{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:HIBSI375B53U45YBAMCW42ULZD","short_pith_number":"pith:HIBSI375","canonical_record":{"source":{"id":"math/0604150","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-04-06T18:34:32Z","cross_cats_sorted":[],"title_canon_sha256":"2fd25a5e82efe61963048de108bf4b66041495a0fb54ea10eb1522b3fa69ed5a","abstract_canon_sha256":"3bf9c43af4c8e7102d1c37c885c084cf90a2b7bb2a6096c25eda1bf19527c502"},"schema_version":"1.0"},"canonical_sha256":"3a03246ffd0f774e770103056e6a8bc8cd40520f4dc55bf6e7137a7befb3eb1d","source":{"kind":"arxiv","id":"math/0604150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604150","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604150v1","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604150","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"HIBSI375B53U","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HIBSI375B53U45YB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HIBSI375","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:HIBSI375B53U45YBAMCW42ULZD","target":"record","payload":{"canonical_record":{"source":{"id":"math/0604150","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-04-06T18:34:32Z","cross_cats_sorted":[],"title_canon_sha256":"2fd25a5e82efe61963048de108bf4b66041495a0fb54ea10eb1522b3fa69ed5a","abstract_canon_sha256":"3bf9c43af4c8e7102d1c37c885c084cf90a2b7bb2a6096c25eda1bf19527c502"},"schema_version":"1.0"},"canonical_sha256":"3a03246ffd0f774e770103056e6a8bc8cd40520f4dc55bf6e7137a7befb3eb1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:34.477090Z","signature_b64":"q4HNI5nxQ9+10jWm8WaQ7gReaX2oimrL42aiEXRNzu/ozgvjhe1dC2Z1iEpUOfU2YuunwAWqBAPKOAYv5Es+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a03246ffd0f774e770103056e6a8bc8cd40520f4dc55bf6e7137a7befb3eb1d","last_reissued_at":"2026-05-18T03:13:34.476438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:34.476438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0604150","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hpm1QvWj2h1uuiTF5HyS9rji1ggVcjLTWOylDMnvzVjyocCAaJI3P66UfXIO1Sw5aAHxjMzFtyciayCtmTopCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:51:28.754162Z"},"content_sha256":"9ccbc44662acc03897a59e0b5af10752e139f71e9d0ea70d3e26d6370e4eeedc","schema_version":"1.0","event_id":"sha256:9ccbc44662acc03897a59e0b5af10752e139f71e9d0ea70d3e26d6370e4eeedc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:HIBSI375B53U45YBAMCW42ULZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived and abelian equivalence of K3 surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Huybrechts","submitted_at":"2006-04-06T18:34:32Z","abstract_excerpt":"Tom Bridgeland constructed explicit stability conditions on K3 surfaces. This paper attempts to shed more light on these particular examples, especially on the hearts of the underlying t-structures.\n  We prove that two K3 surfaces X and X' are derived equivalent if and only if there exist complexified polarizations B+iw and B'+iw' such that the associated abelian categories A(B+iw) and A(B'+iw') are equivalent. We study in detail the minimal objects of A(B+iw) and investigate stability under Fourier-Mukai transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604150","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"08XJa8BJhsAsVOQon6tz+mEc5SihasI08LqQXf8Aw8HFEH6LI5xff7DFpk4/nsD6wp4mMQeWZVZzaJjDP7cYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:51:28.754699Z"},"content_sha256":"66eca2697b3b668cb99d60c0251f175adbc4e552d1afe8b074f18b2c03c7d4f9","schema_version":"1.0","event_id":"sha256:66eca2697b3b668cb99d60c0251f175adbc4e552d1afe8b074f18b2c03c7d4f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIBSI375B53U45YBAMCW42ULZD/bundle.json","state_url":"https://pith.science/pith/HIBSI375B53U45YBAMCW42ULZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIBSI375B53U45YBAMCW42ULZD/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":"2026-06-23T18:51:28Z","links":{"resolver":"https://pith.science/pith/HIBSI375B53U45YBAMCW42ULZD","bundle":"https://pith.science/pith/HIBSI375B53U45YBAMCW42ULZD/bundle.json","state":"https://pith.science/pith/HIBSI375B53U45YBAMCW42ULZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIBSI375B53U45YBAMCW42ULZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:HIBSI375B53U45YBAMCW42ULZD","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":"3bf9c43af4c8e7102d1c37c885c084cf90a2b7bb2a6096c25eda1bf19527c502","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2006-04-06T18:34:32Z","title_canon_sha256":"2fd25a5e82efe61963048de108bf4b66041495a0fb54ea10eb1522b3fa69ed5a"},"schema_version":"1.0","source":{"id":"math/0604150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604150","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604150v1","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604150","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"HIBSI375B53U","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HIBSI375B53U45YB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HIBSI375","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:66eca2697b3b668cb99d60c0251f175adbc4e552d1afe8b074f18b2c03c7d4f9","target":"graph","created_at":"2026-05-18T03:13:34Z","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"},"paper":{"abstract_excerpt":"Tom Bridgeland constructed explicit stability conditions on K3 surfaces. This paper attempts to shed more light on these particular examples, especially on the hearts of the underlying t-structures.\n  We prove that two K3 surfaces X and X' are derived equivalent if and only if there exist complexified polarizations B+iw and B'+iw' such that the associated abelian categories A(B+iw) and A(B'+iw') are equivalent. We study in detail the minimal objects of A(B+iw) and investigate stability under Fourier-Mukai transform.","authors_text":"Daniel Huybrechts","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2006-04-06T18:34:32Z","title":"Derived and abelian equivalence of K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604150","kind":"arxiv","version":1},"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":"sha256:9ccbc44662acc03897a59e0b5af10752e139f71e9d0ea70d3e26d6370e4eeedc","target":"record","created_at":"2026-05-18T03:13:34Z","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":"3bf9c43af4c8e7102d1c37c885c084cf90a2b7bb2a6096c25eda1bf19527c502","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2006-04-06T18:34:32Z","title_canon_sha256":"2fd25a5e82efe61963048de108bf4b66041495a0fb54ea10eb1522b3fa69ed5a"},"schema_version":"1.0","source":{"id":"math/0604150","kind":"arxiv","version":1}},"canonical_sha256":"3a03246ffd0f774e770103056e6a8bc8cd40520f4dc55bf6e7137a7befb3eb1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a03246ffd0f774e770103056e6a8bc8cd40520f4dc55bf6e7137a7befb3eb1d","first_computed_at":"2026-05-18T03:13:34.476438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:34.476438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4HNI5nxQ9+10jWm8WaQ7gReaX2oimrL42aiEXRNzu/ozgvjhe1dC2Z1iEpUOfU2YuunwAWqBAPKOAYv5Es+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:34.477090Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ccbc44662acc03897a59e0b5af10752e139f71e9d0ea70d3e26d6370e4eeedc","sha256:66eca2697b3b668cb99d60c0251f175adbc4e552d1afe8b074f18b2c03c7d4f9"],"state_sha256":"d9840efe1bf5f91779d1246b6968b13e196a5ca0c7c40688f3dace240bd9d757"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGuWjNa1h/1sCvTFX1XzrdcjieUG/7H2vaiD8XAoHSpklFZuwZcotZPRKDU9gcswq+MySTe0SJPp3iF50wpOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:51:28.757381Z","bundle_sha256":"e6dc42d6edff8cdb0cf7e6ac69a2630fddacc94f7ce6c8be476da8c60f998ac0"}}