{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:CRYDPFHXCQDCYJ7USJ55HHBE7K","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":"99f6ed0a8212271206129b1cb275cd8ff49b0d013b02d63e16e3a335c0215b6d","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-10-02T16:49:24Z","title_canon_sha256":"ce9547755f8850e2bb1055aec1e78f34668f7620eb74c8bd1ff91995ddab12fb"},"schema_version":"1.0","source":{"id":"alg-geom/9310001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9310001","created_at":"2026-07-04T15:08:01Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9310001v1","created_at":"2026-07-04T15:08:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9310001","created_at":"2026-07-04T15:08:01Z"},{"alias_kind":"pith_short_12","alias_value":"CRYDPFHXCQDC","created_at":"2026-07-04T15:08:01Z"},{"alias_kind":"pith_short_16","alias_value":"CRYDPFHXCQDCYJ7U","created_at":"2026-07-04T15:08:01Z"},{"alias_kind":"pith_short_8","alias_value":"CRYDPFHX","created_at":"2026-07-04T15:08:01Z"}],"graph_snapshots":[{"event_id":"sha256:82254264f9fbfbf860de77a5753a05ea4c66353ac9473dad317f23490dbd5d79","target":"graph","created_at":"2026-07-04T15:08:01Z","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/alg-geom/9310001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction is a generalization of the polar duality proposed by Batyrev for the case of hypersurfaces.","authors_text":"Lev Borisov","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1993-10-02T16:49:24Z","title":"Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9310001","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":"sha256:576721edc49ecf075b090e5236df31580890fd699ec6ee87df1000d8814d0ead","target":"record","created_at":"2026-07-04T15:08:01Z","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":"99f6ed0a8212271206129b1cb275cd8ff49b0d013b02d63e16e3a335c0215b6d","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-10-02T16:49:24Z","title_canon_sha256":"ce9547755f8850e2bb1055aec1e78f34668f7620eb74c8bd1ff91995ddab12fb"},"schema_version":"1.0","source":{"id":"alg-geom/9310001","kind":"arxiv","version":1}},"canonical_sha256":"14703794f714062c27f4927bd39c24fa863ccaf3e1e487ad99283d1cdd561191","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14703794f714062c27f4927bd39c24fa863ccaf3e1e487ad99283d1cdd561191","first_computed_at":"2026-07-04T15:08:01.583829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:01.583829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rs+p2V81FLyzAfZWpEMn/ZwWFIaZmELSVRx1Bg11bV7LSfL54iBQ+F8QK34AZjLqDMjh07pIUURGR1Rkw0nYBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:01.584212Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9310001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:576721edc49ecf075b090e5236df31580890fd699ec6ee87df1000d8814d0ead","sha256:82254264f9fbfbf860de77a5753a05ea4c66353ac9473dad317f23490dbd5d79"],"state_sha256":"876f08870d7466ecadf287040fc8890e1e8cf9af7b933577400c38b4e292636a"}