{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D7LEFKGAPWUL7CVTKIO2TDI6OK","short_pith_number":"pith:D7LEFKGA","canonical_record":{"source":{"id":"1311.0038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T21:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"f85172d135086b09a7abd213eaab030e71e70d38ec3cf3a43f1508b5a717dd33","abstract_canon_sha256":"1b88330ba2b87032cd6009989d7237c7b7450514a53e3a4f17ccaaf959f6d057"},"schema_version":"1.0"},"canonical_sha256":"1fd642a8c07da8bf8ab3521da98d1e7299f71c6edd30340b671a5fac9500e801","source":{"kind":"arxiv","id":"1311.0038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0038","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0038v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0038","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"D7LEFKGAPWUL","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D7LEFKGAPWUL7CVT","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D7LEFKGA","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D7LEFKGAPWUL7CVTKIO2TDI6OK","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T21:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"f85172d135086b09a7abd213eaab030e71e70d38ec3cf3a43f1508b5a717dd33","abstract_canon_sha256":"1b88330ba2b87032cd6009989d7237c7b7450514a53e3a4f17ccaaf959f6d057"},"schema_version":"1.0"},"canonical_sha256":"1fd642a8c07da8bf8ab3521da98d1e7299f71c6edd30340b671a5fac9500e801","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:42.027119Z","signature_b64":"hQQIbI2YyeRzrrfKrsOca40Yl2I4UuvN2Agmt4y1mExVjzvkhhqmk1c8t7IDbaIMeCAxgvzHEKNIBsmbKLntCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fd642a8c07da8bf8ab3521da98d1e7299f71c6edd30340b671a5fac9500e801","last_reissued_at":"2026-05-18T03:07:42.026202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:42.026202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0038","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":"2026-05-18T03:07:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoFHYFTWUrAeqERD8fTuApYqK1ylNJBYFvRoZwqc54kSZ/eqCxNynZttPl+k/atfQ19Wcl3WSjkuJxpzjAfzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:36:46.059413Z"},"content_sha256":"8ce1b07fae25f6f5a2dd7e8e24e6a4f87a4d8c31edfec7a1d8c1e348981d6fa1","schema_version":"1.0","event_id":"sha256:8ce1b07fae25f6f5a2dd7e8e24e6a4f87a4d8c31edfec7a1d8c1e348981d6fa1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D7LEFKGAPWUL7CVTKIO2TDI6OK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Spectrum of weighted Laplacian operator and its application to uniqueness of K\\\"ahler Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Long Li","submitted_at":"2013-10-31T21:15:14Z","abstract_excerpt":"The purpose of this paper is to provide a new proof of Bando-Mabuchi's uniqueness theorem of K\\\"ahler Einstein metrics on Fano manifolds, based on Chen's weak C^{1,1} geodesic without using any further regularities. Unlike the smooth case, the lack of regularities on the geodesic forbids us to use spectral formula of the weighed Laplacian operator directly. However, we can use smooth geodesics to approximate the weak one, then prove that a sequence of eigenfunctions will converge into the first eigenspace of the weighted Laplacian operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0038","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":"2026-05-18T03:07:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNP+E+qEueFiwWoSpWK3DyH09PNeqepC4/AgUUw+Z2nMdceuVFOdXs1WTakR1YDb/qUlFCprmTxCU8PPqSF7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:36:46.059768Z"},"content_sha256":"610bbea571add7bb0bb1a709802e77277eef8ef3c9d16442c0326d9a047e7e9d","schema_version":"1.0","event_id":"sha256:610bbea571add7bb0bb1a709802e77277eef8ef3c9d16442c0326d9a047e7e9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK/bundle.json","state_url":"https://pith.science/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK/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":"2026-06-03T18:36:46Z","links":{"resolver":"https://pith.science/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK","bundle":"https://pith.science/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK/bundle.json","state":"https://pith.science/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7LEFKGAPWUL7CVTKIO2TDI6OK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D7LEFKGAPWUL7CVTKIO2TDI6OK","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":"1b88330ba2b87032cd6009989d7237c7b7450514a53e3a4f17ccaaf959f6d057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T21:15:14Z","title_canon_sha256":"f85172d135086b09a7abd213eaab030e71e70d38ec3cf3a43f1508b5a717dd33"},"schema_version":"1.0","source":{"id":"1311.0038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0038","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0038v2","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0038","created_at":"2026-05-18T03:07:42Z"},{"alias_kind":"pith_short_12","alias_value":"D7LEFKGAPWUL","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D7LEFKGAPWUL7CVT","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D7LEFKGA","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:610bbea571add7bb0bb1a709802e77277eef8ef3c9d16442c0326d9a047e7e9d","target":"graph","created_at":"2026-05-18T03:07:42Z","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":"The purpose of this paper is to provide a new proof of Bando-Mabuchi's uniqueness theorem of K\\\"ahler Einstein metrics on Fano manifolds, based on Chen's weak C^{1,1} geodesic without using any further regularities. Unlike the smooth case, the lack of regularities on the geodesic forbids us to use spectral formula of the weighed Laplacian operator directly. However, we can use smooth geodesics to approximate the weak one, then prove that a sequence of eigenfunctions will converge into the first eigenspace of the weighted Laplacian operator.","authors_text":"Long Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T21:15:14Z","title":"On the Spectrum of weighted Laplacian operator and its application to uniqueness of K\\\"ahler Einstein metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0038","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":"sha256:8ce1b07fae25f6f5a2dd7e8e24e6a4f87a4d8c31edfec7a1d8c1e348981d6fa1","target":"record","created_at":"2026-05-18T03:07:42Z","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":"1b88330ba2b87032cd6009989d7237c7b7450514a53e3a4f17ccaaf959f6d057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-31T21:15:14Z","title_canon_sha256":"f85172d135086b09a7abd213eaab030e71e70d38ec3cf3a43f1508b5a717dd33"},"schema_version":"1.0","source":{"id":"1311.0038","kind":"arxiv","version":2}},"canonical_sha256":"1fd642a8c07da8bf8ab3521da98d1e7299f71c6edd30340b671a5fac9500e801","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fd642a8c07da8bf8ab3521da98d1e7299f71c6edd30340b671a5fac9500e801","first_computed_at":"2026-05-18T03:07:42.026202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:42.026202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hQQIbI2YyeRzrrfKrsOca40Yl2I4UuvN2Agmt4y1mExVjzvkhhqmk1c8t7IDbaIMeCAxgvzHEKNIBsmbKLntCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:42.027119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ce1b07fae25f6f5a2dd7e8e24e6a4f87a4d8c31edfec7a1d8c1e348981d6fa1","sha256:610bbea571add7bb0bb1a709802e77277eef8ef3c9d16442c0326d9a047e7e9d"],"state_sha256":"a67b9b6f914f03d4ef5aec606f19ea1bd639da14ceb71cf28db8e7858360ca27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YoujDqFiG00NaS4rS0s2Yq+aWSM8zyiw0xMZxsHID7xfS64MO9CNxu09jegiJngI5+nn+/Lcb5tUpI3hvBZwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:36:46.061949Z","bundle_sha256":"95ddf40a3a28180dc5d8e16ca81bb61dffa102a2f5b7da058d7426930dbc431f"}}