{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KOWDPNG7ST4KSWIXORT22YPTCO","short_pith_number":"pith:KOWDPNG7","canonical_record":{"source":{"id":"1411.2882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-11T16:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"44122ace84ef1ea178a8d06c124a73cc2d118ace79cc482aa30f6c6389c4f94b","abstract_canon_sha256":"34bd6706078a7541e44d05e440c5c52a9be9e7780fd2315d4866d96a18b6630a"},"schema_version":"1.0"},"canonical_sha256":"53ac37b4df94f8a959177467ad61f31384acfcdc84b36a094c74ac6213b14fb0","source":{"kind":"arxiv","id":"1411.2882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2882","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2882v1","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2882","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"KOWDPNG7ST4K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KOWDPNG7ST4KSWIX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KOWDPNG7","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KOWDPNG7ST4KSWIXORT22YPTCO","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2882","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-11T16:39:05Z","cross_cats_sorted":[],"title_canon_sha256":"44122ace84ef1ea178a8d06c124a73cc2d118ace79cc482aa30f6c6389c4f94b","abstract_canon_sha256":"34bd6706078a7541e44d05e440c5c52a9be9e7780fd2315d4866d96a18b6630a"},"schema_version":"1.0"},"canonical_sha256":"53ac37b4df94f8a959177467ad61f31384acfcdc84b36a094c74ac6213b14fb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:52.809656Z","signature_b64":"JDdp8sdU0JnzhySXNapgsj4ETVfJsHn7EwQuN2lxjH8th4s1TalECkKDFvyugi5OjlRhhWe0ukhs/nO8dRGjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53ac37b4df94f8a959177467ad61f31384acfcdc84b36a094c74ac6213b14fb0","last_reissued_at":"2026-05-18T02:37:52.809161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:52.809161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2882","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":"2026-05-18T02:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ZaFAo0H/VIu5y383YJQ7EN8cZY7kOv+VIb+KH4AU4bVy+KqEaL/nQ4Tg1mtSyYfIJXUh1gpINnIre27iotfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:52:31.459496Z"},"content_sha256":"564a3b93dcd4bb8ffa6baed338add9f7d470595ae755496306ffbba12f75c39c","schema_version":"1.0","event_id":"sha256:564a3b93dcd4bb8ffa6baed338add9f7d470595ae755496306ffbba12f75c39c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KOWDPNG7ST4KSWIXORT22YPTCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Yang-Mills connections on compact complex tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Indranil Biswas","submitted_at":"2014-11-11T16:39:05Z","abstract_excerpt":"Let $G$ be a connected reductive complex affine algebraic group and $K\\subset G$ a maximal compact subgroup. Let $M$ be a compact complex torus equipped with a flat K\\\"ahler structure and $(E_G ,\\theta)$ a polystable Higgs $G$-bundle on $M$. Take any $C^\\infty$ reduction of structure group $E_K \\subset E_G$ to the subgroup $K$ that solves the Yang--Mills equation for $(E_G ,\\theta)$. We prove that the principal $G$-bundle $E_G$ is polystable and the above reduction $E_K$ solves the Einstein--Hermitian equation for $E_G$. We also prove that for a semistable (respectively, polystable) Higgs $G$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2882","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":"2026-05-18T02:37:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOXAp5FJLQbip1KCML2Xw+mvsPuadRPTseM53X5a2WUYQrIIA1chE3ojAvEn0gHzCmEEFZH3tjhag8f0WqA8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:52:31.459844Z"},"content_sha256":"7851470d479a354529dbc2173460e38a84f26c071177bf1cdc9c3c0b11e07c9a","schema_version":"1.0","event_id":"sha256:7851470d479a354529dbc2173460e38a84f26c071177bf1cdc9c3c0b11e07c9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOWDPNG7ST4KSWIXORT22YPTCO/bundle.json","state_url":"https://pith.science