{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:V7IGX2QOWMCUPORK7LZC366V7D","short_pith_number":"pith:V7IGX2QO","canonical_record":{"source":{"id":"1211.0746","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T02:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"f257aff64ae2477940674bece371c27fa786bfa4f4000626aaf142760989864e","abstract_canon_sha256":"49e230390f0339c1e202688e03cd54ac570aa1046c8a777db5f646b41ab53abe"},"schema_version":"1.0"},"canonical_sha256":"afd06bea0eb30547ba2afaf22dfbd5f8f3144a03ca3c0a7fe2975d6a58e30bcb","source":{"kind":"arxiv","id":"1211.0746","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0746","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0746v3","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0746","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"V7IGX2QOWMCU","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V7IGX2QOWMCUPORK","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V7IGX2QO","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:V7IGX2QOWMCUPORK7LZC366V7D","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0746","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T02:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"f257aff64ae2477940674bece371c27fa786bfa4f4000626aaf142760989864e","abstract_canon_sha256":"49e230390f0339c1e202688e03cd54ac570aa1046c8a777db5f646b41ab53abe"},"schema_version":"1.0"},"canonical_sha256":"afd06bea0eb30547ba2afaf22dfbd5f8f3144a03ca3c0a7fe2975d6a58e30bcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:57.003778Z","signature_b64":"+rcXweJCLhNLK/BFSyGZLF6ddbIYqPfelcqXFP+QiNi6YK2CW6IogCJDI4K4uxLrdsEvbecWcFhSJgGyNR0nCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afd06bea0eb30547ba2afaf22dfbd5f8f3144a03ca3c0a7fe2975d6a58e30bcb","last_reissued_at":"2026-05-18T00:05:57.003173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:57.003173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0746","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gPBy7qoM4F+iWsjo0Qw6y8t6Jw9yowXU4Iflbl8Vlz6v8kSkBt8Oxpjy1W748jbOwW0vFRT5M04utqyVXRrlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:24:49.227715Z"},"content_sha256":"a1a62b31d8a7e75491f2fe2c96976da7d7971c149d780769fa03feaaad3b58ae","schema_version":"1.0","event_id":"sha256:a1a62b31d8a7e75491f2fe2c96976da7d7971c149d780769fa03feaaad3b58ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:V7IGX2QOWMCUPORK7LZC366V7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hitchin's equations on a nonorientable manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Graeme Wilkin, Nan-Kuo Ho, Siye Wu","submitted_at":"2012-11-05T02:30:00Z","abstract_excerpt":"We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies Hitchin's moduli space with the moduli space of flat $K^\\mathbb{C}$-connections, which remains valid when M is non-orientable. This enables us to study Hitchin's moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover $\\tilde{M}$ of $M$ is a K\\\"ahler manifold with odd complex dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0746","kind":"arxiv","version":3},"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":"2026-05-18T00:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ir0GocIDAPGELusJy1jxgkbMcJ9D1iOzQy+Bh4+XUU7Rk+gDBXGeLJ/DOm6ArY74hAcH1dbQ0rW7iFSj3izJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:24:49.228068Z"},"content_sha256":"c7c56760ccfca8c1852a6875ed9e0f4afd5d87396d2f811c61cc5ec703536b2e","schema_version":"1.0","event_id":"sha256:c7c56760ccfca8c1852a6875ed9e0f4afd5d87396d2f811c61cc5ec703536b2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7IGX2QOWMCUPORK7LZC366V7D/bundle.json","state_url":"https://pith.science/pith/V7IGX2QOWMCUPORK7LZC366V7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7IGX2QOWMCUPORK7LZC366V7D/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":"2026-06-12T01:24:49Z","links":{"resolver":"https://pith.science/pith/V7IGX2QOWMCUPORK7LZC366V7D","bundle":"https://pith.science/pith/V7IGX2QOWMCUPORK7LZC366V7D/bundle.json","state":"https://pith.science/pith/V7IGX2QOWMCUPORK7LZC366V7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7IGX2QOWMCUPORK7LZC366V7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:V7IGX2QOWMCUPORK7LZC366V7D","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":"49e230390f0339c1e202688e03cd54ac570aa1046c8a777db5f646b41ab53abe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T02:30:00Z","title_canon_sha256":"f257aff64ae2477940674bece371c27fa786bfa4f4000626aaf142760989864e"},"schema_version":"1.0","source":{"id":"1211.0746","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0746","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0746v3","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0746","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"V7IGX2QOWMCU","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V7IGX2QOWMCUPORK","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V7IGX2QO","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:c7c56760ccfca8c1852a6875ed9e0f4afd5d87396d2f811c61cc5ec703536b2e","target":"graph","created_at":"2026-05-18T00:05:57Z","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 define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies Hitchin's moduli space with the moduli space of flat $K^\\mathbb{C}$-connections, which remains valid when M is non-orientable. This enables us to study Hitchin's moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover $\\tilde{M}$ of $M$ is a K\\\"ahler manifold with odd complex dimensio","authors_text":"Graeme Wilkin, Nan-Kuo Ho, Siye Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T02:30:00Z","title":"Hitchin's equations on a nonorientable manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0746","kind":"arxiv","version":3},"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:a1a62b31d8a7e75491f2fe2c96976da7d7971c149d780769fa03feaaad3b58ae","target":"record","created_at":"2026-05-18T00:05:57Z","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":"49e230390f0339c1e202688e03cd54ac570aa1046c8a777db5f646b41ab53abe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T02:30:00Z","title_canon_sha256":"f257aff64ae2477940674bece371c27fa786bfa4f4000626aaf142760989864e"},"schema_version":"1.0","source":{"id":"1211.0746","kind":"arxiv","version":3}},"canonical_sha256":"afd06bea0eb30547ba2afaf22dfbd5f8f3144a03ca3c0a7fe2975d6a58e30bcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd06bea0eb30547ba2afaf22dfbd5f8f3144a03ca3c0a7fe2975d6a58e30bcb","first_computed_at":"2026-05-18T00:05:57.003173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:57.003173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+rcXweJCLhNLK/BFSyGZLF6ddbIYqPfelcqXFP+QiNi6YK2CW6IogCJDI4K4uxLrdsEvbecWcFhSJgGyNR0nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:57.003778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0746","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1a62b31d8a7e75491f2fe2c96976da7d7971c149d780769fa03feaaad3b58ae","sha256:c7c56760ccfca8c1852a6875ed9e0f4afd5d87396d2f811c61cc5ec703536b2e"],"state_sha256":"edd852b097a0b37f0ce1ea36b9edcfcef3387723219d623171c69b83b775ca17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZDO8AWjuojbD5HEwZzg0Nlmdlf2vLFtCBMlX5LZvv9TmKTMbDfczwXhBjyK1TUT/0W+NsU3CQhbWw0Q2wAuyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:24:49.230135Z","bundle_sha256":"07ad01efb555cc3fd1dd5575834476b5d3151be9b988a747fa4a4df3fa44e15a"}}