{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:I22PWVN3G2IV7SPLJ7PSDA6CYJ","short_pith_number":"pith:I22PWVN3","canonical_record":{"source":{"id":"2010.03545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-10-07T17:47:41Z","cross_cats_sorted":[],"title_canon_sha256":"5a83e7ce5d27183e9a45bab95f7eb70ffcaa51c57f49d3f30022902085153ba0","abstract_canon_sha256":"049f958c47c919ccbd1aeda6754c3bbefae3929b0102650ff792627571de182d"},"schema_version":"1.0"},"canonical_sha256":"46b4fb55bb36915fc9eb4fdf2183c2c26fd9072f99209a07fcb98119a07c5578","source":{"kind":"arxiv","id":"2010.03545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.03545","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"2010.03545v1","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.03545","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"I22PWVN3G2IV","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"pith_short_16","alias_value":"I22PWVN3G2IV7SPL","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"pith_short_8","alias_value":"I22PWVN3","created_at":"2026-07-05T01:41:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:I22PWVN3G2IV7SPLJ7PSDA6CYJ","target":"record","payload":{"canonical_record":{"source":{"id":"2010.03545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-10-07T17:47:41Z","cross_cats_sorted":[],"title_canon_sha256":"5a83e7ce5d27183e9a45bab95f7eb70ffcaa51c57f49d3f30022902085153ba0","abstract_canon_sha256":"049f958c47c919ccbd1aeda6754c3bbefae3929b0102650ff792627571de182d"},"schema_version":"1.0"},"canonical_sha256":"46b4fb55bb36915fc9eb4fdf2183c2c26fd9072f99209a07fcb98119a07c5578","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:41:13.922875Z","signature_b64":"sDDuUsquY2mcA9F6Q1KlL2uotxLxRYNapvAnJMIuHgG6pojg2E6bc7ZVro+7vpIbEViAXWIh89zPaLbPdtNcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b4fb55bb36915fc9eb4fdf2183c2c26fd9072f99209a07fcb98119a07c5578","last_reissued_at":"2026-07-05T01:41:13.922538Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:41:13.922538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.03545","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":"2026-07-05T01:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TapGNotCceiScOB6CgOKpV9h+HGavOimGbRmuFiSxz6aD+0FBmUgGzRmCCEG+kZCoP+8c7b1lGO2AmX9WDPaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:30.485468Z"},"content_sha256":"1eeb9d0d91b3b1b19fc81320100bc6921c369310267dfe70ce30797922186a24","schema_version":"1.0","event_id":"sha256:1eeb9d0d91b3b1b19fc81320100bc6921c369310267dfe70ce30797922186a24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:I22PWVN3G2IV7SPLJ7PSDA6CYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic maps from K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Brice Loustau","submitted_at":"2020-10-07T17:47:41Z","abstract_excerpt":"This report attempts a clean presentation of the theory of harmonic maps from complex and K\\\"ahler manifolds to Riemannian manifolds. After reviewing the theory of harmonic maps between Riemannian manifolds initiated by Eells--Sampson and the Bochner technique, we specialize to K\\\"ahler domains and introduce pluriharmonic maps. We prove a refined Bochner formula due to Siu and Sampson and its main consequences, such as the strong rigidity results of Siu. We also recount the applications to symmetric spaces of noncompact type and their relation to Mostow rigidity. Finally, we explain the key ro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.03545","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.03545/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:41:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z6PbkcE5fN1EF3u3p+CRPabPEuBYrkVBUDN7Px/zNqGaWStvjiLhJi80/f99QQ0hoai/5Tjf05LLd6/BoXgMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:30.486470Z"},"content_sha256":"510abbf5e0f243203d09867567cc0618db86dc1892b66ee4690475476093b474","schema_version":"1.0","event_id":"sha256:510abbf5e0f243203d09867567cc0618db86dc1892b66ee4690475476093b474"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ/bundle.json","state_url":"https://pith.science/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ/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":"2026-08-08T12:31:30Z","links":{"resolver":"https://pith.science/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ","bundle":"https://pith.science/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ/bundle.json","state":"https://pith.science/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I22PWVN3G2IV7SPLJ7PSDA6CYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:I22PWVN3G2IV7SPLJ7PSDA6CYJ","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":"049f958c47c919ccbd1aeda6754c3bbefae3929b0102650ff792627571de182d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-10-07T17:47:41Z","title_canon_sha256":"5a83e7ce5d27183e9a45bab95f7eb70ffcaa51c57f49d3f30022902085153ba0"},"schema_version":"1.0","source":{"id":"2010.03545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.03545","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"2010.03545v1","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.03545","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"I22PWVN3G2IV","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"pith_short_16","alias_value":"I22PWVN3G2IV7SPL","created_at":"2026-07-05T01:41:13Z"},{"alias_kind":"pith_short_8","alias_value":"I22PWVN3","created_at":"2026-07-05T01:41:13Z"}],"graph_snapshots":[{"event_id":"sha256:510abbf5e0f243203d09867567cc0618db86dc1892b66ee4690475476093b474","target":"graph","created_at":"2026-07-05T01:41:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.03545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This report attempts a clean presentation of the theory of harmonic maps from complex and K\\\"ahler manifolds to Riemannian manifolds. After reviewing the theory of harmonic maps between Riemannian manifolds initiated by Eells--Sampson and the Bochner technique, we specialize to K\\\"ahler domains and introduce pluriharmonic maps. We prove a refined Bochner formula due to Siu and Sampson and its main consequences, such as the strong rigidity results of Siu. We also recount the applications to symmetric spaces of noncompact type and their relation to Mostow rigidity. Finally, we explain the key ro","authors_text":"Brice Loustau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-10-07T17:47:41Z","title":"Harmonic maps from K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.03545","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":"sha256:1eeb9d0d91b3b1b19fc81320100bc6921c369310267dfe70ce30797922186a24","target":"record","created_at":"2026-07-05T01:41:13Z","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":"049f958c47c919ccbd1aeda6754c3bbefae3929b0102650ff792627571de182d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-10-07T17:47:41Z","title_canon_sha256":"5a83e7ce5d27183e9a45bab95f7eb70ffcaa51c57f49d3f30022902085153ba0"},"schema_version":"1.0","source":{"id":"2010.03545","kind":"arxiv","version":1}},"canonical_sha256":"46b4fb55bb36915fc9eb4fdf2183c2c26fd9072f99209a07fcb98119a07c5578","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46b4fb55bb36915fc9eb4fdf2183c2c26fd9072f99209a07fcb98119a07c5578","first_computed_at":"2026-07-05T01:41:13.922538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:41:13.922538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sDDuUsquY2mcA9F6Q1KlL2uotxLxRYNapvAnJMIuHgG6pojg2E6bc7ZVro+7vpIbEViAXWIh89zPaLbPdtNcAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:41:13.922875Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.03545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eeb9d0d91b3b1b19fc81320100bc6921c369310267dfe70ce30797922186a24","sha256:510abbf5e0f243203d09867567cc0618db86dc1892b66ee4690475476093b474"],"state_sha256":"4cff60baa2dd9625c7889fe62a8217c9839a197fcc8d254d4a5daafac7fa3f8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w6eC0zF9yylMZbbouCjfMcmlcgnj8cZWUcorLzmE4Uqp4PA8QH02BEIuixcW0tB0S8hkkIywiXG9j5CDQGMfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:31:30.495007Z","bundle_sha256":"1ff13bdc2a77cfa98f5cc94db918a78ace31dd6490fef1962a706a95a6c076d0"}}