{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JYRMMGJZF5MG4SRZIYOAZIUBIA","short_pith_number":"pith:JYRMMGJZ","canonical_record":{"source":{"id":"1004.5482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-30T09:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"de6a0da5a7c29a091004d9546489a71cf346d1118aab325158de975252ca1edc","abstract_canon_sha256":"bc29a622aedadffd0190e7195570652c6dd7ac002a3beebfe520c9e9fcdd9478"},"schema_version":"1.0"},"canonical_sha256":"4e22c619392f586e4a39461c0ca2814024c3cda29cffcf6d9e63f7769d8d62d5","source":{"kind":"arxiv","id":"1004.5482","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5482","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5482v1","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5482","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"JYRMMGJZF5MG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JYRMMGJZF5MG4SRZ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JYRMMGJZ","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JYRMMGJZF5MG4SRZIYOAZIUBIA","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-30T09:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"de6a0da5a7c29a091004d9546489a71cf346d1118aab325158de975252ca1edc","abstract_canon_sha256":"bc29a622aedadffd0190e7195570652c6dd7ac002a3beebfe520c9e9fcdd9478"},"schema_version":"1.0"},"canonical_sha256":"4e22c619392f586e4a39461c0ca2814024c3cda29cffcf6d9e63f7769d8d62d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:09.979549Z","signature_b64":"Q6uuNrQgzjgF9JfQSTRPDePtlP9dDXDrMiAkDz+h9/u4O4UueIxXwss/dsyBnF5NfRZACZaw+ctXxopcQ1UdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e22c619392f586e4a39461c0ca2814024c3cda29cffcf6d9e63f7769d8d62d5","last_reissued_at":"2026-05-18T02:24:09.979056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:09.979056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5482","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":"2026-05-18T02:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SvJQBjUMKbXwyYxdSXHeNOLL7oEGOCJ8oq1Mrh5xW0qc3+PVt6i+nqRliEm4IRH3nTZVFzzLzyP1XOHavbaDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:05:27.048002Z"},"content_sha256":"3c2be26f1f22bc34146ddb7df9b41697334df9c31e03070eb2c13c5582ca1d1e","schema_version":"1.0","event_id":"sha256:3c2be26f1f22bc34146ddb7df9b41697334df9c31e03070eb2c13c5582ca1d1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JYRMMGJZF5MG4SRZIYOAZIUBIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Calabi's metric for the space of Kaehler metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Simone Calamai","submitted_at":"2010-04-30T09:50:26Z","abstract_excerpt":"Given any closed Kaehler manifold we define, following an idea by Eugenio                    Calabi, a Riemannian metric on the space of Kaehler metrics regarded                                                    as an infinite dimensional manifold. We prove several geometrical features of the resulting space, some of which we think were already known to Calabi. In particular, the space is a portion of an infinite dimensional sphere and admits explicit unique smooth solutions for the Cauchy and the Dirichlet problems for the geodesic equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5482","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":"2026-05-18T02:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0e3mh2lnr/sSD7XfCwjOFcxteUZZlRx5TuEUE7OZLySjq7irFn8ishmn/grsCAQnfpZBf7N+bgYYClfeoZgpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T01:05:27.048355Z"},"content_sha256":"e596e64c65d1088af1cdf54a9c472b27d554d69f3ed55fd7404cf7f35d0ce729","schema_version":"1.0","event_id":"sha256:e596e64c65d1088af1cdf54a9c472b27d554d69f3ed55fd7404cf7f35d0ce729"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA/bundle.json","state_url":"https://pith.science/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA/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":"2026-06-21T01:05:27Z","links":{"resolver":"https://pith.science/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA","bundle":"https://pith.science/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA/bundle.json","state":"https://pith.science/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYRMMGJZF5MG4SRZIYOAZIUBIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JYRMMGJZF5MG4SRZIYOAZIUBIA","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":"bc29a622aedadffd0190e7195570652c6dd7ac002a3beebfe520c9e9fcdd9478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-30T09:50:26Z","title_canon_sha256":"de6a0da5a7c29a091004d9546489a71cf346d1118aab325158de975252ca1edc"},"schema_version":"1.0","source":{"id":"1004.5482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5482","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5482v1","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5482","created_at":"2026-05-18T02:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"JYRMMGJZF5MG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JYRMMGJZF5MG4SRZ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JYRMMGJZ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:e596e64c65d1088af1cdf54a9c472b27d554d69f3ed55fd7404cf7f35d0ce729","target":"graph","created_at":"2026-05-18T02:24:09Z","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":"Given any closed Kaehler manifold we define, following an idea by Eugenio                    Calabi, a Riemannian metric on the space of Kaehler metrics regarded                                                    as an infinite dimensional manifold. We prove several geometrical features of the resulting space, some of which we think were already known to Calabi. In particular, the space is a portion of an infinite dimensional sphere and admits explicit unique smooth solutions for the Cauchy and the Dirichlet problems for the geodesic equation.","authors_text":"Simone Calamai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-30T09:50:26Z","title":"The Calabi's metric for the space of Kaehler metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5482","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":"sha256:3c2be26f1f22bc34146ddb7df9b41697334df9c31e03070eb2c13c5582ca1d1e","target":"record","created_at":"2026-05-18T02:24:09Z","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":"bc29a622aedadffd0190e7195570652c6dd7ac002a3beebfe520c9e9fcdd9478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-30T09:50:26Z","title_canon_sha256":"de6a0da5a7c29a091004d9546489a71cf346d1118aab325158de975252ca1edc"},"schema_version":"1.0","source":{"id":"1004.5482","kind":"arxiv","version":1}},"canonical_sha256":"4e22c619392f586e4a39461c0ca2814024c3cda29cffcf6d9e63f7769d8d62d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e22c619392f586e4a39461c0ca2814024c3cda29cffcf6d9e63f7769d8d62d5","first_computed_at":"2026-05-18T02:24:09.979056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:09.979056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q6uuNrQgzjgF9JfQSTRPDePtlP9dDXDrMiAkDz+h9/u4O4UueIxXwss/dsyBnF5NfRZACZaw+ctXxopcQ1UdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:09.979549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c2be26f1f22bc34146ddb7df9b41697334df9c31e03070eb2c13c5582ca1d1e","sha256:e596e64c65d1088af1cdf54a9c472b27d554d69f3ed55fd7404cf7f35d0ce729"],"state_sha256":"bf6b74f6281b0d38f8d200dcc8df6132b7b877b45153c4a87f9e05016d84206e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whGtX+zdHyTKFmykXtF5n/R4rwxlhGJFFPDgrgc5v62F16X2qz8eIZGC2Xs8Md3ISZ3uukKCycUHMMwSbjnOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T01:05:27.050203Z","bundle_sha256":"9af959937be89de05e5cf9d4e02cce80c525add75c4681baca843929ce97bcc7"}}