{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NNO2SIUGGWDFYA2X4AQUUHLY57","short_pith_number":"pith:NNO2SIUG","canonical_record":{"source":{"id":"2501.09474","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-01-16T11:27:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"bafecac3471d8bcf5f077bb702bca471ce181cd8631b1c3019f20c7fece9eb82","abstract_canon_sha256":"569513c5e870adc2d2782af598eb5fe7bf6bf23bc9ac753c29b053389e938197"},"schema_version":"1.0"},"canonical_sha256":"6b5da9228635865c0357e0214a1d78efc998913a7292f64613c00b367d35b4c5","source":{"kind":"arxiv","id":"2501.09474","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09474","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09474v3","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09474","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"NNO2SIUGGWDF","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNO2SIUGGWDFYA2X","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNO2SIUG","created_at":"2026-07-05T10:40:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NNO2SIUGGWDFYA2X4AQUUHLY57","target":"record","payload":{"canonical_record":{"source":{"id":"2501.09474","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-01-16T11:27:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"bafecac3471d8bcf5f077bb702bca471ce181cd8631b1c3019f20c7fece9eb82","abstract_canon_sha256":"569513c5e870adc2d2782af598eb5fe7bf6bf23bc9ac753c29b053389e938197"},"schema_version":"1.0"},"canonical_sha256":"6b5da9228635865c0357e0214a1d78efc998913a7292f64613c00b367d35b4c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:16.249866Z","signature_b64":"4iCuZ45zJU0qqMcBukvA6xlWmoKs3ID9+lYwUIrkhLm6s92HGba67PPLJJNrP2rRWMyuao4zbOUxola6SwDrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b5da9228635865c0357e0214a1d78efc998913a7292f64613c00b367d35b4c5","last_reissued_at":"2026-07-05T10:40:16.249427Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:16.249427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.09474","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":"2026-07-05T10:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hjJkVNVwhRTtGpXxH/8J5JpjpPEqbbPuXSGZP8sj5J+crT4/CiUG6ndcgxLgb6DJJ3iaD3xlAybhDl8g9vWLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:59:11.198779Z"},"content_sha256":"3e0964756e60d241c180c17c8c487c293adc1e1c9c7da004f823487859361e68","schema_version":"1.0","event_id":"sha256:3e0964756e60d241c180c17c8c487c293adc1e1c9c7da004f823487859361e68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NNO2SIUGGWDFYA2X4AQUUHLY57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"hep-th","authors_text":"Georgios Papadopoulos","submitted_at":"2025-01-16T11:27:06Z","abstract_excerpt":"We investigate the geometry of the moduli spaces $\\mathscr{M}_{\\HE}^*(M^{2n})$ of Hermitian-Einstein irreducible connections on a vector bundle $E$ over a K\\\"ahler with torsion (KT) manifold $M^{2n}$ that admits holomorphic and $\\h\\nabla$-covariantly constant vector fields, where $\\h\\nabla$ is the connection with skew-symmetric torsion $H$. We demonstrate that such vector fields induce an action on $\\mathscr{M}_{\\HE}^*(M^{2n})$ that leaves both the metric and complex structure invariant. Moreover, if an additional condition is satisfied, the induced vector fields are covariantly constant with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.09474/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":"2026-07-05T10:40:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wn1RCj86ySarzN+xZWDZd6K1078k3UJxFZCgBO3ad2kP23CUmzv+XovGpA9O3PWtH3OyUlxViJBY6JQytRExAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:59:11.199424Z"},"content_sha256":"c1e0d17b34953bb448028dcb277161441793f26cb4d3c12df5d89cc9b4152f82","schema_version":"1.0","event_id":"sha256:c1e0d17b34953bb448028dcb277161441793f26cb4d3c12df5d89cc9b4152f82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNO2SIUGGWDFYA2X4AQUUHLY57/bundle.json","state_url":"https://pith.science/pith/NNO2SIUGGWDFYA2X4AQUUHLY57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNO2SIUGGWDFYA2X4AQUUHLY57/