{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:S7RHZSIUACOBKDSYS6JQSJ6P5K","short_pith_number":"pith:S7RHZSIU","canonical_record":{"source":{"id":"2411.14362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-11-21T18:01:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c6668435ac01a58e2fa91385948913fcd5fd21b661232fba2b7190b15c9837ed","abstract_canon_sha256":"4191da6d8870b7444281254d5a7f3b8f9ffb321abfbfd385b4a1dcb44ce4e855"},"schema_version":"1.0"},"canonical_sha256":"97e27cc914009c150e5897930927cfeabb8b7646501b2b1cf985318a6771b842","source":{"kind":"arxiv","id":"2411.14362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14362","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14362v2","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14362","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"pith_short_12","alias_value":"S7RHZSIUACOB","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"pith_short_16","alias_value":"S7RHZSIUACOBKDSY","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"pith_short_8","alias_value":"S7RHZSIU","created_at":"2026-07-05T09:56:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:S7RHZSIUACOBKDSYS6JQSJ6P5K","target":"record","payload":{"canonical_record":{"source":{"id":"2411.14362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-11-21T18:01:10Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c6668435ac01a58e2fa91385948913fcd5fd21b661232fba2b7190b15c9837ed","abstract_canon_sha256":"4191da6d8870b7444281254d5a7f3b8f9ffb321abfbfd385b4a1dcb44ce4e855"},"schema_version":"1.0"},"canonical_sha256":"97e27cc914009c150e5897930927cfeabb8b7646501b2b1cf985318a6771b842","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:02.532262Z","signature_b64":"PzuB/XM7nf1TFVRbg0g7iND8sqmHiUet7MLrrbM0p6FriVJrD2qSyYtdz7YmrXcG1bcSUmXFSahi1VcpTkKADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e27cc914009c150e5897930927cfeabb8b7646501b2b1cf985318a6771b842","last_reissued_at":"2026-07-05T09:56:02.531841Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:02.531841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.14362","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":"2026-07-05T09:56:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2WiS1SlYGChX1HZxq1qyBaM3o44n7qVbIwH1KZTIgZapB5oWr9cKPJBwViNS2VOzu9EvtxauMtBY3wMvBD9tCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:35:23.639400Z"},"content_sha256":"d004e60efa4d87a99693434052970ae3ed95357d34908a6108c86bcc4b4fdd99","schema_version":"1.0","event_id":"sha256:d004e60efa4d87a99693434052970ae3ed95357d34908a6108c86bcc4b4fdd99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:S7RHZSIUACOBKDSYS6JQSJ6P5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the geometry of K\\\"ahler--Frobenius manifolds and their classification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"No\\'emie. C. Combe","submitted_at":"2024-11-21T18:01:10Z","abstract_excerpt":"The purpose of this article is to show that flat compact K\\\"ahler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field Theory and closely related to Joyce structure. As a result, we classify all such manifolds. It can be deduced that K\\\"ahler--Frobenius manifolds include certain Calabi--Yau manifolds, complex tori $T=\\mathbb{C}^n/\\mathbb{Z}^n$, generalized (orientable) Hantzsche--Wendt manifolds, hyperelliptic manifolds and manifolds of type $T/G$, where $G$ is a finite group acting on $T$ freely and containing no translations. An exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14362","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/2411.14362/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":"2026-07-05T09:56:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNCespr7fGyFLM+a8JXBTUg17xRfGHy7JMSrs6dWfILbJ1NLPuTNUgSejSmVtok5vfSDIH7SH45KXFwwirRPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:35:23.639926Z"},"content_sha256":"985eda5f5feab57b57b045917ea915437b06e8302baece22e91b9e389e5a4a79","schema_version":"1.0","event_id":"sha256:985eda5f5feab57b57b045917ea915437b06e8302baece22e91b9e389e5a4a79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K/bundle.json","state_url":"https://pith.science/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K/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":"2026-08-13T02:35:23Z","links":{"resolver":"https://pith.science/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K","bundle":"https://pith.science/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K/bundle.json","state":"https://pith.science/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7RHZSIUACOBKDSYS6JQSJ6P5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:S7RHZSIUACOBKDSYS6JQSJ6P5K","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":"4191da6d8870b7444281254d5a7f3b8f9ffb321abfbfd385b4a1dcb44ce4e855","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-11-21T18:01:10Z","title_canon_sha256":"c6668435ac01a58e2fa91385948913fcd5fd21b661232fba2b7190b15c9837ed"},"schema_version":"1.0","source":{"id":"2411.14362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14362","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14362v2","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14362","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"pith_short_12","alias_value":"S7RHZSIUACOB","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"pith_short_16","alias_value":"S7RHZSIUACOBKDSY","created_at":"2026-07-05T09:56:02Z"},{"alias_kind":"pith_short_8","alias_value":"S7RHZSIU","created_at":"2026-07-05T09:56:02Z"}],"graph_snapshots":[{"event_id":"sha256:985eda5f5feab57b57b045917ea915437b06e8302baece22e91b9e389e5a4a79","target":"graph","created_at":"2026-07-05T09:56:02Z","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/2411.14362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this article is to show that flat compact K\\\"ahler manifolds exhibit the structure of a Frobenius manifold, a structure originating in 2D Topological Quantum Field Theory and closely related to Joyce structure. As a result, we classify all such manifolds. It can be deduced that K\\\"ahler--Frobenius manifolds include certain Calabi--Yau manifolds, complex tori $T=\\mathbb{C}^n/\\mathbb{Z}^n$, generalized (orientable) Hantzsche--Wendt manifolds, hyperelliptic manifolds and manifolds of type $T/G$, where $G$ is a finite group acting on $T$ freely and containing no translations. An exp","authors_text":"No\\'emie. C. Combe","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-11-21T18:01:10Z","title":"On the geometry of K\\\"ahler--Frobenius manifolds and their classification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14362","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:d004e60efa4d87a99693434052970ae3ed95357d34908a6108c86bcc4b4fdd99","target":"record","created_at":"2026-07-05T09:56:02Z","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":"4191da6d8870b7444281254d5a7f3b8f9ffb321abfbfd385b4a1dcb44ce4e855","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2024-11-21T18:01:10Z","title_canon_sha256":"c6668435ac01a58e2fa91385948913fcd5fd21b661232fba2b7190b15c9837ed"},"schema_version":"1.0","source":{"id":"2411.14362","kind":"arxiv","version":2}},"canonical_sha256":"97e27cc914009c150e5897930927cfeabb8b7646501b2b1cf985318a6771b842","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e27cc914009c150e5897930927cfeabb8b7646501b2b1cf985318a6771b842","first_computed_at":"2026-07-05T09:56:02.531841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:02.531841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PzuB/XM7nf1TFVRbg0g7iND8sqmHiUet7MLrrbM0p6FriVJrD2qSyYtdz7YmrXcG1bcSUmXFSahi1VcpTkKADA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:02.532262Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d004e60efa4d87a99693434052970ae3ed95357d34908a6108c86bcc4b4fdd99","sha256:985eda5f5feab57b57b045917ea915437b06e8302baece22e91b9e389e5a4a79"],"state_sha256":"c2c6c4a5093a1ba4a4af3533773a53eb7c5c574f833d5938128c8caac3fd1493"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dC/uW58PPq4fjohpPDSedHmwlKv7cHihJiLwG7su1fJf4wqrqS/yjhJLdMQGkx7y+GAq+eq3hm87SCko/Y+NDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T02:35:23.644435Z","bundle_sha256":"116a13a4f5d50f337a065f154e659f1e3966b635379e42a9e7faac1d9db8ec8a"}}