{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SLKIYVHSNV5C5G4YNA47O7G2I7","short_pith_number":"pith:SLKIYVHS","canonical_record":{"source":{"id":"1211.3101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-13T20:38:31Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dc55f55f67f5d6548777926fa53ba263ca1cfce01afdc6cff8c5b22a6a765853","abstract_canon_sha256":"639d6ed181bdb55eb2e3d4a2543c4c1f1758cf2d734309da49539dfd965770f4"},"schema_version":"1.0"},"canonical_sha256":"92d48c54f26d7a2e9b986839f77cda47e5a902f1b2c9575f31b199f27a9857cc","source":{"kind":"arxiv","id":"1211.3101","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3101","created_at":"2026-05-18T03:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3101v1","created_at":"2026-05-18T03:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3101","created_at":"2026-05-18T03:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"SLKIYVHSNV5C","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SLKIYVHSNV5C5G4Y","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SLKIYVHS","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SLKIYVHSNV5C5G4YNA47O7G2I7","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-13T20:38:31Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dc55f55f67f5d6548777926fa53ba263ca1cfce01afdc6cff8c5b22a6a765853","abstract_canon_sha256":"639d6ed181bdb55eb2e3d4a2543c4c1f1758cf2d734309da49539dfd965770f4"},"schema_version":"1.0"},"canonical_sha256":"92d48c54f26d7a2e9b986839f77cda47e5a902f1b2c9575f31b199f27a9857cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:51.869897Z","signature_b64":"qKoyfY8zNG4vzuds3ZfaipepOvprJguXZRYEiCwV8Vssvk1W0TCPWoBiMDNlzWFKt59iseEHGeXaq1fa/xJsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92d48c54f26d7a2e9b986839f77cda47e5a902f1b2c9575f31b199f27a9857cc","last_reissued_at":"2026-05-18T03:40:51.869101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:51.869101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3101","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":"2026-05-18T03:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGGlWqy6Ab5QxNV+hjaAJ+7xqIMMHdV6wIY3RS32wC1uhelosThCi95RkW8z2DEofvoSflrXEtUGalNhfdxFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:48:49.549711Z"},"content_sha256":"f16ef89e0b0389fa2f50f88349cdf9a1b17ccc39a8242055009b8b5bc579e36d","schema_version":"1.0","event_id":"sha256:f16ef89e0b0389fa2f50f88349cdf9a1b17ccc39a8242055009b8b5bc579e36d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SLKIYVHSNV5C5G4YNA47O7G2I7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic Maps and Integrable Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Emma Carberry","submitted_at":"2012-11-13T20:38:31Z","abstract_excerpt":"This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most unwieldy aspect of the spectral curve description is the periodicity conditions and the second aim is to present four different forms for these periodicity conditions and explain their equivalence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3101","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":"2026-05-18T03:40:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZWELafXHdaZwzJPvn/wUKbuixR5SVmMZZpNS3ksqqoRSsiW4aszwWR4qABGmOVptsZdzaKoNCAHIrR2WsIeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:48:49.550358Z"},"content_sha256":"e83bc42e406430abcb51df7895e9921a67e3182117faf6ac41860f8912af2cd9","schema_version":"1.0","event_id":"sha256:e83bc42e406430abcb51df7895e9921a67e3182117faf6ac41860f8912af2cd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLKIYVHSNV5C5G4YNA47O7G2I7/bundle.json","state_url":"https://pith.science/pith/SLKIYVHSNV5C5G4YNA47O7G2I7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLKIYVHSNV5C5G4YNA47O7G2I7/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":"2026-06-04T05:48:49Z","links":{"resolver":"https://pith.science/pith/SLKIYVHSNV5C5G4YNA47O7G2I7","bundle":"https://pith.science/pith/SLKIYVHSNV5C5G4YNA47O7G2I7/bundle.json","state":"https://pith.science/pith/SLKIYVHSNV5C5G4YNA47O7G2I7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLKIYVHSNV5C5G4YNA47O7G2I7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SLKIYVHSNV5C5G4YNA47O7G2I7","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":"639d6ed181bdb55eb2e3d4a2543c4c1f1758cf2d734309da49539dfd965770f4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-13T20:38:31Z","title_canon_sha256":"dc55f55f67f5d6548777926fa53ba263ca1cfce01afdc6cff8c5b22a6a765853"},"schema_version":"1.0","source":{"id":"1211.3101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3101","created_at":"2026-05-18T03:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3101v1","created_at":"2026-05-18T03:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3101","created_at":"2026-05-18T03:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"SLKIYVHSNV5C","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SLKIYVHSNV5C5G4Y","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SLKIYVHS","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:e83bc42e406430abcb51df7895e9921a67e3182117faf6ac41860f8912af2cd9","target":"graph","created_at":"2026-05-18T03:40:51Z","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":"This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most unwieldy aspect of the spectral curve description is the periodicity conditions and the second aim is to present four different forms for these periodicity conditions and explain their equivalence.","authors_text":"Emma Carberry","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-13T20:38:31Z","title":"Harmonic Maps and Integrable Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3101","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:f16ef89e0b0389fa2f50f88349cdf9a1b17ccc39a8242055009b8b5bc579e36d","target":"record","created_at":"2026-05-18T03:40:51Z","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":"639d6ed181bdb55eb2e3d4a2543c4c1f1758cf2d734309da49539dfd965770f4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-13T20:38:31Z","title_canon_sha256":"dc55f55f67f5d6548777926fa53ba263ca1cfce01afdc6cff8c5b22a6a765853"},"schema_version":"1.0","source":{"id":"1211.3101","kind":"arxiv","version":1}},"canonical_sha256":"92d48c54f26d7a2e9b986839f77cda47e5a902f1b2c9575f31b199f27a9857cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92d48c54f26d7a2e9b986839f77cda47e5a902f1b2c9575f31b199f27a9857cc","first_computed_at":"2026-05-18T03:40:51.869101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:51.869101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qKoyfY8zNG4vzuds3ZfaipepOvprJguXZRYEiCwV8Vssvk1W0TCPWoBiMDNlzWFKt59iseEHGeXaq1fa/xJsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:51.869897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f16ef89e0b0389fa2f50f88349cdf9a1b17ccc39a8242055009b8b5bc579e36d","sha256:e83bc42e406430abcb51df7895e9921a67e3182117faf6ac41860f8912af2cd9"],"state_sha256":"80bfe5aa99084822fdced992bde4ec54af751d1f5be5cc9a59e6b6eb659cf806"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w17RYDdV6eUJe9uGi3Q5hDgKJenEc+kQPgKb4n5rgbaEU8HH3Nbq/jRRJTKtQpIBmFp+Ldf+7XEtHYguieB4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:48:49.553291Z","bundle_sha256":"1a9fa7977ef289556c7cc467cc51aaf935b4d72395ca2761e0991a9f7908c456"}}