{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BC7TYUDNFKCFKNQRNWDZ3K7K2T","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":"df7c7f2a3bf9dbbc047e98137c06f378de018da06962734ee0280010531a923f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-05T23:38:29Z","title_canon_sha256":"23ae9455d144756f8aa9592c0c87131e9b6787d57597408f585fd3ac7ee55381"},"schema_version":"1.0","source":{"id":"0907.0899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0899","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0899v1","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0899","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"BC7TYUDNFKCF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BC7TYUDNFKCFKNQR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BC7TYUDN","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7adc4287f7e7d41ce83d869b52db5a286b4d93fa5e3037290a21198344c61659","target":"graph","created_at":"2026-05-18T03:40:14Z","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 study geometric variational problems for a class of nonlinear sigma-models in quantum field theory. Mathematically, one needs to minimize an energy functional on homotopy classes of maps from closed 3-manifolds into compact homogeneous spaces G/H. The minimizers are known as Hopfions and exhibit localized knot-like structure. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each (generalized) homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers in each 2-homotopy class.\n","authors_text":"Sergiy Koshkin","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-05T23:38:29Z","title":"Gauge theory of Faddeev-Skyrme functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0899","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:b2c7a8ad03ba7de99023a4dc5b0caf0e41b24009b93b786b0adae3bd6ce8ec07","target":"record","created_at":"2026-05-18T03:40:14Z","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":"df7c7f2a3bf9dbbc047e98137c06f378de018da06962734ee0280010531a923f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-07-05T23:38:29Z","title_canon_sha256":"23ae9455d144756f8aa9592c0c87131e9b6787d57597408f585fd3ac7ee55381"},"schema_version":"1.0","source":{"id":"0907.0899","kind":"arxiv","version":1}},"canonical_sha256":"08bf3c506d2a845536116d879dabead4e7a2e7b1ca92cfa36362f8fb822b3302","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08bf3c506d2a845536116d879dabead4e7a2e7b1ca92cfa36362f8fb822b3302","first_computed_at":"2026-05-18T03:40:14.829766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:14.829766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3wYn+LfjTqocn/AZFL4Eq2xHpbHy4gnJzGWrPragqt3uP1rIOs3G9CxxGiHXS1YZNOXf+AfLAejQkMP7WsGXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:14.830601Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2c7a8ad03ba7de99023a4dc5b0caf0e41b24009b93b786b0adae3bd6ce8ec07","sha256:7adc4287f7e7d41ce83d869b52db5a286b4d93fa5e3037290a21198344c61659"],"state_sha256":"e687a855cda8fae91fd235440fc51fa51ad452e206bf2882e1b69bcfd759e46e"}