{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N4OOKPJ5WUFBR5HBWPP6CQCD5U","short_pith_number":"pith:N4OOKPJ5","canonical_record":{"source":{"id":"1705.05673","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-16T12:21:01Z","cross_cats_sorted":[],"title_canon_sha256":"ef24ad27bf030d5625fe9b4536f2e117a1dc37631c69dbd74c1b933ada4a8051","abstract_canon_sha256":"9a9c0d7139c6c62bfe3825e1f30018527b23d5283ae7b5a04fa88d800e28fe83"},"schema_version":"1.0"},"canonical_sha256":"6f1ce53d3db50a18f4e1b3dfe14043ed0b18178235cee6cdb16329e53b032c15","source":{"kind":"arxiv","id":"1705.05673","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05673","created_at":"2026-05-18T00:44:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05673v1","created_at":"2026-05-18T00:44:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05673","created_at":"2026-05-18T00:44:20Z"},{"alias_kind":"pith_short_12","alias_value":"N4OOKPJ5WUFB","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N4OOKPJ5WUFBR5HB","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N4OOKPJ5","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N4OOKPJ5WUFBR5HBWPP6CQCD5U","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05673","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-16T12:21:01Z","cross_cats_sorted":[],"title_canon_sha256":"ef24ad27bf030d5625fe9b4536f2e117a1dc37631c69dbd74c1b933ada4a8051","abstract_canon_sha256":"9a9c0d7139c6c62bfe3825e1f30018527b23d5283ae7b5a04fa88d800e28fe83"},"schema_version":"1.0"},"canonical_sha256":"6f1ce53d3db50a18f4e1b3dfe14043ed0b18178235cee6cdb16329e53b032c15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:20.511043Z","signature_b64":"WArV2ELLX5fHTRtsTc8g6VF3F7TkMs5j9eYU5RQ0C0n/FNs5JVEytu6L6cP8bfL7yPgVc9PKi0AUtjkW2/GpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f1ce53d3db50a18f4e1b3dfe14043ed0b18178235cee6cdb16329e53b032c15","last_reissued_at":"2026-05-18T00:44:20.510629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:20.510629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05673","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":"2026-05-18T00:44:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhwHoF192VH5Kf7x8vyKKuyB3A1268UDHuNJpwuuuDZaBPsRmwuX2w5BGjdXZo2DKY4r8V316TOVjBd8+xR7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:48:43.673008Z"},"content_sha256":"cdfffcdbc29b4663c9d3f4ba87c7ef5aa494bcc3f6e0fab8f445ac680b53e7d2","schema_version":"1.0","event_id":"sha256:cdfffcdbc29b4663c9d3f4ba87c7ef5aa494bcc3f6e0fab8f445ac680b53e7d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N4OOKPJ5WUFBR5HBWPP6CQCD5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projective and birational geometry of Grassmannians and other special varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Rick Rischter","submitted_at":"2017-05-16T12:21:01Z","abstract_excerpt":"In the first part of the thesis, we study a classical invariant of projective varieties, the secant defectivity. The second part is devoted to modern algebraic geometry, we study the birational geometry of blow-ups of Grassmannians at points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05673","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":""},"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":"2026-05-18T00:44:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FeNbEdAnlHiNF95BSEPgOEdKHGT51IHcmEzPMrEQZgUnCruF7rEvc1EzOZQ/ORn6IM1wm4oQKCYaRcTNEYk7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:48:43.673365Z"},"content_sha256":"ab3a00ac7a75039432c046313b224a31ce7af4d16e90284edb9f441971f5bf01","schema_version":"1.0","event_id":"sha256:ab3a00ac7a75039432c046313b224a31ce7af4d16e90284edb9f441971f5bf01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U/bundle.json","state_url":"https://pith.science/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U/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":"2026-05-28T04:48:43Z","links":{"resolver":"https://pith.science/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U","bundle":"https://pith.science/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U/bundle.json","state":"https://pith.science/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4OOKPJ5WUFBR5HBWPP6CQCD5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N4OOKPJ5WUFBR5HBWPP6CQCD5U","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":"9a9c0d7139c6c62bfe3825e1f30018527b23d5283ae7b5a04fa88d800e28fe83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-16T12:21:01Z","title_canon_sha256":"ef24ad27bf030d5625fe9b4536f2e117a1dc37631c69dbd74c1b933ada4a8051"},"schema_version":"1.0","source":{"id":"1705.05673","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05673","created_at":"2026-05-18T00:44:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05673v1","created_at":"2026-05-18T00:44:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05673","created_at":"2026-05-18T00:44:20Z"},{"alias_kind":"pith_short_12","alias_value":"N4OOKPJ5WUFB","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N4OOKPJ5WUFBR5HB","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N4OOKPJ5","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:ab3a00ac7a75039432c046313b224a31ce7af4d16e90284edb9f441971f5bf01","target":"graph","created_at":"2026-05-18T00:44:20Z","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":"In the first part of the thesis, we study a classical invariant of projective varieties, the secant defectivity. The second part is devoted to modern algebraic geometry, we study the birational geometry of blow-ups of Grassmannians at points.","authors_text":"Rick Rischter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-16T12:21:01Z","title":"Projective and birational geometry of Grassmannians and other special varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05673","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:cdfffcdbc29b4663c9d3f4ba87c7ef5aa494bcc3f6e0fab8f445ac680b53e7d2","target":"record","created_at":"2026-05-18T00:44:20Z","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":"9a9c0d7139c6c62bfe3825e1f30018527b23d5283ae7b5a04fa88d800e28fe83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-16T12:21:01Z","title_canon_sha256":"ef24ad27bf030d5625fe9b4536f2e117a1dc37631c69dbd74c1b933ada4a8051"},"schema_version":"1.0","source":{"id":"1705.05673","kind":"arxiv","version":1}},"canonical_sha256":"6f1ce53d3db50a18f4e1b3dfe14043ed0b18178235cee6cdb16329e53b032c15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f1ce53d3db50a18f4e1b3dfe14043ed0b18178235cee6cdb16329e53b032c15","first_computed_at":"2026-05-18T00:44:20.510629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:20.510629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WArV2ELLX5fHTRtsTc8g6VF3F7TkMs5j9eYU5RQ0C0n/FNs5JVEytu6L6cP8bfL7yPgVc9PKi0AUtjkW2/GpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:20.511043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05673","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdfffcdbc29b4663c9d3f4ba87c7ef5aa494bcc3f6e0fab8f445ac680b53e7d2","sha256:ab3a00ac7a75039432c046313b224a31ce7af4d16e90284edb9f441971f5bf01"],"state_sha256":"82226cc10d6491d4cd1b4531e0801179427b0afd927576dfc7b9a67414400c2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHLdoebINI0qfnFioF/nug48ECBFXfJ3zubEyQb72gJLnabD5xgSmWF2T0vhb9yoolPdqyf62XrvvNI+UDnaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:48:43.675306Z","bundle_sha256":"897dc1f66b565a27b65bdca878c811f33203cb515a6bee8e9c7b7abbaf6d88ec"}}