{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V2QHU5LMEMNTKWDWJRW2FDVXSP","short_pith_number":"pith:V2QHU5LM","canonical_record":{"source":{"id":"1304.5028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T06:16:54Z","cross_cats_sorted":[],"title_canon_sha256":"53d7408b51378f3c1cd1de09067f5429ad033556eb52fa8fd57b87d03188f3b0","abstract_canon_sha256":"56ba5426954a08c3869339e49063eb0ea25a8bbaf84a27744dac5bf2cf76bcab"},"schema_version":"1.0"},"canonical_sha256":"aea07a756c231b3558764c6da28eb793e9737094b635050c6cd7b31564811c24","source":{"kind":"arxiv","id":"1304.5028","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5028","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5028v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5028","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"V2QHU5LMEMNT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"V2QHU5LMEMNTKWDW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"V2QHU5LM","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V2QHU5LMEMNTKWDWJRW2FDVXSP","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T06:16:54Z","cross_cats_sorted":[],"title_canon_sha256":"53d7408b51378f3c1cd1de09067f5429ad033556eb52fa8fd57b87d03188f3b0","abstract_canon_sha256":"56ba5426954a08c3869339e49063eb0ea25a8bbaf84a27744dac5bf2cf76bcab"},"schema_version":"1.0"},"canonical_sha256":"aea07a756c231b3558764c6da28eb793e9737094b635050c6cd7b31564811c24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:41.988332Z","signature_b64":"REt7c3myAVlcC7KAUJzWHmPUe83MVvdmO37FWzW8m0mMnLYn3L4Et4o7uL4GjeomStGJt9tV6ByC61qHiywECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aea07a756c231b3558764c6da28eb793e9737094b635050c6cd7b31564811c24","last_reissued_at":"2026-05-18T03:27:41.987625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:41.987625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5028","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":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6z2MRxIm+2sUT6vkgetphS6sAPKpGYAEzEfdKbteKskKyropFAPzKhKWXwPuWVCi+1qk2Soy+yY9rTo+j5HDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:49:40.070801Z"},"content_sha256":"11575b072bdf8ea4433c8df005558d612d1fc2f893292f3b711611e403379026","schema_version":"1.0","event_id":"sha256:11575b072bdf8ea4433c8df005558d612d1fc2f893292f3b711611e403379026"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V2QHU5LMEMNTKWDWJRW2FDVXSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic morphisms and moment maps on hyper-K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"E. Loubeau, M. Benyounes, R. Pantilie","submitted_at":"2013-04-18T06:16:54Z","abstract_excerpt":"We characterise the actions, by holomorphic isometries on a K\\\"ahler manifold with zero first Betti number, of an abelian Lie group of dim\\geq 2, for which the moment map is horizontally weakly conformal (with respect to some Euclidean structure on the Lie algebra of the group). Furthermore, we study the hyper-K\\\"ahler moment map $\\phi$ induced by an abelian Lie group T acting by triholomorphic isometries on a hyper-K\\\"ahler manifold M, with zero first Betti number, thus obtaining the following: If dim T=1 then $\\phi$ is a harmonic morphism. Moreover, we illustrate this on the tangent bundle o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5028","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":"2026-05-18T03:27:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJF51D8h1G+rMlTtW+wslGf1XS9wLyCFHoW1o1eT6+OYemcOAZwUkAfbbjZQb9ad6Eaao8PStM976TJLO2tgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:49:40.071529Z"},"content_sha256":"c319a1df1da924a697fa983d5090e896e685b65fc10eab89f615020badeea71e","schema_version":"1.0","event_id":"sha256:c319a1df1da924a697fa983d5090e896e685b65fc10eab89f615020badeea71e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP/bundle.json","state_url":"https://pith.science/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP/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":"2026-06-09T15:49:40Z","links":{"resolver":"https://pith.science/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP","bundle":"https://pith.science/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP/bundle.json","state":"https://pith.science/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2QHU5LMEMNTKWDWJRW2FDVXSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V2QHU5LMEMNTKWDWJRW2FDVXSP","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":"56ba5426954a08c3869339e49063eb0ea25a8bbaf84a27744dac5bf2cf76bcab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T06:16:54Z","title_canon_sha256":"53d7408b51378f3c1cd1de09067f5429ad033556eb52fa8fd57b87d03188f3b0"},"schema_version":"1.0","source":{"id":"1304.5028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5028","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5028v1","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5028","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"V2QHU5LMEMNT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"V2QHU5LMEMNTKWDW","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"V2QHU5LM","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:c319a1df1da924a697fa983d5090e896e685b65fc10eab89f615020badeea71e","target":"graph","created_at":"2026-05-18T03:27:41Z","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 characterise the actions, by holomorphic isometries on a K\\\"ahler manifold with zero first Betti number, of an abelian Lie group of dim\\geq 2, for which the moment map is horizontally weakly conformal (with respect to some Euclidean structure on the Lie algebra of the group). Furthermore, we study the hyper-K\\\"ahler moment map $\\phi$ induced by an abelian Lie group T acting by triholomorphic isometries on a hyper-K\\\"ahler manifold M, with zero first Betti number, thus obtaining the following: If dim T=1 then $\\phi$ is a harmonic morphism. Moreover, we illustrate this on the tangent bundle o","authors_text":"E. Loubeau, M. Benyounes, R. Pantilie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T06:16:54Z","title":"Harmonic morphisms and moment maps on hyper-K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5028","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":"sha256:11575b072bdf8ea4433c8df005558d612d1fc2f893292f3b711611e403379026","target":"record","created_at":"2026-05-18T03:27:41Z","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":"56ba5426954a08c3869339e49063eb0ea25a8bbaf84a27744dac5bf2cf76bcab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-18T06:16:54Z","title_canon_sha256":"53d7408b51378f3c1cd1de09067f5429ad033556eb52fa8fd57b87d03188f3b0"},"schema_version":"1.0","source":{"id":"1304.5028","kind":"arxiv","version":1}},"canonical_sha256":"aea07a756c231b3558764c6da28eb793e9737094b635050c6cd7b31564811c24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aea07a756c231b3558764c6da28eb793e9737094b635050c6cd7b31564811c24","first_computed_at":"2026-05-18T03:27:41.987625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:41.987625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"REt7c3myAVlcC7KAUJzWHmPUe83MVvdmO37FWzW8m0mMnLYn3L4Et4o7uL4GjeomStGJt9tV6ByC61qHiywECA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:41.988332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11575b072bdf8ea4433c8df005558d612d1fc2f893292f3b711611e403379026","sha256:c319a1df1da924a697fa983d5090e896e685b65fc10eab89f615020badeea71e"],"state_sha256":"4ddb9de9314055823c2273d2bcec7757d5d969a0d91a4277aa7e64b33053358f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIVb7t128gGlARPX0PYxs9Fsns4LoOtBsdkTpov7GhDKm4ORNhl2KHrQUU1KiL5TrcCEcWoDG3xYbSC4HgeeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:49:40.075519Z","bundle_sha256":"ba457862f136a93adbe4241935729509c217326f7131ee25081e36bc730957e1"}}