{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4L4USLQ44P3HQZLD3YKRBAH7AZ","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":"dede1334129b94f973f3a5bfd8761d215e8a994ff4a8413192454349b301aad5","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-19T13:59:59Z","title_canon_sha256":"eacf62ed22c77f178cf17d0bad4cfe80d79cf83567f3d82680947012418c465c"},"schema_version":"1.0","source":{"id":"1709.06434","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06434","created_at":"2026-05-17T23:46:50Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06434v2","created_at":"2026-05-17T23:46:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06434","created_at":"2026-05-17T23:46:50Z"},{"alias_kind":"pith_short_12","alias_value":"4L4USLQ44P3H","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4L4USLQ44P3HQZLD","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4L4USLQ4","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:d7ff89edeead1211f199767a26252f03765b85b220432483a42d21e30762bd09","target":"graph","created_at":"2026-05-17T23:46:50Z","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":"We show that a $\\mathbb{P}$-object and simple configurations of $\\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. We also observe that the category generated by the structure sheaf of a smooth projective variety over the complex numbers only depends on its graded cohomology algebra.","authors_text":"Andreas Hochenegger, Andreas Krug","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-19T13:59:59Z","title":"Formality of $\\mathbb{P}$-objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06434","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":"sha256:223e14a4cec1c4eda36158a4043ad5955f7b2201af9218b1040a853c97c6d800","target":"record","created_at":"2026-05-17T23:46:50Z","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":"dede1334129b94f973f3a5bfd8761d215e8a994ff4a8413192454349b301aad5","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-19T13:59:59Z","title_canon_sha256":"eacf62ed22c77f178cf17d0bad4cfe80d79cf83567f3d82680947012418c465c"},"schema_version":"1.0","source":{"id":"1709.06434","kind":"arxiv","version":2}},"canonical_sha256":"e2f9492e1ce3f6786563de151080ff0655db7b9c5ce1ef1a4a3d87ca5d95399a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2f9492e1ce3f6786563de151080ff0655db7b9c5ce1ef1a4a3d87ca5d95399a","first_computed_at":"2026-05-17T23:46:50.528299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:50.528299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OwwDxSd8iZ2jofCkpHNCWly5Vc52Q5ol6uN8SaX+z1bSpDyChwmBYX7bFxI7LkvjNblVOpVP0yINWTSRTsmiCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:50.528874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06434","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:223e14a4cec1c4eda36158a4043ad5955f7b2201af9218b1040a853c97c6d800","sha256:d7ff89edeead1211f199767a26252f03765b85b220432483a42d21e30762bd09"],"state_sha256":"266f7cd6af3dd305febfa28fe00beb33c92617941a495b756085e4d655d9b0ec"}