{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:EO7TDRVUPIC25CZMZ2SM4DKQMZ","short_pith_number":"pith:EO7TDRVU","canonical_record":{"source":{"id":"0907.2063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-07-12T20:46:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d53673894381cf84cc9b53241cffcdedfd7734ccbb1c0f211bd3542a962d77e1","abstract_canon_sha256":"4ccfe0bd6b325b3118da08818f06f72f40a16fb7825a2414aa0046ff5c0ec4e4"},"schema_version":"1.0"},"canonical_sha256":"23bf31c6b47a05ae8b2ccea4ce0d506650442d7720fb246a30cbd1bbab8b9320","source":{"kind":"arxiv","id":"0907.2063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2063","created_at":"2026-05-18T02:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2063v2","created_at":"2026-05-18T02:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2063","created_at":"2026-05-18T02:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"EO7TDRVUPIC2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EO7TDRVUPIC25CZM","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EO7TDRVU","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:EO7TDRVUPIC25CZMZ2SM4DKQMZ","target":"record","payload":{"canonical_record":{"source":{"id":"0907.2063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-07-12T20:46:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d53673894381cf84cc9b53241cffcdedfd7734ccbb1c0f211bd3542a962d77e1","abstract_canon_sha256":"4ccfe0bd6b325b3118da08818f06f72f40a16fb7825a2414aa0046ff5c0ec4e4"},"schema_version":"1.0"},"canonical_sha256":"23bf31c6b47a05ae8b2ccea4ce0d506650442d7720fb246a30cbd1bbab8b9320","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:03.631649Z","signature_b64":"F9GhfrvsRY0PYXYv/IOJOzcO/yusVW+k9M7Z84mObW4K3vIO/znLL7rP35VV6zup7cBI3lXxmtRKPalsriItBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23bf31c6b47a05ae8b2ccea4ce0d506650442d7720fb246a30cbd1bbab8b9320","last_reissued_at":"2026-05-18T02:13:03.631063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:03.631063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.2063","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":"2026-05-18T02:13:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qAR+b6Zi0TSyiMyYSdMXfyh1qyGOft21A3Plet4UmoG3JPeuW1Alu+LEuy8dy9XG/sKzEVb4CDs3WkhPp1UDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:17:33.301932Z"},"content_sha256":"0bf6fca85ca87ff44c9ee7143294c6f4c503834a48990159808814174352dcb6","schema_version":"1.0","event_id":"sha256:0bf6fca85ca87ff44c9ee7143294c6f4c503834a48990159808814174352dcb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:EO7TDRVUPIC25CZMZ2SM4DKQMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Paul Seidel","submitted_at":"2009-07-12T20:46:50Z","abstract_excerpt":"We consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y^2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2063","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":""},"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":"2026-05-18T02:13:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAQz/oDAvsNJb4SQQy+r0J0ops8OQ4GcNMysX84DXQZBlIzNBLY194NsysKMRCzpxZIq4dOahujOQ3m2/0mFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:17:33.302263Z"},"content_sha256":"75a93839183fcdb28815e3bbc43789ef789c68ad0896f29810dc05fa99b69be9","schema_version":"1.0","event_id":"sha256:75a93839183fcdb28815e3bbc43789ef789c68ad0896f29810dc05fa99b69be9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ/bundle.json","state_url":"https://pith.science/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ/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":"2026-06-28T10:17:33Z","links":{"resolver":"https://pith.science/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ","bundle":"https://pith.science/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ/bundle.json","state":"https://pith.science/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EO7TDRVUPIC25CZMZ2SM4DKQMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EO7TDRVUPIC25CZMZ2SM4DKQMZ","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":"4ccfe0bd6b325b3118da08818f06f72f40a16fb7825a2414aa0046ff5c0ec4e4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-07-12T20:46:50Z","title_canon_sha256":"d53673894381cf84cc9b53241cffcdedfd7734ccbb1c0f211bd3542a962d77e1"},"schema_version":"1.0","source":{"id":"0907.2063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2063","created_at":"2026-05-18T02:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2063v2","created_at":"2026-05-18T02:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2063","created_at":"2026-05-18T02:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"EO7TDRVUPIC2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EO7TDRVUPIC25CZM","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EO7TDRVU","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:75a93839183fcdb28815e3bbc43789ef789c68ad0896f29810dc05fa99b69be9","target":"graph","created_at":"2026-05-18T02:13:03Z","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 consider the suspension operation on Lefschetz fibrations, which takes p(x) to p(x)-y^2. This leaves the Fukaya category of the fibration invariant, and changes the category of the fibre (or more precisely, the subcategory consisting of a basis of vanishing cycles) in a specific way. As an application, we prove part of Homological Mirror Symmetry for the total spaces of canonical bundles over toric del Pezzo surfaces.","authors_text":"Paul Seidel","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-07-12T20:46:50Z","title":"Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2063","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":"sha256:0bf6fca85ca87ff44c9ee7143294c6f4c503834a48990159808814174352dcb6","target":"record","created_at":"2026-05-18T02:13:03Z","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":"4ccfe0bd6b325b3118da08818f06f72f40a16fb7825a2414aa0046ff5c0ec4e4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-07-12T20:46:50Z","title_canon_sha256":"d53673894381cf84cc9b53241cffcdedfd7734ccbb1c0f211bd3542a962d77e1"},"schema_version":"1.0","source":{"id":"0907.2063","kind":"arxiv","version":2}},"canonical_sha256":"23bf31c6b47a05ae8b2ccea4ce0d506650442d7720fb246a30cbd1bbab8b9320","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23bf31c6b47a05ae8b2ccea4ce0d506650442d7720fb246a30cbd1bbab8b9320","first_computed_at":"2026-05-18T02:13:03.631063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:03.631063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F9GhfrvsRY0PYXYv/IOJOzcO/yusVW+k9M7Z84mObW4K3vIO/znLL7rP35VV6zup7cBI3lXxmtRKPalsriItBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:03.631649Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bf6fca85ca87ff44c9ee7143294c6f4c503834a48990159808814174352dcb6","sha256:75a93839183fcdb28815e3bbc43789ef789c68ad0896f29810dc05fa99b69be9"],"state_sha256":"7f6cd842d921f6f2d8745b7125efedf7b337f08cf9b6be8c2b810c65c6fdccbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I+DmrmbzaO71oepK22kEYqPOvmZQzzHw2UfBSbHbaJ8c3M6MJOOnbASfptsLwiKg1lx3MwEMxn6x3F2u/XykCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:17:33.304112Z","bundle_sha256":"29cd7339de12cb2026ca927d2f3a9597fdffdc0e78b5261df11af25dc68f3160"}}