{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:FFTM6ADZXI7P4NPY6TC5EXQ4IN","short_pith_number":"pith:FFTM6ADZ","canonical_record":{"source":{"id":"alg-geom/9404001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1994-04-05T10:22:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fa20556dc341bf2f2044074117509b6cf05acfaaa9f6ae292e2f26f96532e0ab","abstract_canon_sha256":"65ccdcdaaa4c27e8783bf1ec286ee1dc319ecb37de859004a17a949f8477e170"},"schema_version":"1.0"},"canonical_sha256":"2966cf0079ba3efe35f8f4c5d25e1c435396fde2ba1c605c07ed59033a11c074","source":{"kind":"arxiv","id":"alg-geom/9404001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9404001","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9404001v1","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9404001","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"FFTM6ADZXI7P","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"pith_short_16","alias_value":"FFTM6ADZXI7P4NPY","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"pith_short_8","alias_value":"FFTM6ADZ","created_at":"2026-07-04T15:08:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:FFTM6ADZXI7P4NPY6TC5EXQ4IN","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9404001","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1994-04-05T10:22:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fa20556dc341bf2f2044074117509b6cf05acfaaa9f6ae292e2f26f96532e0ab","abstract_canon_sha256":"65ccdcdaaa4c27e8783bf1ec286ee1dc319ecb37de859004a17a949f8477e170"},"schema_version":"1.0"},"canonical_sha256":"2966cf0079ba3efe35f8f4c5d25e1c435396fde2ba1c605c07ed59033a11c074","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:02.191636Z","signature_b64":"hkRfSLD4nUsp6TuUiFz9yFaHlkGBjtiujfq2tS1HHf+5emffY3eCVvTl9kKQ77r8qo0zPBSxvHIgZwEkUJNABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2966cf0079ba3efe35f8f4c5d25e1c435396fde2ba1c605c07ed59033a11c074","last_reissued_at":"2026-07-04T15:08:02.191274Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:02.191274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9404001","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":"2026-07-04T15:08:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPFE3I6e3bOBP127kKxG7hK3M2BpscnjEV3DDFV2nm+3FT3dqSfq8zjW+1vfQAUoavXg74Jd4Ri1AZ/d5+AmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T06:31:24.093410Z"},"content_sha256":"31747583f32d58ed88f479874b54d4d80b286a6145fbc140259f0aa47f7695b1","schema_version":"1.0","event_id":"sha256:31747583f32d58ed88f479874b54d4d80b286a6145fbc140259f0aa47f7695b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:FFTM6ADZXI7P4NPY6TC5EXQ4IN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector bundles on curves and generalized theta functions: recent results and open problems","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Arnaud Beauville","submitted_at":"1994-04-05T10:22:54Z","abstract_excerpt":"Riemann surface carries a natural line bundle, the determinant bundle. The space of sections of this line bundle (or its multiples) constitutes a natural non-abelian generalization of the spaces of theta functions on the Jacobian. There has been much progress in the last few years towards a better understanding of these spaces, including a rigorous proof of the celebrated Verlinde formula which gives their dimension. This survey paper tries to explain what is now known and what remains open."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9404001","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/alg-geom/9404001/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":"2026-07-04T15:08:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0JvMgYmgunMdsQLiC22tOA32YWB8dDsnFkoQJNC8SeXDg4pT6LCL1I43WnWNsmGfhVgJNg84fuUOL67pfQZcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T06:31:24.093812Z"},"content_sha256":"1f017245e8944876888f81e7d2b45eb0429e00fd8bcea69b71c081a9bbb69b16","schema_version":"1.0","event_id":"sha256:1f017245e8944876888f81e7d2b45eb0429e00fd8bcea69b71c081a9bbb69b16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN/bundle.json","state_url":"https://pith.science/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN/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":"2026-08-13T06:31:24Z","links":{"resolver":"https://pith.science/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN","bundle":"https://pith.science/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN/bundle.json","state":"https://pith.science/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFTM6ADZXI7P4NPY6TC5EXQ4IN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:FFTM6ADZXI7P4NPY6TC5EXQ4IN","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":"65ccdcdaaa4c27e8783bf1ec286ee1dc319ecb37de859004a17a949f8477e170","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1994-04-05T10:22:54Z","title_canon_sha256":"fa20556dc341bf2f2044074117509b6cf05acfaaa9f6ae292e2f26f96532e0ab"},"schema_version":"1.0","source":{"id":"alg-geom/9404001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9404001","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9404001v1","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9404001","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"FFTM6ADZXI7P","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"pith_short_16","alias_value":"FFTM6ADZXI7P4NPY","created_at":"2026-07-04T15:08:02Z"},{"alias_kind":"pith_short_8","alias_value":"FFTM6ADZ","created_at":"2026-07-04T15:08:02Z"}],"graph_snapshots":[{"event_id":"sha256:1f017245e8944876888f81e7d2b45eb0429e00fd8bcea69b71c081a9bbb69b16","target":"graph","created_at":"2026-07-04T15:08:02Z","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/alg-geom/9404001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Riemann surface carries a natural line bundle, the determinant bundle. The space of sections of this line bundle (or its multiples) constitutes a natural non-abelian generalization of the spaces of theta functions on the Jacobian. There has been much progress in the last few years towards a better understanding of these spaces, including a rigorous proof of the celebrated Verlinde formula which gives their dimension. This survey paper tries to explain what is now known and what remains open.","authors_text":"Arnaud Beauville","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1994-04-05T10:22:54Z","title":"Vector bundles on curves and generalized theta functions: recent results and open problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9404001","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":"sha256:31747583f32d58ed88f479874b54d4d80b286a6145fbc140259f0aa47f7695b1","target":"record","created_at":"2026-07-04T15:08:02Z","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":"65ccdcdaaa4c27e8783bf1ec286ee1dc319ecb37de859004a17a949f8477e170","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1994-04-05T10:22:54Z","title_canon_sha256":"fa20556dc341bf2f2044074117509b6cf05acfaaa9f6ae292e2f26f96532e0ab"},"schema_version":"1.0","source":{"id":"alg-geom/9404001","kind":"arxiv","version":1}},"canonical_sha256":"2966cf0079ba3efe35f8f4c5d25e1c435396fde2ba1c605c07ed59033a11c074","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2966cf0079ba3efe35f8f4c5d25e1c435396fde2ba1c605c07ed59033a11c074","first_computed_at":"2026-07-04T15:08:02.191274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:02.191274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hkRfSLD4nUsp6TuUiFz9yFaHlkGBjtiujfq2tS1HHf+5emffY3eCVvTl9kKQ77r8qo0zPBSxvHIgZwEkUJNABA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:02.191636Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9404001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31747583f32d58ed88f479874b54d4d80b286a6145fbc140259f0aa47f7695b1","sha256:1f017245e8944876888f81e7d2b45eb0429e00fd8bcea69b71c081a9bbb69b16"],"state_sha256":"585d372c89d44fac6dc9a7fc46cf7755d3e1491a4215978341793ac4302c2778"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UWFlQ8iz6ZvtzCHLx8nWj3E2jYe8ZdVj+F7oMY3y50NT2Oy2XoGY6eXa6kOw39oGNw8whztiU6ensSq1wiGiBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T06:31:24.096870Z","bundle_sha256":"ffd673d7b88dcb8735d3cf8c9dcb608deda9c5d19c62593d438247f83ecd4004"}}