{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:IRKEFEQNUV33PEWPTUJXU6LPTQ","short_pith_number":"pith:IRKEFEQN","canonical_record":{"source":{"id":"2004.07374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-15T22:15:03Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"136a57963c2b31100169d8a6a219010440adf7f453421a46ad1e0b41a06a8c2d","abstract_canon_sha256":"937b760c78f5ad9323bb694ad0895555f354b4f3c1b00807b03a9571d406af47"},"schema_version":"1.0"},"canonical_sha256":"445442920da577b792cf9d137a796f9c18afb976711132904cfb9ad6abfad911","source":{"kind":"arxiv","id":"2004.07374","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.07374","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"2004.07374v2","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.07374","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"IRKEFEQNUV33","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_16","alias_value":"IRKEFEQNUV33PEWP","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_8","alias_value":"IRKEFEQN","created_at":"2026-07-05T02:14:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:IRKEFEQNUV33PEWPTUJXU6LPTQ","target":"record","payload":{"canonical_record":{"source":{"id":"2004.07374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-15T22:15:03Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"136a57963c2b31100169d8a6a219010440adf7f453421a46ad1e0b41a06a8c2d","abstract_canon_sha256":"937b760c78f5ad9323bb694ad0895555f354b4f3c1b00807b03a9571d406af47"},"schema_version":"1.0"},"canonical_sha256":"445442920da577b792cf9d137a796f9c18afb976711132904cfb9ad6abfad911","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:09.835074Z","signature_b64":"0ylDtnM1WRHU1UFY8WfLs9+aG5p/rH2fRUkchNPnPi6tjj763mmMVf5Gw20vJxuCgQeJmdseKA8Dtu0ISa2cBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"445442920da577b792cf9d137a796f9c18afb976711132904cfb9ad6abfad911","last_reissued_at":"2026-07-05T02:14:09.834675Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:09.834675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.07374","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOHKsXNkO0RcS82I3jbjUERl4NeLIyjYngTkjZ5nMFyTrLOGS1otTDQYAXjXoVFuc7p12+f28ytAWR5Fb4zdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:53:59.766160Z"},"content_sha256":"8019640604b0deb2d29808bb47f7e051bca90d2fff66d3df609576cc57333574","schema_version":"1.0","event_id":"sha256:8019640604b0deb2d29808bb47f7e051bca90d2fff66d3df609576cc57333574"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:IRKEFEQNUV33PEWPTUJXU6LPTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homological mirror symmetry for Milnor fibers of simple singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Kazushi Ueda, Yanki Lekili","submitted_at":"2020-04-15T22:15:03Z","abstract_excerpt":"We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix factorizations and Calabi--Yau completions. As an application, we give an explicit computation of the Hochschild cohomology group of the derived $n$-preprojective algebra of a Dynkin quiver for any $n \\geq 1$, and the symplectic cohomology group of the Milnor fiber of any simple singularity in any dimension greater than one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.07374","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/2004.07374/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BAHpNiTYhUCFD8nhcFruGmmXjUtBogD+1b/QFzGR5ywhCm4Li8Yt+Qtg4v+8Zn/OU4BaaLTpB5C8Oi6frIqMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:53:59.766708Z"},"content_sha256":"ce6ecb86b2398ed77a380ec5611d75cc1b691e5c98c0cf170f916badf205ba21","schema_version":"1.0","event_id":"sha256:ce6ecb86b2398ed77a380ec5611d75cc1b691e5c98c0cf170f916badf205ba21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ/bundle.json","state_url":"https://pith.science/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ/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":"2026-08-12T14:53:59Z","links":{"resolver":"https://pith.science/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ","bundle":"https://pith.science/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ/bundle.json","state":"https://pith.science/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IRKEFEQNUV33PEWPTUJXU6LPTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:IRKEFEQNUV33PEWPTUJXU6LPTQ","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":"937b760c78f5ad9323bb694ad0895555f354b4f3c1b00807b03a9571d406af47","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-15T22:15:03Z","title_canon_sha256":"136a57963c2b31100169d8a6a219010440adf7f453421a46ad1e0b41a06a8c2d"},"schema_version":"1.0","source":{"id":"2004.07374","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.07374","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"2004.07374v2","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.07374","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"IRKEFEQNUV33","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_16","alias_value":"IRKEFEQNUV33PEWP","created_at":"2026-07-05T02:14:09Z"},{"alias_kind":"pith_short_8","alias_value":"IRKEFEQN","created_at":"2026-07-05T02:14:09Z"}],"graph_snapshots":[{"event_id":"sha256:ce6ecb86b2398ed77a380ec5611d75cc1b691e5c98c0cf170f916badf205ba21","target":"graph","created_at":"2026-07-05T02:14:09Z","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/2004.07374/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix factorizations and Calabi--Yau completions. As an application, we give an explicit computation of the Hochschild cohomology group of the derived $n$-preprojective algebra of a Dynkin quiver for any $n \\geq 1$, and the symplectic cohomology group of the Milnor fiber of any simple singularity in any dimension greater than one.","authors_text":"Kazushi Ueda, Yanki Lekili","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-15T22:15:03Z","title":"Homological mirror symmetry for Milnor fibers of simple singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.07374","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":"sha256:8019640604b0deb2d29808bb47f7e051bca90d2fff66d3df609576cc57333574","target":"record","created_at":"2026-07-05T02:14:09Z","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":"937b760c78f5ad9323bb694ad0895555f354b4f3c1b00807b03a9571d406af47","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-15T22:15:03Z","title_canon_sha256":"136a57963c2b31100169d8a6a219010440adf7f453421a46ad1e0b41a06a8c2d"},"schema_version":"1.0","source":{"id":"2004.07374","kind":"arxiv","version":2}},"canonical_sha256":"445442920da577b792cf9d137a796f9c18afb976711132904cfb9ad6abfad911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"445442920da577b792cf9d137a796f9c18afb976711132904cfb9ad6abfad911","first_computed_at":"2026-07-05T02:14:09.834675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:09.834675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ylDtnM1WRHU1UFY8WfLs9+aG5p/rH2fRUkchNPnPi6tjj763mmMVf5Gw20vJxuCgQeJmdseKA8Dtu0ISa2cBA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:09.835074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.07374","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8019640604b0deb2d29808bb47f7e051bca90d2fff66d3df609576cc57333574","sha256:ce6ecb86b2398ed77a380ec5611d75cc1b691e5c98c0cf170f916badf205ba21"],"state_sha256":"adf78a419a4907b604547cccc3363f9fd0971766a0baeebadeaac3c1eea28881"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P+MvhLnoUa6GiY0ruRyNVAGgkPrjyDJuT1RqJY0NR9BtMvO+Xtvj+1Nj4J6x+rIO23R+d3ETkUtNwttgbewsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:53:59.770747Z","bundle_sha256":"94c45e4bddf912f19c53d81f56b21ca3041409234075f6b381816b3ed0f38938"}}