{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZIVE3KCPCXTZ4B7HS2Y627ELEW","short_pith_number":"pith:ZIVE3KCP","canonical_record":{"source":{"id":"1908.02803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-07T19:14:40Z","cross_cats_sorted":[],"title_canon_sha256":"916b32c0d888b32da59248c7255f3792e190e308a438588df6d7b20aaae8e4c9","abstract_canon_sha256":"30148b0488382fd0acbebe583795b702b732859254999332caca80f10a6be756"},"schema_version":"1.0"},"canonical_sha256":"ca2a4da84f15e79e07e796b1ed7c8b25a958f43814e464d0088eda9d461c34f4","source":{"kind":"arxiv","id":"1908.02803","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02803","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02803v1","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02803","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZIVE3KCPCXTZ","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ZIVE3KCPCXTZ4B7H","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ZIVE3KCP","created_at":"2026-07-05T03:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZIVE3KCPCXTZ4B7HS2Y627ELEW","target":"record","payload":{"canonical_record":{"source":{"id":"1908.02803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-07T19:14:40Z","cross_cats_sorted":[],"title_canon_sha256":"916b32c0d888b32da59248c7255f3792e190e308a438588df6d7b20aaae8e4c9","abstract_canon_sha256":"30148b0488382fd0acbebe583795b702b732859254999332caca80f10a6be756"},"schema_version":"1.0"},"canonical_sha256":"ca2a4da84f15e79e07e796b1ed7c8b25a958f43814e464d0088eda9d461c34f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:30:36.519489Z","signature_b64":"xKjetqo86A5Ay03hhioNHJqno8iVSWJCp/rxP91eSADGWTDULDWXHhqcGBgwAlPKEf/AJswdIdYVRaUFSZm2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca2a4da84f15e79e07e796b1ed7c8b25a958f43814e464d0088eda9d461c34f4","last_reissued_at":"2026-07-05T03:30:36.519070Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:30:36.519070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.02803","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:30:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+OIaXiBdOn9k6eKNTtDnczMtcKNgAeQaJcv03t+nupbURWyxA/sgCqJZZorYN2ugktBkdMgw4ONhEdg8r6KnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:47:18.683335Z"},"content_sha256":"51cb1050795158398537ce3f50aec669ce4994eb3a3e200ef2edf6f7a65de2d6","schema_version":"1.0","event_id":"sha256:51cb1050795158398537ce3f50aec669ce4994eb3a3e200ef2edf6f7a65de2d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZIVE3KCPCXTZ4B7HS2Y627ELEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fano hypersurfaces with arbitrarily large degrees of irrationality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Stapleton, Nathan Chen","submitted_at":"2019-08-07T19:14:40Z","abstract_excerpt":"We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index e, then the degree of irrationality of a very general complex Fano hypersurface of index e and dimension n is bounded from below by a constant times $\\sqrt{n}$. To our knowledge this gives the first examples of rationally connected varieties with degrees of irrationality greater than 3. The proof follows a degeneration to characteristic p argument which Koll\\'ar used to prove nonrationality of Fano hypersurfaces. Along the way we show that in a family of varieties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02803","kind":"arxiv","version":1},"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/1908.02803/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":"2026-07-05T03:30:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRs8W37UhS7vMvKGPf0HI7tXfZ96L6PVvxZuk664f7ulSqC1t23ajWm5MdlVkLjVcExV/lm79lIsQHB9/YFFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:47:18.683978Z"},"content_sha256":"3738844e03a353ba06353a17ef9b86ed23f55e0f5ac5f90dc418b8d875b0efcc","schema_version":"1.0","event_id":"sha256:3738844e03a353ba06353a17ef9b86ed23f55e0f5ac5f90dc418b8d875b0efcc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW/bundle.json","state_url":"https://pith.science/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW/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":"2026-08-16T05:47:18Z","links":{"resolver":"https://pith.science/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW","bundle":"https://pith.science/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW/bundle.json","state":"https://pith.science/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIVE3KCPCXTZ4B7HS2Y627ELEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZIVE3KCPCXTZ4B7HS2Y627ELEW","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":"30148b0488382fd0acbebe583795b702b732859254999332caca80f10a6be756","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-07T19:14:40Z","title_canon_sha256":"916b32c0d888b32da59248c7255f3792e190e308a438588df6d7b20aaae8e4c9"},"schema_version":"1.0","source":{"id":"1908.02803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02803","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02803v1","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02803","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZIVE3KCPCXTZ","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ZIVE3KCPCXTZ4B7H","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ZIVE3KCP","created_at":"2026-07-05T03:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:3738844e03a353ba06353a17ef9b86ed23f55e0f5ac5f90dc418b8d875b0efcc","target":"graph","created_at":"2026-07-05T03:30:36Z","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/1908.02803/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that complex Fano hypersurfaces can have arbitrarily large degrees of irrationality. More precisely, if we fix a Fano index e, then the degree of irrationality of a very general complex Fano hypersurface of index e and dimension n is bounded from below by a constant times $\\sqrt{n}$. To our knowledge this gives the first examples of rationally connected varieties with degrees of irrationality greater than 3. The proof follows a degeneration to characteristic p argument which Koll\\'ar used to prove nonrationality of Fano hypersurfaces. Along the way we show that in a family of varieties","authors_text":"David Stapleton, Nathan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-07T19:14:40Z","title":"Fano hypersurfaces with arbitrarily large degrees of irrationality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02803","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":"sha256:51cb1050795158398537ce3f50aec669ce4994eb3a3e200ef2edf6f7a65de2d6","target":"record","created_at":"2026-07-05T03:30:36Z","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":"30148b0488382fd0acbebe583795b702b732859254999332caca80f10a6be756","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-07T19:14:40Z","title_canon_sha256":"916b32c0d888b32da59248c7255f3792e190e308a438588df6d7b20aaae8e4c9"},"schema_version":"1.0","source":{"id":"1908.02803","kind":"arxiv","version":1}},"canonical_sha256":"ca2a4da84f15e79e07e796b1ed7c8b25a958f43814e464d0088eda9d461c34f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca2a4da84f15e79e07e796b1ed7c8b25a958f43814e464d0088eda9d461c34f4","first_computed_at":"2026-07-05T03:30:36.519070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:30:36.519070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xKjetqo86A5Ay03hhioNHJqno8iVSWJCp/rxP91eSADGWTDULDWXHhqcGBgwAlPKEf/AJswdIdYVRaUFSZm2BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:30:36.519489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51cb1050795158398537ce3f50aec669ce4994eb3a3e200ef2edf6f7a65de2d6","sha256:3738844e03a353ba06353a17ef9b86ed23f55e0f5ac5f90dc418b8d875b0efcc"],"state_sha256":"1792aff634171ca0e0a2b22147f3b44183f599f8beedca9a1952f39f13296c8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gj6q7/gPo9Jak/FjeTJBNQvACR4VSU54JjPu8OwxXOzRjalDQod0DoxRPX+CGU3ZTLkTrlQPeZ/JxxW2ChZ8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:47:18.690674Z","bundle_sha256":"fcc7421fbb0972a8e673597e9484826e16304c42f6dc2f077ebf30ae04d22d5a"}}