{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JE44MLK3L6QYUFX4MV2CKRBVTC","short_pith_number":"pith:JE44MLK3","canonical_record":{"source":{"id":"1107.0456","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-03T12:59:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"052e93262629d65bc9975e17afa9c2c5b2e2196299dff492cfeab2555a0604f7","abstract_canon_sha256":"1a0634db9dd3ad4b0680ad6725f1ad81a29e920d69b8078573a21b23baf7807a"},"schema_version":"1.0"},"canonical_sha256":"4939c62d5b5fa18a16fc65742544359899175415e4a3a2afb50024f7f77488e3","source":{"kind":"arxiv","id":"1107.0456","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0456","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0456v4","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0456","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"JE44MLK3L6QY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JE44MLK3L6QYUFX4","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JE44MLK3","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JE44MLK3L6QYUFX4MV2CKRBVTC","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0456","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-03T12:59:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"052e93262629d65bc9975e17afa9c2c5b2e2196299dff492cfeab2555a0604f7","abstract_canon_sha256":"1a0634db9dd3ad4b0680ad6725f1ad81a29e920d69b8078573a21b23baf7807a"},"schema_version":"1.0"},"canonical_sha256":"4939c62d5b5fa18a16fc65742544359899175415e4a3a2afb50024f7f77488e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:35.903405Z","signature_b64":"UeyKVvim3fDAMNOwZ1AxNm6xHHBzPWAmOT89K4BQHkJiDZgkTykkAoUDEx7ymwm8+U6KgZOj0+Ydk6F/ELQPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4939c62d5b5fa18a16fc65742544359899175415e4a3a2afb50024f7f77488e3","last_reissued_at":"2026-05-18T03:34:35.902695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:35.902695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0456","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRs9dVpgq8xfX8PKvmo6Dx996HNFrcCQ7XfYu3F0IF2FwB+pTOhI//kYhCCEQ4avG13Fb3YsSzUMkBaIXOlbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:13:28.510594Z"},"content_sha256":"d43bf64a787d3d36b6836eaa95f58d49fff1ea46bdaed514fb12c4140623776b","schema_version":"1.0","event_id":"sha256:d43bf64a787d3d36b6836eaa95f58d49fff1ea46bdaed514fb12c4140623776b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JE44MLK3L6QYUFX4MV2CKRBVTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation of extremal metrics, complex manifolds and the relative Futaki invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Carl Tipler, Santiago R. Simanca, Yann Rollin","submitted_at":"2011-07-03T12:59:00Z","abstract_excerpt":"Let (X,\\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\\\"ahler class \\Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative to G is nondegenerate at g. Consider a smooth family $(M \\to B)$ of polarized complex deformations of (X,\\Omega)\\simeq (M_0,\\Theta_0) provided with a holomorphic action of G with trivial action on B. Then for every t\\in B sufficiently small, there exists an h^{1,1}(X)-dimensional family of extremal Kaehler metrics on M_t whose K\\\"ahler classes are arbitraril"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0456","kind":"arxiv","version":4},"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":"2026-05-18T03:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OkTpLGZ4GxqNbY9NOBwZ4TKgC+hRJ3pZPSbQZTFgdavdOV3rhVtp9gNy3A34atXoa61bg/qDWkK1NmdP5v22AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T20:13:28.510941Z"},"content_sha256":"1dcccac1fd4a4477539178c13cf7335dc911582c9a8a843d1672ce919c21f6d4","schema_version":"1.0","event_id":"sha256:1dcccac1fd4a4477539178c13cf7335dc911582c9a8a843d1672ce919c21f6d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JE44MLK3L6QYUFX4MV2CKRBVTC/bundle.json","state_url":"https://pith.science/pith/JE44MLK3L6QYUFX4MV2CKRBVTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JE44MLK3L6QYUFX4MV2CKRBVTC/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":"2026-06-21T20:13:28Z","links":{"resolver":"https://pith.science/pith/JE44MLK3L6QYUFX4MV2CKRBVTC","bundle":"https://pith.science/pith/JE44MLK3L6QYUFX4MV2CKRBVTC/bundle.json","state":"https://pith.science/pith/JE44MLK3L6QYUFX4MV2CKRBVTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JE44MLK3L6QYUFX4MV2CKRBVTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JE44MLK3L6QYUFX4MV2CKRBVTC","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":"1a0634db9dd3ad4b0680ad6725f1ad81a29e920d69b8078573a21b23baf7807a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-03T12:59:00Z","title_canon_sha256":"052e93262629d65bc9975e17afa9c2c5b2e2196299dff492cfeab2555a0604f7"},"schema_version":"1.0","source":{"id":"1107.0456","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0456","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0456v4","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0456","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"JE44MLK3L6QY","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JE44MLK3L6QYUFX4","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JE44MLK3","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:1dcccac1fd4a4477539178c13cf7335dc911582c9a8a843d1672ce919c21f6d4","target":"graph","created_at":"2026-05-18T03:34:35Z","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":"Let (X,\\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\\\"ahler class \\Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative to G is nondegenerate at g. Consider a smooth family $(M \\to B)$ of polarized complex deformations of (X,\\Omega)\\simeq (M_0,\\Theta_0) provided with a holomorphic action of G with trivial action on B. Then for every t\\in B sufficiently small, there exists an h^{1,1}(X)-dimensional family of extremal Kaehler metrics on M_t whose K\\\"ahler classes are arbitraril","authors_text":"Carl Tipler, Santiago R. Simanca, Yann Rollin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-03T12:59:00Z","title":"Deformation of extremal metrics, complex manifolds and the relative Futaki invariant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0456","kind":"arxiv","version":4},"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:d43bf64a787d3d36b6836eaa95f58d49fff1ea46bdaed514fb12c4140623776b","target":"record","created_at":"2026-05-18T03:34:35Z","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":"1a0634db9dd3ad4b0680ad6725f1ad81a29e920d69b8078573a21b23baf7807a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-03T12:59:00Z","title_canon_sha256":"052e93262629d65bc9975e17afa9c2c5b2e2196299dff492cfeab2555a0604f7"},"schema_version":"1.0","source":{"id":"1107.0456","kind":"arxiv","version":4}},"canonical_sha256":"4939c62d5b5fa18a16fc65742544359899175415e4a3a2afb50024f7f77488e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4939c62d5b5fa18a16fc65742544359899175415e4a3a2afb50024f7f77488e3","first_computed_at":"2026-05-18T03:34:35.902695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:35.902695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UeyKVvim3fDAMNOwZ1AxNm6xHHBzPWAmOT89K4BQHkJiDZgkTykkAoUDEx7ymwm8+U6KgZOj0+Ydk6F/ELQPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:35.903405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0456","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d43bf64a787d3d36b6836eaa95f58d49fff1ea46bdaed514fb12c4140623776b","sha256:1dcccac1fd4a4477539178c13cf7335dc911582c9a8a843d1672ce919c21f6d4"],"state_sha256":"aabcbf214f640dce8aa37db8c61347269e3273d894836a2a81ec11af4557dac6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3RT0zKDWRG2Cm1pzACRu+Ep4kVqLloq3IPMQ83Lvio4q+zCeJdfrIOqy2xx6dSbGkY6yV9g4xopTMWXQrAl6Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T20:13:28.513218Z","bundle_sha256":"45b610960827af431e8066e17945cb3f9e0ebe91d2a8803fb6867e8f118b2bdf"}}