{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:JFROX4T5Y5TWCXNGJ6KG7C53OF","short_pith_number":"pith:JFROX4T5","schema_version":"1.0","canonical_sha256":"4962ebf27dc767615da64f946f8bbb71434558fabb66063bf5b9f649500f296b","source":{"kind":"arxiv","id":"math/0207021","version":2},"attestation_state":"computed","paper":{"title":"Dirichlet branes, homological mirror symmetry, and stability","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Michael R. Douglas (Rutgers/INI/IHES)","submitted_at":"2002-07-02T16:32:57Z","abstract_excerpt":"We discuss some mathematical conjectures which have come out of the Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich's homological mirror symmetry conjecture, and \"physics proofs\" for many of the subsequent conjectures based on it, such as the representation of Calabi-Yau monodromy by autoequivalences of the derived category."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0207021","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2002-07-02T16:32:57Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"e7f4de04c43f913ef5cf308d2ff4a13d42c0d41564e0374b829c33b73873a871","abstract_canon_sha256":"3e514af519284cadac3c929271964809a7d1e406b2298e87daa9e325e3ccbd17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:24:46.430272Z","signature_b64":"OyNn9ANcR2jXt/OtP3V06t8Ckzw3n8WaiVmnaYR75DjuiWO+Dv5h1U+/V5i6TQA878F8ODBHIfnLWh9CdF+TAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4962ebf27dc767615da64f946f8bbb71434558fabb66063bf5b9f649500f296b","last_reissued_at":"2026-07-05T02:24:46.429888Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:24:46.429888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirichlet branes, homological mirror symmetry, and stability","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Michael R. Douglas (Rutgers/INI/IHES)","submitted_at":"2002-07-02T16:32:57Z","abstract_excerpt":"We discuss some mathematical conjectures which have come out of the Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich's homological mirror symmetry conjecture, and \"physics proofs\" for many of the subsequent conjectures based on it, such as the representation of Calabi-Yau monodromy by autoequivalences of the derived category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207021","kind":"arxiv","version":2},"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/0207021/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0207021","created_at":"2026-07-05T02:24:46.429944+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0207021v2","created_at":"2026-07-05T02:24:46.429944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0207021","created_at":"2026-07-05T02:24:46.429944+00:00"},{"alias_kind":"pith_short_12","alias_value":"JFROX4T5Y5TW","created_at":"2026-07-05T02:24:46.429944+00:00"},{"alias_kind":"pith_short_16","alias_value":"JFROX4T5Y5TWCXNG","created_at":"2026-07-05T02:24:46.429944+00:00"},{"alias_kind":"pith_short_8","alias_value":"JFROX4T5","created_at":"2026-07-05T02:24:46.429944+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.15251","citing_title":"Stability conditions on the canonical line bundle of $\\mathbb{P}^3$","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF","json":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF.json","graph_json":"https://pith.science/api/pith-number/JFROX4T5Y5TWCXNGJ6KG7C53OF/graph.json","events_json":"https://pith.science/api/pith-number/JFROX4T5Y5TWCXNGJ6KG7C53OF/events.json","paper":"https://pith.science/paper/JFROX4T5"},"agent_actions":{"view_html":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF","download_json":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF.json","view_paper":"https://pith.science/paper/JFROX4T5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0207021&json=true","fetch_graph":"https://pith.science/api/pith-number/JFROX4T5Y5TWCXNGJ6KG7C53OF/graph.json","fetch_events":"https://pith.science/api/pith-number/JFROX4T5Y5TWCXNGJ6KG7C53OF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF/action/storage_attestation","attest_author":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF/action/author_attestation","sign_citation":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF/action/citation_signature","submit_replication":"https://pith.science/pith/JFROX4T5Y5TWCXNGJ6KG7C53OF/action/replication_record"}},"created_at":"2026-07-05T02:24:46.429944+00:00","updated_at":"2026-07-05T02:24:46.429944+00:00"}