{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CF2EZBDM6T3T5R2XD52RZNR4ML","short_pith_number":"pith:CF2EZBDM","schema_version":"1.0","canonical_sha256":"11744c846cf4f73ec7571f751cb63c62c42fd15e3d76a19d8f8301de99dd7b91","source":{"kind":"arxiv","id":"1009.4372","version":1},"attestation_state":"computed","paper":{"title":"Stability conditions via spherical objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Huybrechts","submitted_at":"2010-09-22T14:34:14Z","abstract_excerpt":"An object in the bounded derived category D^b(Coh(X)) of coherent sheaves on a complex projective K3 surface X is spherical if it is rigid and simple. Although spherical objects form only a discrete set in the moduli stack of complexes, they determine much of the structure of X and D^b(Coh(X)). Here we show that a stability condition on D^b(Coh(X)) is determined by the stability of spherical objects."},"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":"1009.4372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-22T14:34:14Z","cross_cats_sorted":[],"title_canon_sha256":"bfe23774e03c3c329e9b026caad2316166728c4bd5f03cc84c08b10f80b19d18","abstract_canon_sha256":"9926cc7a085adb2753f2caece6c345f722637dcc7cfe889eae526d7b557a6e21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:43.858214Z","signature_b64":"4wRJyOzLuONAWh1Lq0+n5BxrfqEAeAMvCVSDpZzJMtjCs5BZDAxhQi+5AOrAEWdwUCNTTPBq4qkEigd4P5Y3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11744c846cf4f73ec7571f751cb63c62c42fd15e3d76a19d8f8301de99dd7b91","last_reissued_at":"2026-05-18T03:13:43.857281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:43.857281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability conditions via spherical objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Huybrechts","submitted_at":"2010-09-22T14:34:14Z","abstract_excerpt":"An object in the bounded derived category D^b(Coh(X)) of coherent sheaves on a complex projective K3 surface X is spherical if it is rigid and simple. Although spherical objects form only a discrete set in the moduli stack of complexes, they determine much of the structure of X and D^b(Coh(X)). Here we show that a stability condition on D^b(Coh(X)) is determined by the stability of spherical objects."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4372","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":""},"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":"1009.4372","created_at":"2026-05-18T03:13:43.857480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4372v1","created_at":"2026-05-18T03:13:43.857480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4372","created_at":"2026-05-18T03:13:43.857480+00:00"},{"alias_kind":"pith_short_12","alias_value":"CF2EZBDM6T3T","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CF2EZBDM6T3T5R2X","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CF2EZBDM","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML","json":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML.json","graph_json":"https://pith.science/api/pith-number/CF2EZBDM6T3T5R2XD52RZNR4ML/graph.json","events_json":"https://pith.science/api/pith-number/CF2EZBDM6T3T5R2XD52RZNR4ML/events.json","paper":"https://pith.science/paper/CF2EZBDM"},"agent_actions":{"view_html":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML","download_json":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML.json","view_paper":"https://pith.science/paper/CF2EZBDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4372&json=true","fetch_graph":"https://pith.science/api/pith-number/CF2EZBDM6T3T5R2XD52RZNR4ML/graph.json","fetch_events":"https://pith.science/api/pith-number/CF2EZBDM6T3T5R2XD52RZNR4ML/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML/action/storage_attestation","attest_author":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML/action/author_attestation","sign_citation":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML/action/citation_signature","submit_replication":"https://pith.science/pith/CF2EZBDM6T3T5R2XD52RZNR4ML/action/replication_record"}},"created_at":"2026-05-18T03:13:43.857480+00:00","updated_at":"2026-05-18T03:13:43.857480+00:00"}