{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GUS7Y3JPCCW7VCYPLNZJQZPFXI","short_pith_number":"pith:GUS7Y3JP","canonical_record":{"source":{"id":"2506.11746","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-13T13:00:34Z","cross_cats_sorted":["math.CV","math.GT","math.RT"],"title_canon_sha256":"da7b9249eb83d99480a88730bd605a025103a97c3805ca4845a2ce7c9f933ea5","abstract_canon_sha256":"bc4f9780e2fe4a05fee55674c7c745b17ee67481099ce6e514048d0f67194402"},"schema_version":"1.0"},"canonical_sha256":"3525fc6d2f10adfa8b0f5b729865e5ba2abbe6474b61da848f7cdd06857820b0","source":{"kind":"arxiv","id":"2506.11746","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11746","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11746v1","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11746","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"GUS7Y3JPCCW7","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"pith_short_16","alias_value":"GUS7Y3JPCCW7VCYP","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"pith_short_8","alias_value":"GUS7Y3JP","created_at":"2026-07-05T11:21:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GUS7Y3JPCCW7VCYPLNZJQZPFXI","target":"record","payload":{"canonical_record":{"source":{"id":"2506.11746","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-13T13:00:34Z","cross_cats_sorted":["math.CV","math.GT","math.RT"],"title_canon_sha256":"da7b9249eb83d99480a88730bd605a025103a97c3805ca4845a2ce7c9f933ea5","abstract_canon_sha256":"bc4f9780e2fe4a05fee55674c7c745b17ee67481099ce6e514048d0f67194402"},"schema_version":"1.0"},"canonical_sha256":"3525fc6d2f10adfa8b0f5b729865e5ba2abbe6474b61da848f7cdd06857820b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:10.150719Z","signature_b64":"CnzIB8qXLxJuDYdcCmBl6WoXMz+eizJ8nEnfXCkNGMlgoedQ6cmhV/Pch36S9mwDA+xWFaAhMYbrBupmFCfPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3525fc6d2f10adfa8b0f5b729865e5ba2abbe6474b61da848f7cdd06857820b0","last_reissued_at":"2026-07-05T11:21:10.150269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:10.150269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.11746","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":"2026-07-05T11:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PS2FJmK/okVcA7jrP4ccGfXAKZnibrYMeW5CVyP2vKkbMA2O9asrdliVkA627aAmcV9ZhbXFq4nZXh4xMeWODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:06:11.633477Z"},"content_sha256":"5292fdd76d6e61f9024d42a53b3e169870a3238eb4751f047d18be61ee010de3","schema_version":"1.0","event_id":"sha256:5292fdd76d6e61f9024d42a53b3e169870a3238eb4751f047d18be61ee010de3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GUS7Y3JPCCW7VCYPLNZJQZPFXI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex harmonic maps and rank 2 higher Teichm\\\"uller theory","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CV","math.GT","math.RT"],"primary_cat":"math.DG","authors_text":"Christian El Emam, Nathaniel Sagman","submitted_at":"2025-06-13T13:00:34Z","abstract_excerpt":"We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichm\\\"uller theory, with a focus on rank $2$ Hitchin components.\n  Complex harmonic maps lead to various generalizations of objects from the theory of Higgs bundles; for instance, the Hitchin fibration, cyclic Higgs bundles, and the affine Toda equations. Beyond such generalizations, we also find a relation between complex harmonic maps and opers.\n  Within the realm of higher Teichm\\\"uller theory, for any rank $2$ Hitchin