{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:SFJYV4JH56ZXYZWGTUIOE4DEOL","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":"40990ab84e26b68ce6696aac0bad7a0dd17f88a8c3cf1076a1888c73421ee2ee","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-07-24T16:11:58Z","title_canon_sha256":"b217ae4fe8230d8db655104bb53cc2c00026c69fcc2b72997650bf5f12c40d0c"},"schema_version":"1.0","source":{"id":"hep-th/0307245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0307245","created_at":"2026-07-04T14:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0307245v2","created_at":"2026-07-04T14:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0307245","created_at":"2026-07-04T14:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"SFJYV4JH56ZX","created_at":"2026-07-04T14:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"SFJYV4JH56ZXYZWG","created_at":"2026-07-04T14:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"SFJYV4JH","created_at":"2026-07-04T14:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:df00f7f371fa34c0b4249e348a3d4543c345b81b378e22896b677d2bd84fb00d","target":"graph","created_at":"2026-07-04T14:31:59Z","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/hep-th/0307245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These notes are a writeup of lectures given at the twelfth Oporto meeting on ``Geometry, Topology, and Physics,'' and at the Adelaide workshop ``Strings and Mathematics 2003,'' primarily geared towards a physics audience. We review current work relating boundary states in the open string B model on Calabi-Yau manifolds to sheaves. Such relationships provide us with a mechanism for counting open string states in situations where the physical spectrum calculation is nearly intractable -- after translating to mathematics, such calculations become easy. We describe several different approaches to ","authors_text":"E. Sharpe","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2003-07-24T16:11:58Z","title":"Lectures on D-branes and Sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0307245","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":"sha256:4ae0a6a91ab5d46f9d39692670e9f683db3af548d97ec25f824fe89bdf860bd7","target":"record","created_at":"2026-07-04T14:31:59Z","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":"40990ab84e26b68ce6696aac0bad7a0dd17f88a8c3cf1076a1888c73421ee2ee","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2003-07-24T16:11:58Z","title_canon_sha256":"b217ae4fe8230d8db655104bb53cc2c00026c69fcc2b72997650bf5f12c40d0c"},"schema_version":"1.0","source":{"id":"hep-th/0307245","kind":"arxiv","version":2}},"canonical_sha256":"91538af127efb37c66c69d10e2706472e840acb40d515c6e68519ebffac38f10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91538af127efb37c66c69d10e2706472e840acb40d515c6e68519ebffac38f10","first_computed_at":"2026-07-04T14:31:59.742591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:31:59.742591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/zLcIwjOmxSpvQwKehzOG3UaRN2EO+rDzyK0nTnyQj98Hfks+xvO065FrD7KjUjrd+khrRgSrjPdgSx/8iILDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:31:59.742980Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0307245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ae0a6a91ab5d46f9d39692670e9f683db3af548d97ec25f824fe89bdf860bd7","sha256:df00f7f371fa34c0b4249e348a3d4543c345b81b378e22896b677d2bd84fb00d"],"state_sha256":"49bb41573a042e5a98ff21e0018a0dc2ef218e3e7c0cd8b7a454d47a2a4eaff0"}