{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:5EL22LWMYOGGWUX6QEYIYB5PSG","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":"e517490f655dc0f135e88fae7474f1ba2dbe8cd654fafe9e02295f2cc531e4d5","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2006-11-20T20:28:14Z","title_canon_sha256":"23cda40cf2683f91881383ac8a924841d804a606acc4dfe881b5d6b60b15610b"},"schema_version":"1.0","source":{"id":"math/0611617","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611617","created_at":"2026-07-04T15:57:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611617v2","created_at":"2026-07-04T15:57:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611617","created_at":"2026-07-04T15:57:09Z"},{"alias_kind":"pith_short_12","alias_value":"5EL22LWMYOGG","created_at":"2026-07-04T15:57:09Z"},{"alias_kind":"pith_short_16","alias_value":"5EL22LWMYOGGWUX6","created_at":"2026-07-04T15:57:09Z"},{"alias_kind":"pith_short_8","alias_value":"5EL22LWM","created_at":"2026-07-04T15:57:09Z"}],"graph_snapshots":[{"event_id":"sha256:b396124c52cbdf85857a7351ac380c0df3ec94387a14ea9dfabc980828f31223","target":"graph","created_at":"2026-07-04T15:57:09Z","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/0611617/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These are notes for a minicourse on Hall algebras given at the ICTP in Trieste in January 2006. After giving the definition and first properties of Hall algebras, we study in some details the classical Hall algebra, the Hall algebra of quivers, and the Hall algebra of coherent sheaves on smooth projective curves. The last section deals with the Hall algebras in the context of derived categories. (The figures only seem to come out nicely in the .ps file)","authors_text":"Olivier Schiffmann","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2006-11-20T20:28:14Z","title":"Lectures on Hall algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611617","kind":"arxiv","version":2},"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":"sha256:85cac3b4ea520729b8265387c12852bae188d19b73b8f9426726ffad66b8f83b","target":"record","created_at":"2026-07-04T15:57:09Z","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":"e517490f655dc0f135e88fae7474f1ba2dbe8cd654fafe9e02295f2cc531e4d5","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2006-11-20T20:28:14Z","title_canon_sha256":"23cda40cf2683f91881383ac8a924841d804a606acc4dfe881b5d6b60b15610b"},"schema_version":"1.0","source":{"id":"math/0611617","kind":"arxiv","version":2}},"canonical_sha256":"e917ad2eccc38c6b52fe81308c07af919af986cbfe58d68be58e8213a879ab07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e917ad2eccc38c6b52fe81308c07af919af986cbfe58d68be58e8213a879ab07","first_computed_at":"2026-07-04T15:57:09.631379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:57:09.631379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wnReRNjrSTSpB0Jy0OglpKgV0NMhXDJNTdjOAPRAeyBhs1m3Jj2A75s9uU4z2e8NTByoMqBu9JEbbMOS8kyUCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:57:09.631733Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611617","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85cac3b4ea520729b8265387c12852bae188d19b73b8f9426726ffad66b8f83b","sha256:b396124c52cbdf85857a7351ac380c0df3ec94387a14ea9dfabc980828f31223"],"state_sha256":"2fb56c2b26f9ca98c70acc03cfa4de752ced823d87804512547aca35dfb002ce"}