{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FGKT7IACZOEK6XZ6KCR7LREJ4L","short_pith_number":"pith:FGKT7IAC","canonical_record":{"source":{"id":"1208.1021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-05T15:15:28Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"fca8a29d7ebcc94144123f58aa565cde0ef93798411e62e2ddc96f8bb1c2756d","abstract_canon_sha256":"c44d05db3a849a80e6f36c4ee9cedbbb21a0b02bac4b8de2f94c95376b6dec16"},"schema_version":"1.0"},"canonical_sha256":"29953fa002cb88af5f3e50a3f5c489e2cecd6544c6ac48fafcb518f9679166dc","source":{"kind":"arxiv","id":"1208.1021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1021","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1021v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1021","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"FGKT7IACZOEK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FGKT7IACZOEK6XZ6","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FGKT7IAC","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FGKT7IACZOEK6XZ6KCR7LREJ4L","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-05T15:15:28Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"fca8a29d7ebcc94144123f58aa565cde0ef93798411e62e2ddc96f8bb1c2756d","abstract_canon_sha256":"c44d05db3a849a80e6f36c4ee9cedbbb21a0b02bac4b8de2f94c95376b6dec16"},"schema_version":"1.0"},"canonical_sha256":"29953fa002cb88af5f3e50a3f5c489e2cecd6544c6ac48fafcb518f9679166dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:20.780756Z","signature_b64":"i0HSWGwi19n/oFGG6ZianAOji2bgjECF/6Lt9p9pIhKZwUa+xXDYk8pMHQVu+nhqKpM39HhPdfDSCcjH55LPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29953fa002cb88af5f3e50a3f5c489e2cecd6544c6ac48fafcb518f9679166dc","last_reissued_at":"2026-05-18T03:49:20.779755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:20.779755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1021","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1c/H8WSqtudgsdqfeOzpPXGglwJrK4vkdpOZeYHaNh592cf4jUMqkALzfowZ7boEvclyH//IZFlWmiTSazD2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:08:28.384179Z"},"content_sha256":"efde24678b4f9065134daa32d1be0293931422cf9decfa1bef22038766f78f5d","schema_version":"1.0","event_id":"sha256:efde24678b4f9065134daa32d1be0293931422cf9decfa1bef22038766f78f5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FGKT7IACZOEK6XZ6KCR7LREJ4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the space of Kahler potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.DG","authors_text":"Weiyong He","submitted_at":"2012-08-05T15:15:28Z","abstract_excerpt":"We consider the geodesic equation for the generalized Kahler potential with only mixed second derivatives bounded. We show that given such two generalized Kahler potentials, there is a unique geodesic segment such that for each point on the geodesic, the generalized Kahler potential has uniformly bounded mixed second derivatives (in manifold directions). This generalizes a fundamental theorem of Chen \\cite{Chen00} on the space of Kahler potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1021","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbHwuJMYDKgn5LVGps65kB1LfZlCWFjIHER0i4+WkNZtydrqjbvFf1l3DUUY+aIU/7jtRGzAM6MHMsMTq6RIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:08:28.384543Z"},"content_sha256":"c512626a7f9b92daa56ab70dd4264c67d4e4bd1ceb1c308ff98759410a52df1e","schema_version":"1.0","event_id":"sha256:c512626a7f9b92daa56ab70dd4264c67d4e4bd1ceb1c308ff98759410a52df1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L/bundle.json","state_url":"https://pith.science/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L/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":"2026-06-22T15:08:28Z","links":{"resolver":"https://pith.science/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L","bundle":"https://pith.science/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L/bundle.json","state":"https://pith.science/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGKT7IACZOEK6XZ6KCR7LREJ4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FGKT7IACZOEK6XZ6KCR7LREJ4L","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":"c44d05db3a849a80e6f36c4ee9cedbbb21a0b02bac4b8de2f94c95376b6dec16","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-05T15:15:28Z","title_canon_sha256":"fca8a29d7ebcc94144123f58aa565cde0ef93798411e62e2ddc96f8bb1c2756d"},"schema_version":"1.0","source":{"id":"1208.1021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1021","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1021v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1021","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"FGKT7IACZOEK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FGKT7IACZOEK6XZ6","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FGKT7IAC","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:c512626a7f9b92daa56ab70dd4264c67d4e4bd1ceb1c308ff98759410a52df1e","target":"graph","created_at":"2026-05-18T03:49:20Z","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 consider the geodesic equation for the generalized Kahler potential with only mixed second derivatives bounded. We show that given such two generalized Kahler potentials, there is a unique geodesic segment such that for each point on the geodesic, the generalized Kahler potential has uniformly bounded mixed second derivatives (in manifold directions). This generalizes a fundamental theorem of Chen \\cite{Chen00} on the space of Kahler potentials.","authors_text":"Weiyong He","cross_cats":["math.AP","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-05T15:15:28Z","title":"On the space of Kahler potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1021","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:efde24678b4f9065134daa32d1be0293931422cf9decfa1bef22038766f78f5d","target":"record","created_at":"2026-05-18T03:49:20Z","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":"c44d05db3a849a80e6f36c4ee9cedbbb21a0b02bac4b8de2f94c95376b6dec16","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-05T15:15:28Z","title_canon_sha256":"fca8a29d7ebcc94144123f58aa565cde0ef93798411e62e2ddc96f8bb1c2756d"},"schema_version":"1.0","source":{"id":"1208.1021","kind":"arxiv","version":1}},"canonical_sha256":"29953fa002cb88af5f3e50a3f5c489e2cecd6544c6ac48fafcb518f9679166dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29953fa002cb88af5f3e50a3f5c489e2cecd6544c6ac48fafcb518f9679166dc","first_computed_at":"2026-05-18T03:49:20.779755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:20.779755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i0HSWGwi19n/oFGG6ZianAOji2bgjECF/6Lt9p9pIhKZwUa+xXDYk8pMHQVu+nhqKpM39HhPdfDSCcjH55LPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:20.780756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efde24678b4f9065134daa32d1be0293931422cf9decfa1bef22038766f78f5d","sha256:c512626a7f9b92daa56ab70dd4264c67d4e4bd1ceb1c308ff98759410a52df1e"],"state_sha256":"a7d30ac904b98ee26b63848d31e14071b3aea01ebd93caf91a7bba6e16506001"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgBgHgnw7n/CH0aFVi7ILdD9JpkEbbtKJ6RI8fcEO5+zlO9e/CdcFwFsUlP7Kl8BK0ljSOHoO//Q+YDj6UPpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:08:28.386549Z","bundle_sha256":"b9207a28eb23201ff875cd10e2463139cbff1d8c2df2ad4682913e916e200c05"}}