/pith/KOWDPNG7ST4KSWIXORT22YPTCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOWDPNG7ST4KSWIXORT22YPTCO/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":"2026-06-02T03:52:31Z","links":{"resolver":"https://pith.science/pith/KOWDPNG7ST4KSWIXORT22YPTCO","bundle":"https://pith.science/pith/KOWDPNG7ST4KSWIXORT22YPTCO/bundle.json","state":"https://pith.science/pith/KOWDPNG7ST4KSWIXORT22YPTCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOWDPNG7ST4KSWIXORT22YPTCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KOWDPNG7ST4KSWIXORT22YPTCO","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":"34bd6706078a7541e44d05e440c5c52a9be9e7780fd2315d4866d96a18b6630a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-11T16:39:05Z","title_canon_sha256":"44122ace84ef1ea178a8d06c124a73cc2d118ace79cc482aa30f6c6389c4f94b"},"schema_version":"1.0","source":{"id":"1411.2882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2882","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2882v1","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2882","created_at":"2026-05-18T02:37:52Z"},{"alias_kind":"pith_short_12","alias_value":"KOWDPNG7ST4K","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KOWDPNG7ST4KSWIX","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KOWDPNG7","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:7851470d479a354529dbc2173460e38a84f26c071177bf1cdc9c3c0b11e07c9a","target":"graph","created_at":"2026-05-18T02:37:52Z","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":"Let $G$ be a connected reductive complex affine algebraic group and $K\\subset G$ a maximal compact subgroup. Let $M$ be a compact complex torus equipped with a flat K\\\"ahler structure and $(E_G ,\\theta)$ a polystable Higgs $G$-bundle on $M$. Take any $C^\\infty$ reduction of structure group $E_K \\subset E_G$ to the subgroup $K$ that solves the Yang--Mills equation for $(E_G ,\\theta)$. We prove that the principal $G$-bundle $E_G$ is polystable and the above reduction $E_K$ solves the Einstein--Hermitian equation for $E_G$. We also prove that for a semistable (respectively, polystable) Higgs $G$-","authors_text":"Indranil Biswas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-11T16:39:05Z","title":"Yang-Mills connections on compact complex tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2882","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":"sha256:564a3b93dcd4bb8ffa6baed338add9f7d470595ae755496306ffbba12f75c39c","target":"record","created_at":"2026-05-18T02:37:52Z","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":"34bd6706078a7541e44d05e440c5c52a9be9e7780fd2315d4866d96a18b6630a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-11T16:39:05Z","title_canon_sha256":"44122ace84ef1ea178a8d06c124a73cc2d118ace79cc482aa30f6c6389c4f94b"},"schema_version":"1.0","source":{"id":"1411.2882","kind":"arxiv","version":1}},"canonical_sha256":"53ac37b4df94f8a959177467ad61f31384acfcdc84b36a094c74ac6213b14fb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53ac37b4df94f8a959177467ad61f31384acfcdc84b36a094c74ac6213b14fb0","first_computed_at":"2026-05-18T02:37:52.809161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:52.809161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JDdp8sdU0JnzhySXNapgsj4ETVfJsHn7EwQuN2lxjH8th4s1TalECkKDFvyugi5OjlRhhWe0ukhs/nO8dRGjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:52.809656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:564a3b93dcd4bb8ffa6baed338add9f7d470595ae755496306ffbba12f75c39c","sha256:7851470d479a354529dbc2173460e38a84f26c071177bf1cdc9c3c0b11e07c9a"],"state_sha256":"7efaf26da81a852ccc7564c8550c913d2ec582b34e580b52b63549ec05666840"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7DoUmHDvRoMqZpFyGI/LaitT5LkRYULy+UMSFsgTeE8+Qf2sGmaaNRZ/PeJCpJs50kMejnwWWKUK5zOK9MDHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:52:31.461815Z","bundle_sha256":"d7d9c9f66d5ca599fcdc5c6b6e66e6569e7ae742955b30c3fc46cf8cd1264ef6"}}