{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S5SFIGQUWSUEJRRP2YHMMOJSW5","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":"1345a9024c40e6b90cc40850db6e46c4d0d96acc5760dce88b03fe96a9edad40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-07T07:46:37Z","title_canon_sha256":"97b7242a90e711d9d86c71be947293a70e957a0e743608891ff1d9beab4d091b"},"schema_version":"1.0","source":{"id":"1408.1504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1504","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1504v1","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1504","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"S5SFIGQUWSUE","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S5SFIGQUWSUEJRRP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S5SFIGQU","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:e00feb3c3f11b749c3133dccbd5fb0d08d38e5279d4d0b4618b238ce0841b760","target":"graph","created_at":"2026-05-18T02:45:40Z","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":"A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of this bundle and a Laplace operator. We apply our main theorem, itself a generalization of a Theorem of Takahashi, to generalize the theory of do Carmo and Wallach and to describe the moduli space of harmonic maps satisfying the gauge and the Einstein-Hermitian conditions from a compact Rieannian manifold into a Grassmannian. As an application, several rigidity results are exihibited. In particular we generalize a rigidity theorem due to Calabi in the case of holomo","authors_text":"Yasuyuki Nagatomo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-07T07:46:37Z","title":"Harmonic maps into Grassmannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1504","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":"sha256:0f65e525a3d4d50acaaca09841b9b585d65ec7039c24dee53278d688a322c330","target":"record","created_at":"2026-05-18T02:45:40Z","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":"1345a9024c40e6b90cc40850db6e46c4d0d96acc5760dce88b03fe96a9edad40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-07T07:46:37Z","title_canon_sha256":"97b7242a90e711d9d86c71be947293a70e957a0e743608891ff1d9beab4d091b"},"schema_version":"1.0","source":{"id":"1408.1504","kind":"arxiv","version":1}},"canonical_sha256":"9764541a14b4a844c62fd60ec63932b7685574aa4d05e7370f760c5112c0854e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9764541a14b4a844c62fd60ec63932b7685574aa4d05e7370f760c5112c0854e","first_computed_at":"2026-05-18T02:45:40.300879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:40.300879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O+Pe/iWs5Vfks9vAcrIfuFLfuO8CgVw0R4EejuAEZjSlcj6xlV0/4xfl2lPfsQ3V6xrIVi176BCNtSFc6Y+iBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:40.301346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f65e525a3d4d50acaaca09841b9b585d65ec7039c24dee53278d688a322c330","sha256:e00feb3c3f11b749c3133dccbd5fb0d08d38e5279d4d0b4618b238ce0841b760"],"state_sha256":"a52697f1af3c13be6d3538e57921d03cbffc15b8d7d603c704930ec5311d7f08"}