{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ST2XV4IMIWCID34ASKH3MVOWRP","short_pith_number":"pith:ST2XV4IM","canonical_record":{"source":{"id":"1011.6016","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-28T07:43:23Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b93e3391608d59d6246d708011e70e1ac278737b64dd35f4fb1dd06c3fd77d4f","abstract_canon_sha256":"160976e480f862d8ab9174fda36a7179c52ce91d0f92eef1322c603c0d171abd"},"schema_version":"1.0"},"canonical_sha256":"94f57af10c458481ef80928fb655d68bcdcff6786a0da9bff70f0b636a46f337","source":{"kind":"arxiv","id":"1011.6016","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6016","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6016v2","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6016","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"ST2XV4IMIWCI","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"ST2XV4IMIWCID34A","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"ST2XV4IM","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ST2XV4IMIWCID34ASKH3MVOWRP","target":"record","payload":{"canonical_record":{"source":{"id":"1011.6016","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-28T07:43:23Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"b93e3391608d59d6246d708011e70e1ac278737b64dd35f4fb1dd06c3fd77d4f","abstract_canon_sha256":"160976e480f862d8ab9174fda36a7179c52ce91d0f92eef1322c603c0d171abd"},"schema_version":"1.0"},"canonical_sha256":"94f57af10c458481ef80928fb655d68bcdcff6786a0da9bff70f0b636a46f337","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:01.426467Z","signature_b64":"FlUEt8SR4HZm44gHY2FvHiSuoZG/euh3iKgmUZJk9y7iH/VWDgsTGh1avQ2yTV3tfgg/Q/qkuR+23+HblgGSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94f57af10c458481ef80928fb655d68bcdcff6786a0da9bff70f0b636a46f337","last_reissued_at":"2026-05-18T02:58:01.425985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:01.425985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.6016","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrEgdysR39hri316nqabuYVgvIQCBod+fj3UvPdWoJwsn/N6b892dk7/NxmNs2R0gni2XHkytvUTxWrdpRMIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:05:17.134927Z"},"content_sha256":"fde1a587ae81d40a6a8d37d669704e477e9557ba296a36f297671eb33898b9e2","schema_version":"1.0","event_id":"sha256:fde1a587ae81d40a6a8d37d669704e477e9557ba296a36f297671eb33898b9e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ST2XV4IMIWCID34ASKH3MVOWRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity Formulae and Holomorphicity of Harmonic Maps between K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Yuxin Dong","submitted_at":"2010-11-28T07:43:23Z","abstract_excerpt":"In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E\"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to establish some monotonicity formulae of the partial energies of pluriharmonic maps into any Kaehler manifolds and harmonic maps into Kaehler manifolds with strongly semi-negative curvature respectively. These monotonicity inequalities enable us to derive some holomorphicity and Liouville type results for these pluriharmonic maps and harmonic maps. We also use t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6016","kind":"arxiv","version":2},"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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lLUH4BGDdCJvHv7pJoDv6G+FnViLn3Hd4kgc8yY6J3sU4ZkVTKXk83CQLTSKyaXz7b0ziujrs2U27zeBQ2mrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:05:17.135690Z"},"content_sha256":"9d5e80432a30e633e7f6a37a87f7fd1cd9f9ce2302eb88a9708bebef41706fd3","schema_version":"1.0","event_id":"sha256:9d5e80432a30e633e7f6a37a87f7fd1cd9f9ce2302eb88a9708bebef41706fd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ST2XV4IMIWCID34ASKH3MVOWRP/bundle.json","state_url":"https://pith.science/pith/ST2XV4IMIWCID34ASKH3MVOWRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ST2XV4IMIWCID34ASKH3MVOWRP/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":"2026-06-06T15:05:17Z","links":{"resolver":"https://pith.science/pith/ST2XV4IMIWCID34ASKH3MVOWRP","bundle":"https://pith.science/pith/ST2XV4IMIWCID34ASKH3MVOWRP/bundle.json","state":"https://pith.science/pith/ST2XV4IMIWCID34ASKH3MVOWRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ST2XV4IMIWCID34ASKH3MVOWRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ST2XV4IMIWCID34ASKH3MVOWRP","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":"160976e480f862d8ab9174fda36a7179c52ce91d0f92eef1322c603c0d171abd","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-28T07:43:23Z","title_canon_sha256":"b93e3391608d59d6246d708011e70e1ac278737b64dd35f4fb1dd06c3fd77d4f"},"schema_version":"1.0","source":{"id":"1011.6016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6016","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6016v2","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6016","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"ST2XV4IMIWCI","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"ST2XV4IMIWCID34A","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"ST2XV4IM","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:9d5e80432a30e633e7f6a37a87f7fd1cd9f9ce2302eb88a9708bebef41706fd3","target":"graph","created_at":"2026-05-18T02:58:01Z","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":"In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E\"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to establish some monotonicity formulae of the partial energies of pluriharmonic maps into any Kaehler manifolds and harmonic maps into Kaehler manifolds with strongly semi-negative curvature respectively. These monotonicity inequalities enable us to derive some holomorphicity and Liouville type results for these pluriharmonic maps and harmonic maps. We also use t","authors_text":"Yuxin Dong","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-28T07:43:23Z","title":"Monotonicity Formulae and Holomorphicity of Harmonic Maps between K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6016","kind":"arxiv","version":2},"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:fde1a587ae81d40a6a8d37d669704e477e9557ba296a36f297671eb33898b9e2","target":"record","created_at":"2026-05-18T02:58:01Z","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":"160976e480f862d8ab9174fda36a7179c52ce91d0f92eef1322c603c0d171abd","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-11-28T07:43:23Z","title_canon_sha256":"b93e3391608d59d6246d708011e70e1ac278737b64dd35f4fb1dd06c3fd77d4f"},"schema_version":"1.0","source":{"id":"1011.6016","kind":"arxiv","version":2}},"canonical_sha256":"94f57af10c458481ef80928fb655d68bcdcff6786a0da9bff70f0b636a46f337","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94f57af10c458481ef80928fb655d68bcdcff6786a0da9bff70f0b636a46f337","first_computed_at":"2026-05-18T02:58:01.425985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:01.425985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FlUEt8SR4HZm44gHY2FvHiSuoZG/euh3iKgmUZJk9y7iH/VWDgsTGh1avQ2yTV3tfgg/Q/qkuR+23+HblgGSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:01.426467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fde1a587ae81d40a6a8d37d669704e477e9557ba296a36f297671eb33898b9e2","sha256:9d5e80432a30e633e7f6a37a87f7fd1cd9f9ce2302eb88a9708bebef41706fd3"],"state_sha256":"a97867c53c71e7a503779c421540d00e2d98eede5a9369a74a6cb85daa75eb88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0xYJzQT7zzC/cih4AmaFsf5qmEJ50sIbAXQ/9A9MishQul4ciFtOb+vHm+KpbJZk3J7FEb2fu/Q4MW2vVhs8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:05:17.139704Z","bundle_sha256":"c0e2a38a56b08f2f83e4e07618fa12d50270f73cae08d4f8fac4a84f4f8b9503"}}