{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:5OUVTOK2NSTCKXXC4DOFG2BPIZ","short_pith_number":"pith:5OUVTOK2","canonical_record":{"source":{"id":"math/0703267","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-09T14:53:27Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"3ff2c5b2422d90ea5a790c929418d5bf6037a5a762582d9414d59b772e537ac5","abstract_canon_sha256":"37a1bad595d45d8a330f1045f8b6767daf5ec62d264b917d9871392076f27be3"},"schema_version":"1.0"},"canonical_sha256":"eba959b95a6ca6255ee2e0dc53682f46585580f9fdf5d2979dff8a9a59527199","source":{"kind":"arxiv","id":"math/0703267","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703267","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703267v3","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703267","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"5OUVTOK2NSTC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5OUVTOK2NSTCKXXC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5OUVTOK2","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:5OUVTOK2NSTCKXXC4DOFG2BPIZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0703267","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-09T14:53:27Z","cross_cats_sorted":["hep-th","math.SG"],"title_canon_sha256":"3ff2c5b2422d90ea5a790c929418d5bf6037a5a762582d9414d59b772e537ac5","abstract_canon_sha256":"37a1bad595d45d8a330f1045f8b6767daf5ec62d264b917d9871392076f27be3"},"schema_version":"1.0"},"canonical_sha256":"eba959b95a6ca6255ee2e0dc53682f46585580f9fdf5d2979dff8a9a59527199","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:22.809614Z","signature_b64":"/IroyGQfDFgQYlerVSArFoTYzkdfVTrIp0jIsfIbNSjEkked5HnBqChOIXLdoAgfI0kSvN7+BGLjk86bTAQsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eba959b95a6ca6255ee2e0dc53682f46585580f9fdf5d2979dff8a9a59527199","last_reissued_at":"2026-05-18T03:19:22.809033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:22.809033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0703267","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8UJJHqPi8luo7mim156eMEBCTbe8LrODrv2v3CUB/t/DZ4Qb96twNz9hL0Xh5ivKcys0OZw7wQENFxZkGG50Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T18:37:10.670373Z"},"content_sha256":"a86b4b0ae4735d50a82f38e63adc94627a927423d73fc0b729939dcd3fca1d2d","schema_version":"1.0","event_id":"sha256:a86b4b0ae4735d50a82f38e63adc94627a927423d73fc0b729939dcd3fca1d2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:5OUVTOK2NSTCKXXC4DOFG2BPIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.AG","authors_text":"Kazushi Ueda, Masahito Yamazaki","submitted_at":"2007-03-09T14:53:27Z","abstract_excerpt":"We formulate a conjecture which describes the Fukaya category of an exact Lefschetz fibration defined by a Laurent polynomial in two variables in terms of a pair consisting of a consistent dimer model and a perfect matching on it. We prove this conjecture in some cases, and obtain homological mirror symmetry for quotient stacks of toric del Pezzo surfaces by finite subgroups of the torus as a corollary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703267","kind":"arxiv","version":3},"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":"2026-05-18T03:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pC2wBvKnoUzpjKzp5v0nePVCjBo4hW53oDxhEE0hUdUSb6HBQgS2PlYypjwpCaO4md3EzNONAi3w6o443PSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T18:37:10.670724Z"},"content_sha256":"7aa97ce5c0ac05b112271637d47809f0e96faf51b11a947bbf617120fd576176","schema_version":"1.0","event_id":"sha256:7aa97ce5c0ac05b112271637d47809f0e96faf51b11a947bbf617120fd576176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ/bundle.json","state_url":"https://pith.science/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ/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":"2026-05-20T18:37:10Z","links":{"resolver":"https://pith.science/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ","bundle":"https://pith.science/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ/bundle.json","state":"https://pith.science/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5OUVTOK2NSTCKXXC4DOFG2BPIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:5OUVTOK2NSTCKXXC4DOFG2BPIZ","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":"37a1bad595d45d8a330f1045f8b6767daf5ec62d264b917d9871392076f27be3","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-09T14:53:27Z","title_canon_sha256":"3ff2c5b2422d90ea5a790c929418d5bf6037a5a762582d9414d59b772e537ac5"},"schema_version":"1.0","source":{"id":"math/0703267","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703267","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703267v3","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703267","created_at":"2026-05-18T03:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"5OUVTOK2NSTC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5OUVTOK2NSTCKXXC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5OUVTOK2","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:7aa97ce5c0ac05b112271637d47809f0e96faf51b11a947bbf617120fd576176","target":"graph","created_at":"2026-05-18T03:19:22Z","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 formulate a conjecture which describes the Fukaya category of an exact Lefschetz fibration defined by a Laurent polynomial in two variables in terms of a pair consisting of a consistent dimer model and a perfect matching on it. We prove this conjecture in some cases, and obtain homological mirror symmetry for quotient stacks of toric del Pezzo surfaces by finite subgroups of the torus as a corollary.","authors_text":"Kazushi Ueda, Masahito Yamazaki","cross_cats":["hep-th","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-09T14:53:27Z","title":"Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703267","kind":"arxiv","version":3},"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:a86b4b0ae4735d50a82f38e63adc94627a927423d73fc0b729939dcd3fca1d2d","target":"record","created_at":"2026-05-18T03:19:22Z","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":"37a1bad595d45d8a330f1045f8b6767daf5ec62d264b917d9871392076f27be3","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-09T14:53:27Z","title_canon_sha256":"3ff2c5b2422d90ea5a790c929418d5bf6037a5a762582d9414d59b772e537ac5"},"schema_version":"1.0","source":{"id":"math/0703267","kind":"arxiv","version":3}},"canonical_sha256":"eba959b95a6ca6255ee2e0dc53682f46585580f9fdf5d2979dff8a9a59527199","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eba959b95a6ca6255ee2e0dc53682f46585580f9fdf5d2979dff8a9a59527199","first_computed_at":"2026-05-18T03:19:22.809033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:22.809033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/IroyGQfDFgQYlerVSArFoTYzkdfVTrIp0jIsfIbNSjEkked5HnBqChOIXLdoAgfI0kSvN7+BGLjk86bTAQsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:22.809614Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703267","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a86b4b0ae4735d50a82f38e63adc94627a927423d73fc0b729939dcd3fca1d2d","sha256:7aa97ce5c0ac05b112271637d47809f0e96faf51b11a947bbf617120fd576176"],"state_sha256":"c2face07771fa4d99c6c3ad68aebf5846975f23ef10f7692411d863c0ee965b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNNQiFoit9EbwNBbpogVF6jNZ1hvmTRwR8EuQnwwT/RVK3foaXcNNea72TQXAHQeLhavVLEymGu3+bEzbO1VBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T18:37:10.672829Z","bundle_sha256":"51df887d18e75fe5bc7042665069997a4333f71c539b3cc33d72cdf63752e619"}}