{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UOAB2KSZZMTR5NLF2X2SRGXQWL","short_pith_number":"pith:UOAB2KSZ","canonical_record":{"source":{"id":"1412.7023","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T15:16:30Z","cross_cats_sorted":[],"title_canon_sha256":"c46ab755a511fb71f45643447d5089c44c6fa5afaa3be12fa9baae552c31d837","abstract_canon_sha256":"241709a70f940a207e312bcbb788b9887eab693d53ef88f1352272af029fa475"},"schema_version":"1.0"},"canonical_sha256":"a3801d2a59cb271eb565d5f5289af0b2cda288756491a0e43400706f68ea7967","source":{"kind":"arxiv","id":"1412.7023","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7023","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7023v2","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7023","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"UOAB2KSZZMTR","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UOAB2KSZZMTR5NLF","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UOAB2KSZ","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UOAB2KSZZMTR5NLF2X2SRGXQWL","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7023","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T15:16:30Z","cross_cats_sorted":[],"title_canon_sha256":"c46ab755a511fb71f45643447d5089c44c6fa5afaa3be12fa9baae552c31d837","abstract_canon_sha256":"241709a70f940a207e312bcbb788b9887eab693d53ef88f1352272af029fa475"},"schema_version":"1.0"},"canonical_sha256":"a3801d2a59cb271eb565d5f5289af0b2cda288756491a0e43400706f68ea7967","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:13.127854Z","signature_b64":"J1DP2Jf9wmhLrt7d54Xj3FD1ZUAfockCeEvNgLWBBD7rpZJtN3z3k6p+1UnQcKg+ZbVrh/FaiIaxQBC9+Tl8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3801d2a59cb271eb565d5f5289af0b2cda288756491a0e43400706f68ea7967","last_reissued_at":"2026-05-18T02:28:13.127230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:13.127230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7023","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":"2026-05-18T02:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQjv5hLh/DaQOLfhz/FnpdN6AIUBu3449ShZIdz3FGbVHaFqYb5etHb2vUOFrImZnkbqosIQMp7gYoyaPhUUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:45:30.893786Z"},"content_sha256":"ea022d02ac495a5ba09020a7e599f38d0df65c26dac0bc167d7ed7cf34dd195c","schema_version":"1.0","event_id":"sha256:ea022d02ac495a5ba09020a7e599f38d0df65c26dac0bc167d7ed7cf34dd195c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UOAB2KSZZMTR5NLF2X2SRGXQWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Gauss maps in positive characteristic in view of images, fibers, and field extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atsushi Ito, Katsuhisa Furukawa","submitted_at":"2014-12-22T15:16:30Z","abstract_excerpt":"The Gauss map of a projective variety $X \\subset \\mathbb{P}^N$ is a rational map from $X$ to a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varieties $F$ and $Y$, we construct a projective variety $X$ whose Gauss map has $F$ as its general fiber and has $Y$ as its image. More generally, we give such construction for families of varieties over $Y$ instead of fixed $F$. (2) At least in the case when the characteristic is not equal to $2$, any inseparable field extension appears as the extension induced from the Gauss map of some $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7023","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":"2026-05-18T02:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uN0LixDPzfFDENmNjcWdaf4zrwx9sVzXUwW6l42vk6/BTIBSub2ER15U8wGCvBzRb/yb9I3GhBOfIXCZ8U60Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:45:30.894140Z"},"content_sha256":"3a66ee735933a46c197d86df50e60e69609e1c6ce6f1aefba80feda1e3eb3e69","schema_version":"1.0","event_id":"sha256:3a66ee735933a46c197d86df50e60e69609e1c6ce6f1aefba80feda1e3eb3e69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL/bundle.json","state_url":"https://pith.science/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL/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":"2026-06-24T18:45:30Z","links":{"resolver":"https://pith.science/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL","bundle":"https://pith.science/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL/bundle.json","state":"https://pith.science/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOAB2KSZZMTR5NLF2X2SRGXQWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UOAB2KSZZMTR5NLF2X2SRGXQWL","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":"241709a70f940a207e312bcbb788b9887eab693d53ef88f1352272af029fa475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T15:16:30Z","title_canon_sha256":"c46ab755a511fb71f45643447d5089c44c6fa5afaa3be12fa9baae552c31d837"},"schema_version":"1.0","source":{"id":"1412.7023","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7023","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7023v2","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7023","created_at":"2026-05-18T02:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"UOAB2KSZZMTR","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UOAB2KSZZMTR5NLF","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UOAB2KSZ","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:3a66ee735933a46c197d86df50e60e69609e1c6ce6f1aefba80feda1e3eb3e69","target":"graph","created_at":"2026-05-18T02:28:13Z","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":"The Gauss map of a projective variety $X \\subset \\mathbb{P}^N$ is a rational map from $X$ to a Grassmann variety. In positive characteristic, we show the following results. (1) For given projective varieties $F$ and $Y$, we construct a projective variety $X$ whose Gauss map has $F$ as its general fiber and has $Y$ as its image. More generally, we give such construction for families of varieties over $Y$ instead of fixed $F$. (2) At least in the case when the characteristic is not equal to $2$, any inseparable field extension appears as the extension induced from the Gauss map of some $X$.","authors_text":"Atsushi Ito, Katsuhisa Furukawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T15:16:30Z","title":"On Gauss maps in positive characteristic in view of images, fibers, and field extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7023","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:ea022d02ac495a5ba09020a7e599f38d0df65c26dac0bc167d7ed7cf34dd195c","target":"record","created_at":"2026-05-18T02:28:13Z","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":"241709a70f940a207e312bcbb788b9887eab693d53ef88f1352272af029fa475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-22T15:16:30Z","title_canon_sha256":"c46ab755a511fb71f45643447d5089c44c6fa5afaa3be12fa9baae552c31d837"},"schema_version":"1.0","source":{"id":"1412.7023","kind":"arxiv","version":2}},"canonical_sha256":"a3801d2a59cb271eb565d5f5289af0b2cda288756491a0e43400706f68ea7967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3801d2a59cb271eb565d5f5289af0b2cda288756491a0e43400706f68ea7967","first_computed_at":"2026-05-18T02:28:13.127230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:13.127230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J1DP2Jf9wmhLrt7d54Xj3FD1ZUAfockCeEvNgLWBBD7rpZJtN3z3k6p+1UnQcKg+ZbVrh/FaiIaxQBC9+Tl8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:13.127854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7023","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea022d02ac495a5ba09020a7e599f38d0df65c26dac0bc167d7ed7cf34dd195c","sha256:3a66ee735933a46c197d86df50e60e69609e1c6ce6f1aefba80feda1e3eb3e69"],"state_sha256":"7d0ed7faccbb966890f126331d40fb36dd90c7c8018c66d1d88eaf3ddaf384fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GlMxqC4+3YMt81yTuBRW+0VlBp6cde46caUVjN23FSsF8bhRLQ0d6TTB0DnMg2Gwf32binkj7Ccqoy49schAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:45:30.896167Z","bundle_sha256":"0398ca17d267ae26d63da663fed574ed1ddc811bd986d5def2346bf8a71e905e"}}