{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CY23763A35TDFJ6WSIQXGRCLJ7","short_pith_number":"pith:CY23763A","canonical_record":{"source":{"id":"1307.5070","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-18T20:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"e6ae3d5a3b4be80f3da0263d966d3909e1fc9676b2cc68d89b7b89e6be2f6929","abstract_canon_sha256":"89d3c65fb5ea2d3f352714243cc9f209c3220d4d43afa91b2087c9591dfee5d5"},"schema_version":"1.0"},"canonical_sha256":"1635bffb60df6632a7d6922173444b4fe174bc728f6f5c073906f61124b468d7","source":{"kind":"arxiv","id":"1307.5070","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5070","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5070v4","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5070","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"CY23763A35TD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CY23763A35TDFJ6W","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CY23763A","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CY23763A35TDFJ6WSIQXGRCLJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5070","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-18T20:07:07Z","cross_cats_sorted":[],"title_canon_sha256":"e6ae3d5a3b4be80f3da0263d966d3909e1fc9676b2cc68d89b7b89e6be2f6929","abstract_canon_sha256":"89d3c65fb5ea2d3f352714243cc9f209c3220d4d43afa91b2087c9591dfee5d5"},"schema_version":"1.0"},"canonical_sha256":"1635bffb60df6632a7d6922173444b4fe174bc728f6f5c073906f61124b468d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:23.744625Z","signature_b64":"FZupTa9Vzg7BudVdeYExw3rijQ7jJeX/AFzXzFtj3KCI/eQHEMPx9mhOeMgFD0Bw3ABM5Mg9N1jvX0J7NaiUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1635bffb60df6632a7d6922173444b4fe174bc728f6f5c073906f61124b468d7","last_reissued_at":"2026-05-18T00:50:23.743918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:23.743918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5070","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tj3LmAUK4tQ7tue/Y6b/hdUNpzt37+FE3aB2CmapvHwt/sPHTsoBuTlUxqsrzrSeMoDXw0J5WuSWIwL+gG7YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:56:53.056272Z"},"content_sha256":"ea0005d90d66bc917e86cd8f087f9f56d930a7cabf97cb87a3ff73b42b42e8ae","schema_version":"1.0","event_id":"sha256:ea0005d90d66bc917e86cd8f087f9f56d930a7cabf97cb87a3ff73b42b42e8ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CY23763A35TDFJ6WSIQXGRCLJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Landau--Ginzburg mirror theorem without concavity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J\\'er\\'emy Gu\\'er\\'e","submitted_at":"2013-07-18T20:07:07Z","abstract_excerpt":"We provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory and viewed as the counterpart of a non-convex Gromov--Witten potential via the physical LG/CY correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob's virtual cycle in genus zero. In the non-concave case of the so-called chain invertible polynomials, it yields a compatibility theorem with the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5070","kind":"arxiv","version":4},"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":"2026-05-18T00:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npBVMkw4zVV/FPLC45he7X7DBeo7Oe8y66XEOFGn33poB7CHmcuAxc7Hg9TCuKoCpf8JaQVYGLwTM6V++BF9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:56:53.057066Z"},"content_sha256":"80ff9541e7b859f6c40b012b8d8cb717b628cc7e80484ccd16daa851eb467364","schema_version":"1.0","event_id":"sha256:80ff9541e7b859f6c40b012b8d8cb717b628cc7e80484ccd16daa851eb467364"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CY23763A35TDFJ6WSIQXGRCLJ7/bundle.json","state_url":"https://pith.science/pith/CY23763A35TDFJ6WSIQXGRCLJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CY23763A35TDFJ6WSIQXGRCLJ7/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":"2026-06-11T22:56:53Z","links":{"resolver":"https://pith.science/pith/CY23763A35TDFJ6WSIQXGRCLJ7","bundle":"https://pith.science/pith/CY23763A35TDFJ6WSIQXGRCLJ7/bundle.json","state":"https://pith.science/pith/CY23763A35TDFJ6WSIQXGRCLJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CY23763A35TDFJ6WSIQXGRCLJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CY23763A35TDFJ6WSIQXGRCLJ7","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":"89d3c65fb5ea2d3f352714243cc9f209c3220d4d43afa91b2087c9591dfee5d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-18T20:07:07Z","title_canon_sha256":"e6ae3d5a3b4be80f3da0263d966d3909e1fc9676b2cc68d89b7b89e6be2f6929"},"schema_version":"1.0","source":{"id":"1307.5070","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5070","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5070v4","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5070","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"CY23763A35TD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CY23763A35TDFJ6W","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CY23763A","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:80ff9541e7b859f6c40b012b8d8cb717b628cc7e80484ccd16daa851eb467364","target":"graph","created_at":"2026-05-18T00:50:23Z","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 provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory and viewed as the counterpart of a non-convex Gromov--Witten potential via the physical LG/CY correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob's virtual cycle in genus zero. In the non-concave case of the so-called chain invertible polynomials, it yields a compatibility theorem with the ","authors_text":"J\\'er\\'emy Gu\\'er\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-18T20:07:07Z","title":"A Landau--Ginzburg mirror theorem without concavity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5070","kind":"arxiv","version":4},"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:ea0005d90d66bc917e86cd8f087f9f56d930a7cabf97cb87a3ff73b42b42e8ae","target":"record","created_at":"2026-05-18T00:50:23Z","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":"89d3c65fb5ea2d3f352714243cc9f209c3220d4d43afa91b2087c9591dfee5d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-18T20:07:07Z","title_canon_sha256":"e6ae3d5a3b4be80f3da0263d966d3909e1fc9676b2cc68d89b7b89e6be2f6929"},"schema_version":"1.0","source":{"id":"1307.5070","kind":"arxiv","version":4}},"canonical_sha256":"1635bffb60df6632a7d6922173444b4fe174bc728f6f5c073906f61124b468d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1635bffb60df6632a7d6922173444b4fe174bc728f6f5c073906f61124b468d7","first_computed_at":"2026-05-18T00:50:23.743918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:23.743918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZupTa9Vzg7BudVdeYExw3rijQ7jJeX/AFzXzFtj3KCI/eQHEMPx9mhOeMgFD0Bw3ABM5Mg9N1jvX0J7NaiUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:23.744625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5070","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea0005d90d66bc917e86cd8f087f9f56d930a7cabf97cb87a3ff73b42b42e8ae","sha256:80ff9541e7b859f6c40b012b8d8cb717b628cc7e80484ccd16daa851eb467364"],"state_sha256":"50330d3defe1e50e6f2011af90ac180cd705f8eebeaa1027f352a1d05f89c900"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/f0ghYw9csnaCpwrCkbGO9kUrPRMYe1iwWlPyEecqjE64HtUp0k0+nW+3YGTrRkbXE+/IEinYmpSonOQParICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:56:53.061521Z","bundle_sha256":"7b5460e0e5f88fde84012f1c949abc31abb3200617ad412df0f237864d6ec012"}}