{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:V4MX52UGVBU4LEWXBCCLNI7IHO","short_pith_number":"pith:V4MX52UG","canonical_record":{"source":{"id":"2411.15774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-24T10:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"e8447b16480c7de8f862f74cb864803450cee011026776163f1a6e81aa973c2c","abstract_canon_sha256":"d966c1f49112c558615436c5955edc4cb6265995fd29fc9f2f87bb11d501f57c"},"schema_version":"1.0"},"canonical_sha256":"af197eea86a869c592d70884b6a3e83b8d555b1eec81ca51d004241812a3ab2d","source":{"kind":"arxiv","id":"2411.15774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15774","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15774v1","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15774","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"V4MX52UGVBU4","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"pith_short_16","alias_value":"V4MX52UGVBU4LEWX","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"pith_short_8","alias_value":"V4MX52UG","created_at":"2026-07-05T09:39:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:V4MX52UGVBU4LEWXBCCLNI7IHO","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-24T10:27:57Z","cross_cats_sorted":[],"title_canon_sha256":"e8447b16480c7de8f862f74cb864803450cee011026776163f1a6e81aa973c2c","abstract_canon_sha256":"d966c1f49112c558615436c5955edc4cb6265995fd29fc9f2f87bb11d501f57c"},"schema_version":"1.0"},"canonical_sha256":"af197eea86a869c592d70884b6a3e83b8d555b1eec81ca51d004241812a3ab2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:40.963994Z","signature_b64":"O+dHvX+ElRjjjbercEPuseiXhWO7WI/j2IxgiMtHQSw4AGCgQeo4ffByxFdcBDTe5Mtl5gaRLHIveS9Hbi/eCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af197eea86a869c592d70884b6a3e83b8d555b1eec81ca51d004241812a3ab2d","last_reissued_at":"2026-07-05T09:39:40.963554Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:40.963554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15774","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":"2026-07-05T09:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a4noFHt5n2h6u3yYrtNT3unE1iqEyl5e3vBCmGBzQgq3Im57MWPmI+e0LIvgVt3tZrbUHX5SK5Ew/EYTU87ECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:25:44.522463Z"},"content_sha256":"d02caf26662df6f20314368500968ff8d845e62fb1b4e83b67c3fc2b228afaaa","schema_version":"1.0","event_id":"sha256:d02caf26662df6f20314368500968ff8d845e62fb1b4e83b67c3fc2b228afaaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:V4MX52UGVBU4LEWXBCCLNI7IHO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on a theorem of Narasimhan and Ramanan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jagadish Pine","submitted_at":"2024-11-24T10:27:57Z","abstract_excerpt":"In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with trivial determinant is isomorphic to $\\mathbb{P}^3$. Our proof relies on a criterion by Bauer and Szemberg, which characterizes projective spaces among smooth Fano varieties using Seshadri constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15774","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/2411.15774/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":"2026-07-05T09:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQwRrtRi8rFFhtLhnR6zD448RRxjnFijubg3WeKZ3p+QX7vRumEI456uzgNqkAUF9MxnjsWcHWWmbfuM52/ODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:25:44.522989Z"},"content_sha256":"5b32e45282251fb7e2a38fc7b54b4b38686be4f68a16a2eb5e4e53272d666c31","schema_version":"1.0","event_id":"sha256:5b32e45282251fb7e2a38fc7b54b4b38686be4f68a16a2eb5e4e53272d666c31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4MX52UGVBU4LEWXBCCLNI7IHO/bundle.json","state_url":"https://pith.science/pith/V4MX52UGVBU4LEWXBCCLNI7IHO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4MX52UGVBU4LEWXBCCLNI7IHO/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":"2026-08-13T00:25:44Z","links":{"resolver":"https://pith.science/pith/V4MX52UGVBU4LEWXBCCLNI7IHO","bundle":"https://pith.science/pith/V4MX52UGVBU4LEWXBCCLNI7IHO/bundle.json","state":"https://pith.science/pith/V4MX52UGVBU4LEWXBCCLNI7IHO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4MX52UGVBU4LEWXBCCLNI7IHO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:V4MX52UGVBU4LEWXBCCLNI7IHO","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":"d966c1f49112c558615436c5955edc4cb6265995fd29fc9f2f87bb11d501f57c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-24T10:27:57Z","title_canon_sha256":"e8447b16480c7de8f862f74cb864803450cee011026776163f1a6e81aa973c2c"},"schema_version":"1.0","source":{"id":"2411.15774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15774","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15774v1","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15774","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"V4MX52UGVBU4","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"pith_short_16","alias_value":"V4MX52UGVBU4LEWX","created_at":"2026-07-05T09:39:40Z"},{"alias_kind":"pith_short_8","alias_value":"V4MX52UG","created_at":"2026-07-05T09:39:40Z"}],"graph_snapshots":[{"event_id":"sha256:5b32e45282251fb7e2a38fc7b54b4b38686be4f68a16a2eb5e4e53272d666c31","target":"graph","created_at":"2026-07-05T09:39:40Z","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/2411.15774/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with trivial determinant is isomorphic to $\\mathbb{P}^3$. Our proof relies on a criterion by Bauer and Szemberg, which characterizes projective spaces among smooth Fano varieties using Seshadri constants.","authors_text":"Jagadish Pine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-24T10:27:57Z","title":"A remark on a theorem of Narasimhan and Ramanan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15774","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:d02caf26662df6f20314368500968ff8d845e62fb1b4e83b67c3fc2b228afaaa","target":"record","created_at":"2026-07-05T09:39:40Z","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":"d966c1f49112c558615436c5955edc4cb6265995fd29fc9f2f87bb11d501f57c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-24T10:27:57Z","title_canon_sha256":"e8447b16480c7de8f862f74cb864803450cee011026776163f1a6e81aa973c2c"},"schema_version":"1.0","source":{"id":"2411.15774","kind":"arxiv","version":1}},"canonical_sha256":"af197eea86a869c592d70884b6a3e83b8d555b1eec81ca51d004241812a3ab2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af197eea86a869c592d70884b6a3e83b8d555b1eec81ca51d004241812a3ab2d","first_computed_at":"2026-07-05T09:39:40.963554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:40.963554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O+dHvX+ElRjjjbercEPuseiXhWO7WI/j2IxgiMtHQSw4AGCgQeo4ffByxFdcBDTe5Mtl5gaRLHIveS9Hbi/eCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:40.963994Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d02caf26662df6f20314368500968ff8d845e62fb1b4e83b67c3fc2b228afaaa","sha256:5b32e45282251fb7e2a38fc7b54b4b38686be4f68a16a2eb5e4e53272d666c31"],"state_sha256":"e687d7e5eee66f5cefcc4be12bdd1e426a654619d67877fa5b082f81370b91db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sKQit1W/zktaWlEQLfGLj22eiQVk44Z0EkQTwYUve7DIOvYEhK4FzTadAHk8vEmK41/sdYxGU6cdik5Keo4IDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:25:44.526712Z","bundle_sha256":"5fa91c7d130f1d155d8ff04f886f503fc681da3eb2e7802cc742be20323364b0"}}