256":"5ae801902d2f5ef131b60dd1b24f77ace4afbbf6178226da8503a7a575ca3184"},"schema_version":"1.0","source":{"id":"1805.05028","kind":"arxiv","version":1}},"canonical_sha256":"a51b145cc308d2bc27215deeb9565f7f5f709f289fed56b4578a6c872318e1b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a51b145cc308d2bc27215deeb9565f7f5f709f289fed56b4578a6c872318e1b5","first_computed_at":"2026-05-18T00:16:04.029057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:04.029057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h5JILn70OqN6Wnf+9kThYcdIJ+RTn5Ue+dxvdnzk5FJoAmSzA0hiWzt8moCdZ/sb/i+nkds7NHznAxjCZp/pCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:04.029485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac36d790c2cf500e11c87e1f35af44a68a2c41da6eca991ffed4848c82dae879","sha256:da45367ff6ccb65ab357558e1fabb6803c65f6ca0824b8c81548b9cab10e4a22"],"state_sha256":"849a0abb7511212f52f45286644300743114b3029201fc1ccd96577d883c7972"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qopiSHDzxYcJvXS1px1kkE6ZU+tj1nlzauxXIRD+vK527huypA+Nse6fHXycUVbZajlnn0xfpcr8H3mK4w9LBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:26:38.473538Z","bundle_sha256":"4bee7346968ad07d7bcb5bdb099817fc22baf8e2d8034c9f22c6048891e269e6"}}