com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11746","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.11746/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWHeuaNX80vmumL7hSfnws9WF45JAeR0BXgPkfoudLK1uog6WKnMFnskFHx0wf+XluE+mP14adTtBvLH7h1xCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T00:06:11.634416Z"},"content_sha256":"742fdfbecc4476d986268b44a00c6d5349f3c0243f214204d51cc7f3a20812eb","schema_version":"1.0","event_id":"sha256:742fdfbecc4476d986268b44a00c6d5349f3c0243f214204d51cc7f3a20812eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI/bundle.json","state_url":"https://pith.science/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI/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":"2026-08-08T00:06:11Z","links":{"resolver":"https://pith.science/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI","bundle":"https://pith.science/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI/bundle.json","state":"https://pith.science/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUS7Y3JPCCW7VCYPLNZJQZPFXI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GUS7Y3JPCCW7VCYPLNZJQZPFXI","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":"bc4f9780e2fe4a05fee55674c7c745b17ee67481099ce6e514048d0f67194402","cross_cats_sorted":["math.CV","math.GT","math.RT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-13T13:00:34Z","title_canon_sha256":"da7b9249eb83d99480a88730bd605a025103a97c3805ca4845a2ce7c9f933ea5"},"schema_version":"1.0","source":{"id":"2506.11746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11746","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11746v1","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11746","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"GUS7Y3JPCCW7","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"pith_short_16","alias_value":"GUS7Y3JPCCW7VCYP","created_at":"2026-07-05T11:21:10Z"},{"alias_kind":"pith_short_8","alias_value":"GUS7Y3JP","created_at":"2026-07-05T11:21:10Z"}],"graph_snapshots":[{"event_id":"sha256:742fdfbecc4476d986268b44a00c6d5349f3c0243f214204d51cc7f3a20812eb","target":"graph","created_at":"2026-07-05T11:21:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.11746/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichm\\\"uller theory, with a focus on rank $2$ Hitchin components.\n  Complex harmonic maps lead to various generalizations of objects from the theory of Higgs bundles; for instance, the Hitchin fibration, cyclic Higgs bundles, and the affine Toda equations. Beyond such generalizations, we also find a relation between complex harmonic maps and opers.\n  Within the realm of higher Teichm\\\"uller theory, for any rank $2$ Hitchin com","authors_text":"Christian El Emam, Nathaniel Sagman","cross_cats":["math.CV","math.GT","math.RT"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-13T13:00:34Z","title":"Complex harmonic maps and rank 2 higher Teichm\\\"uller theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11746","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":"sha256:5292fdd76d6e61f9024d42a53b3e169870a3238eb4751f047d18be61ee010de3","target":"record","created_at":"2026-07-05T11:21:10Z","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":"bc4f9780e2fe4a05fee55674c7c745b17ee67481099ce6e514048d0f67194402","cross_cats_sorted":["math.CV","math.GT","math.RT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-13T13:00:34Z","title_canon_sha256":"da7b9249eb83d99480a88730bd605a025103a97c3805ca4845a2ce7c9f933ea5"},"schema_version":"1.0","source":{"id":"2506.11746","kind":"arxiv","version":1}},"canonical_sha256":"3525fc6d2f10adfa8b0f5b729865e5ba2abbe6474b61da848f7cdd06857820b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3525fc6d2f10adfa8b0f5b729865e5ba2abbe6474b61da848f7cdd06857820b0","first_computed_at":"2026-07-05T11:21:10.150269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:10.150269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CnzIB8qXLxJuDYdcCmBl6WoXMz+eizJ8nEnfXCkNGMlgoedQ6cmhV/Pch36S9mwDA+xWFaAhMYbrBupmFCfPBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:10.150719Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5292fdd76d6e61f9024d42a53b3e169870a3238eb4751f047d18be61ee010de3","sha256:742fdfbecc4476d986268b44a00c6d5349f3c0243f214204d51cc7f3a20812eb"],"state_sha256":"05adbb84861673a43335efe4557bc279c41080fab83a98479eb7260c2ad9c91b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVnxzojA1IfuLwDYjomQEHxPe+xdAJpK5GqQeJrTTtILmzBQjhet2ErP8o+9yRvngcHOkqL36cchh+2RkJgSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T00:06:11.717843Z","bundle_sha256":"9a4dba933f78823ae40199fdc6dd427e1982b978ff7ce02a6edc7862faea0778"}}