{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MKVITLBZMJ26WUONCZ5KVHLPTF","short_pith_number":"pith:MKVITLBZ","canonical_record":{"source":{"id":"1002.1767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-09T03:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"3ac1cfec1aa99b0f1acca2605336eb44c094fd5451c825ca16f918a6e913463c","abstract_canon_sha256":"e233bd7e4218070ffd257a80636df00e865809c04f7307a2b7f0e5d8a8574ea3"},"schema_version":"1.0"},"canonical_sha256":"62aa89ac396275eb51cd167aaa9d6f99614112466bff5fb134cf35f802dbc95f","source":{"kind":"arxiv","id":"1002.1767","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1767","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1767v2","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1767","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"MKVITLBZMJ26","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"pith_short_16","alias_value":"MKVITLBZMJ26WUON","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"pith_short_8","alias_value":"MKVITLBZ","created_at":"2026-07-04T17:31:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MKVITLBZMJ26WUONCZ5KVHLPTF","target":"record","payload":{"canonical_record":{"source":{"id":"1002.1767","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-09T03:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"3ac1cfec1aa99b0f1acca2605336eb44c094fd5451c825ca16f918a6e913463c","abstract_canon_sha256":"e233bd7e4218070ffd257a80636df00e865809c04f7307a2b7f0e5d8a8574ea3"},"schema_version":"1.0"},"canonical_sha256":"62aa89ac396275eb51cd167aaa9d6f99614112466bff5fb134cf35f802dbc95f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:31:06.112174Z","signature_b64":"9nlhg8S9n7cGCi9afLbRxtmvuGK6blNjl18tDCglL7O36bYCLOq1gDC8/RNuihQN/SwmE7lvVEMZOVlTxOSBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62aa89ac396275eb51cd167aaa9d6f99614112466bff5fb134cf35f802dbc95f","last_reissued_at":"2026-07-04T17:31:06.111811Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:31:06.111811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.1767","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PVHVEzrghkBSUzHCZsjqsmpMb8JbEITF2zBpEZaq637fEyqhHQWPRPFnKAxg4DMXZ7H8sLLxZ+Hi/ZTdc1ETDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:17:42.576786Z"},"content_sha256":"531147bb9459d70cd51f98437deea7a41c40459a96371bc6946c6f634bdfbd3a","schema_version":"1.0","event_id":"sha256:531147bb9459d70cd51f98437deea7a41c40459a96371bc6946c6f634bdfbd3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MKVITLBZMJ26WUONCZ5KVHLPTF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"G2 geometry and integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"David Baraglia","submitted_at":"2010-02-09T03:56:32Z","abstract_excerpt":"We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real simple Lie group in the rank 2 case. We prove that such representations are described by a conformal structure and class of Higgs bundle we call cyclic and we show cyclic Higgs bundles correspond to a form of the affine Toda equations. In each case we relate cyclic Higgs bundles to geometric structures on the surface. We elucidate the geometry of generic 2-plane distributions in 5 dimensions, relating it to a parabolic geometry associated to the split real form of $G_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1767","kind":"arxiv","version":2},"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/1002.1767/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":"2026-07-04T17:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOy/2FTrDn2eV3Gr7ttCvY3e5Zc05OoQw0MFclXomNpdHGyZBk3ynimsiCIOPUIDet+9y2Cxu0MN/ewhXE8WCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:17:42.577287Z"},"content_sha256":"c4a4c9571495d16b4588448a3b38b6893622398afc9dd347f91bd1b56ee6bc5a","schema_version":"1.0","event_id":"sha256:c4a4c9571495d16b4588448a3b38b6893622398afc9dd347f91bd1b56ee6bc5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKVITLBZMJ26WUONCZ5KVHLPTF/bundle.json","state_url":"https://pith.science/pith/MKVITLBZMJ26WUONCZ5KVHLPTF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKVITLBZMJ26WUONCZ5KVHLPTF/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":"2026-08-11T03:17:42Z","links":{"resolver":"https://pith.science/pith/MKVITLBZMJ26WUONCZ5KVHLPTF","bundle":"https://pith.science/pith/MKVITLBZMJ26WUONCZ5KVHLPTF/bundle.json","state":"https://pith.science/pith/MKVITLBZMJ26WUONCZ5KVHLPTF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKVITLBZMJ26WUONCZ5KVHLPTF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MKVITLBZMJ26WUONCZ5KVHLPTF","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":"e233bd7e4218070ffd257a80636df00e865809c04f7307a2b7f0e5d8a8574ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-09T03:56:32Z","title_canon_sha256":"3ac1cfec1aa99b0f1acca2605336eb44c094fd5451c825ca16f918a6e913463c"},"schema_version":"1.0","source":{"id":"1002.1767","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1767","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1767v2","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1767","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"MKVITLBZMJ26","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"pith_short_16","alias_value":"MKVITLBZMJ26WUON","created_at":"2026-07-04T17:31:06Z"},{"alias_kind":"pith_short_8","alias_value":"MKVITLBZ","created_at":"2026-07-04T17:31:06Z"}],"graph_snapshots":[{"event_id":"sha256:c4a4c9571495d16b4588448a3b38b6893622398afc9dd347f91bd1b56ee6bc5a","target":"graph","created_at":"2026-07-04T17:31:06Z","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/1002.1767/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real simple Lie group in the rank 2 case. We prove that such representations are described by a conformal structure and class of Higgs bundle we call cyclic and we show cyclic Higgs bundles correspond to a form of the affine Toda equations. In each case we relate cyclic Higgs bundles to geometric structures on the surface. We elucidate the geometry of generic 2-plane distributions in 5 dimensions, relating it to a parabolic geometry associated to the split real form of $G_2","authors_text":"David Baraglia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-09T03:56:32Z","title":"G2 geometry and integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1767","kind":"arxiv","version":2},"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":"sha256:531147bb9459d70cd51f98437deea7a41c40459a96371bc6946c6f634bdfbd3a","target":"record","created_at":"2026-07-04T17:31:06Z","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":"e233bd7e4218070ffd257a80636df00e865809c04f7307a2b7f0e5d8a8574ea3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-09T03:56:32Z","title_canon_sha256":"3ac1cfec1aa99b0f1acca2605336eb44c094fd5451c825ca16f918a6e913463c"},"schema_version":"1.0","source":{"id":"1002.1767","kind":"arxiv","version":2}},"canonical_sha256":"62aa89ac396275eb51cd167aaa9d6f99614112466bff5fb134cf35f802dbc95f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62aa89ac396275eb51cd167aaa9d6f99614112466bff5fb134cf35f802dbc95f","first_computed_at":"2026-07-04T17:31:06.111811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:31:06.111811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nlhg8S9n7cGCi9afLbRxtmvuGK6blNjl18tDCglL7O36bYCLOq1gDC8/RNuihQN/SwmE7lvVEMZOVlTxOSBCw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:31:06.112174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1767","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:531147bb9459d70cd51f98437deea7a41c40459a96371bc6946c6f634bdfbd3a","sha256:c4a4c9571495d16b4588448a3b38b6893622398afc9dd347f91bd1b56ee6bc5a"],"state_sha256":"63a7aff6c8c4be9c50b866646fbf334046bbb9e55145f96994514d2766dd50e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C6RgYrMJTbXnWTUqzW6pH8EccpWG3upY4xq+XMA/lVQSfxujBgBOkxh4+rzkj9hQxM1PGmTICbsuuEcdJuR4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T03:17:42.599713Z","bundle_sha256":"537c98fde428860e138102deb903cb653466d0769b3636612255fa6766a8657c"}}