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":"2026-08-11T05:59:11Z","links":{"resolver":"https://pith.science/pith/NNO2SIUGGWDFYA2X4AQUUHLY57","bundle":"https://pith.science/pith/NNO2SIUGGWDFYA2X4AQUUHLY57/bundle.json","state":"https://pith.science/pith/NNO2SIUGGWDFYA2X4AQUUHLY57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNO2SIUGGWDFYA2X4AQUUHLY57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NNO2SIUGGWDFYA2X4AQUUHLY57","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":"569513c5e870adc2d2782af598eb5fe7bf6bf23bc9ac753c29b053389e938197","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-01-16T11:27:06Z","title_canon_sha256":"bafecac3471d8bcf5f077bb702bca471ce181cd8631b1c3019f20c7fece9eb82"},"schema_version":"1.0","source":{"id":"2501.09474","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09474","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09474v3","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09474","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"pith_short_12","alias_value":"NNO2SIUGGWDF","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNO2SIUGGWDFYA2X","created_at":"2026-07-05T10:40:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNO2SIUG","created_at":"2026-07-05T10:40:16Z"}],"graph_snapshots":[{"event_id":"sha256:c1e0d17b34953bb448028dcb277161441793f26cb4d3c12df5d89cc9b4152f82","target":"graph","created_at":"2026-07-05T10:40:16Z","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/2501.09474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the geometry of the moduli spaces $\\mathscr{M}_{\\HE}^*(M^{2n})$ of Hermitian-Einstein irreducible connections on a vector bundle $E$ over a K\\\"ahler with torsion (KT) manifold $M^{2n}$ that admits holomorphic and $\\h\\nabla$-covariantly constant vector fields, where $\\h\\nabla$ is the connection with skew-symmetric torsion $H$. We demonstrate that such vector fields induce an action on $\\mathscr{M}_{\\HE}^*(M^{2n})$ that leaves both the metric and complex structure invariant. Moreover, if an additional condition is satisfied, the induced vector fields are covariantly constant with ","authors_text":"Georgios Papadopoulos","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-01-16T11:27:06Z","title":"Geometry and symmetries of Hermitian-Einstein and instanton connection moduli spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09474","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":"sha256:3e0964756e60d241c180c17c8c487c293adc1e1c9c7da004f823487859361e68","target":"record","created_at":"2026-07-05T10:40:16Z","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":"569513c5e870adc2d2782af598eb5fe7bf6bf23bc9ac753c29b053389e938197","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-01-16T11:27:06Z","title_canon_sha256":"bafecac3471d8bcf5f077bb702bca471ce181cd8631b1c3019f20c7fece9eb82"},"schema_version":"1.0","source":{"id":"2501.09474","kind":"arxiv","version":3}},"canonical_sha256":"6b5da9228635865c0357e0214a1d78efc998913a7292f64613c00b367d35b4c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b5da9228635865c0357e0214a1d78efc998913a7292f64613c00b367d35b4c5","first_computed_at":"2026-07-05T10:40:16.249427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:40:16.249427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4iCuZ45zJU0qqMcBukvA6xlWmoKs3ID9+lYwUIrkhLm6s92HGba67PPLJJNrP2rRWMyuao4zbOUxola6SwDrAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:40:16.249866Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.09474","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e0964756e60d241c180c17c8c487c293adc1e1c9c7da004f823487859361e68","sha256:c1e0d17b34953bb448028dcb277161441793f26cb4d3c12df5d89cc9b4152f82"],"state_sha256":"e0462aa5255df3ae2da9f30e9d54a8e5dbc489991b42885eed494b2a953801bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AB6srr8TF+uXe974sQhcNw5rB6PbNzW/+87l6+9VU4mWzWbCuaL6SIMFRllmNmMXgCbp31C3Jje8RR5rMcrAAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T05:59:11.205127Z","bundle_sha256":"85bdf195ff1a1c56229752835e108f8cad8b9ec082607500852e192fbcc3f504"}}