{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:5MW7GK4XUZWSR37MGKLVCZQA5A","short_pith_number":"pith:5MW7GK4X","canonical_record":{"source":{"id":"math/0205267","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-05-25T18:48:11Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"8791f0a6429a37e4193ac1ef289ab57fc777048bf12dcfd6a722a2f59af80c77","abstract_canon_sha256":"7395c4fef0df0f018f473b21a5f0525ff32e2db4cbb57af53b7215ce55633cac"},"schema_version":"1.0"},"canonical_sha256":"eb2df32b97a66d28efec3297516600e80686dcbcb4acb33544ab25e20c355a0c","source":{"kind":"arxiv","id":"math/0205267","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205267","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205267v3","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205267","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"5MW7GK4XUZWS","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"pith_short_16","alias_value":"5MW7GK4XUZWSR37M","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"pith_short_8","alias_value":"5MW7GK4X","created_at":"2026-07-04T14:36:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:5MW7GK4XUZWSR37MGKLVCZQA5A","target":"record","payload":{"canonical_record":{"source":{"id":"math/0205267","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2002-05-25T18:48:11Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"8791f0a6429a37e4193ac1ef289ab57fc777048bf12dcfd6a722a2f59af80c77","abstract_canon_sha256":"7395c4fef0df0f018f473b21a5f0525ff32e2db4cbb57af53b7215ce55633cac"},"schema_version":"1.0"},"canonical_sha256":"eb2df32b97a66d28efec3297516600e80686dcbcb4acb33544ab25e20c355a0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:13.723544Z","signature_b64":"vCPrVUlcK/qGtfWG1L6jLe24/hQFrwIhH5SxgvD8x3XEuQEX6YYYGQH1yLUU4QJQMBNmQwN/kEzB8HsoX7fYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb2df32b97a66d28efec3297516600e80686dcbcb4acb33544ab25e20c355a0c","last_reissued_at":"2026-07-04T14:36:13.723111Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:13.723111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0205267","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":"2026-07-04T14:36:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOAqxELmbAnI7NK7t8rt35WhHITS2p8ZKwTZK6eGGe8GOz0AJFtjPd+qoeNR+LnEdQFOti6KdX4LfJxLgALZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:29:57.736871Z"},"content_sha256":"56820403ceb16c8823ebc0740209d818e5cb0aef8f010211b8f59d6c5991b6b9","schema_version":"1.0","event_id":"sha256:56820403ceb16c8823ebc0740209d818e5cb0aef8f010211b8f59d6c5991b6b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:5MW7GK4XUZWSR37MGKLVCZQA5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative projective curves and quantum loop algebras","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Olivier Schiffmann","submitted_at":"2002-05-25T18:48:11Z","abstract_excerpt":"We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent subalgebra of the affinization of the correponding Kac-Moody algebra. In particular this yieds a geometric realization of the quantized enveloping algebra of 2-toroidal (or elliptic) algebras of types D_4, E_6, E_7 or E_8 in terms of weighted projective lines of genus one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205267","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/math/0205267/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":"2026-07-04T14:36:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BiQVy8bZ1JNhteFx56gTV3zp707jvbGOmUKbXFIMdlGerSln5gEuh+Cd4ckWolcY/FuLhEmyLzJUC8H0jNPoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:29:57.737593Z"},"content_sha256":"81d258ccd2c03a1c066832c6acf3c8a0a27ba473399b667145a63bf64117dbcf","schema_version":"1.0","event_id":"sha256:81d258ccd2c03a1c066832c6acf3c8a0a27ba473399b667145a63bf64117dbcf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5MW7GK4XUZWSR37MGKLVCZQA5A/bundle.json","state_url":"https://pith.science/pith/5MW7GK4XUZWSR37MGKLVCZQA5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5MW7GK4XUZWSR37MGKLVCZQA5A/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":"2026-08-12T14:29:57Z","links":{"resolver":"https://pith.science/pith/5MW7GK4XUZWSR37MGKLVCZQA5A","bundle":"https://pith.science/pith/5MW7GK4XUZWSR37MGKLVCZQA5A/bundle.json","state":"https://pith.science/pith/5MW7GK4XUZWSR37MGKLVCZQA5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5MW7GK4XUZWSR37MGKLVCZQA5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:5MW7GK4XUZWSR37MGKLVCZQA5A","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":"7395c4fef0df0f018f473b21a5f0525ff32e2db4cbb57af53b7215ce55633cac","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.QA","submitted_at":"2002-05-25T18:48:11Z","title_canon_sha256":"8791f0a6429a37e4193ac1ef289ab57fc777048bf12dcfd6a722a2f59af80c77"},"schema_version":"1.0","source":{"id":"math/0205267","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205267","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205267v3","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205267","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"5MW7GK4XUZWS","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"pith_short_16","alias_value":"5MW7GK4XUZWSR37M","created_at":"2026-07-04T14:36:13Z"},{"alias_kind":"pith_short_8","alias_value":"5MW7GK4X","created_at":"2026-07-04T14:36:13Z"}],"graph_snapshots":[{"event_id":"sha256:81d258ccd2c03a1c066832c6acf3c8a0a27ba473399b667145a63bf64117dbcf","target":"graph","created_at":"2026-07-04T14:36:13Z","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/math/0205267/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent subalgebra of the affinization of the correponding Kac-Moody algebra. In particular this yieds a geometric realization of the quantized enveloping algebra of 2-toroidal (or elliptic) algebras of types D_4, E_6, E_7 or E_8 in terms of weighted projective lines of genus one.","authors_text":"Olivier Schiffmann","cross_cats":["math.RA"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2002-05-25T18:48:11Z","title":"Noncommutative projective curves and quantum loop algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205267","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":"sha256:56820403ceb16c8823ebc0740209d818e5cb0aef8f010211b8f59d6c5991b6b9","target":"record","created_at":"2026-07-04T14:36:13Z","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":"7395c4fef0df0f018f473b21a5f0525ff32e2db4cbb57af53b7215ce55633cac","cross_cats_sorted":["math.RA"],"license":"","primary_cat":"math.QA","submitted_at":"2002-05-25T18:48:11Z","title_canon_sha256":"8791f0a6429a37e4193ac1ef289ab57fc777048bf12dcfd6a722a2f59af80c77"},"schema_version":"1.0","source":{"id":"math/0205267","kind":"arxiv","version":3}},"canonical_sha256":"eb2df32b97a66d28efec3297516600e80686dcbcb4acb33544ab25e20c355a0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb2df32b97a66d28efec3297516600e80686dcbcb4acb33544ab25e20c355a0c","first_computed_at":"2026-07-04T14:36:13.723111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:13.723111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vCPrVUlcK/qGtfWG1L6jLe24/hQFrwIhH5SxgvD8x3XEuQEX6YYYGQH1yLUU4QJQMBNmQwN/kEzB8HsoX7fYBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:13.723544Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205267","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56820403ceb16c8823ebc0740209d818e5cb0aef8f010211b8f59d6c5991b6b9","sha256:81d258ccd2c03a1c066832c6acf3c8a0a27ba473399b667145a63bf64117dbcf"],"state_sha256":"bfd76ad12c1e4700ee11cab95a95b25506641545341dd16155fdfd50e5b286f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W5dgcKYHxRHKXLsw0onFYve/g6fKY/YaPlGsu95i+xs7qwzwx0FlcxDQoP8wpfpwIJRAOqLzO/CfbFKADVy8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:29:57.749911Z","bundle_sha256":"5d36b27afb9ba360861c56fe8f7c8c9f2e42883dddd7f258ecf9891d0d456b1b"}}