{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:A7O2WHHNIS7OS4MQRCFAEQU6VW","short_pith_number":"pith:A7O2WHHN","canonical_record":{"source":{"id":"1111.2963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-12T20:37:11Z","cross_cats_sorted":[],"title_canon_sha256":"b0b410cf869d46c0fde3b4f225ad3aabf52e15e2df94db482a073f57d5506ab0","abstract_canon_sha256":"60967f0acd8c24d61e2e06bae443ac231cda559fca63ffd4f65a2cf04da52d1d"},"schema_version":"1.0"},"canonical_sha256":"07ddab1ced44bee97190888a02429ead946ab0ba0c508f238b07d65c47ea1164","source":{"kind":"arxiv","id":"1111.2963","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2963","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2963v3","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2963","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"A7O2WHHNIS7O","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A7O2WHHNIS7OS4MQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A7O2WHHN","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:A7O2WHHNIS7OS4MQRCFAEQU6VW","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-12T20:37:11Z","cross_cats_sorted":[],"title_canon_sha256":"b0b410cf869d46c0fde3b4f225ad3aabf52e15e2df94db482a073f57d5506ab0","abstract_canon_sha256":"60967f0acd8c24d61e2e06bae443ac231cda559fca63ffd4f65a2cf04da52d1d"},"schema_version":"1.0"},"canonical_sha256":"07ddab1ced44bee97190888a02429ead946ab0ba0c508f238b07d65c47ea1164","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:42.255190Z","signature_b64":"isqYoaXuL5fngJYoeC4zPD7hEc8wIcnd/53cl5f9OqQLMAoCfy6FTofSGMQC4ZRK+RBTLheG5Tb7di09gXXDBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07ddab1ced44bee97190888a02429ead946ab0ba0c508f238b07d65c47ea1164","last_reissued_at":"2026-05-18T00:52:42.254468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:42.254468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2963","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eD7OCzsbjK6cxX6kF9jHTNeG6YHsJvG/xMbunWiIgezydXV4xpVCxmA85JdhCIesegClvT2mwDjiB0JXIt/6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:06:26.781194Z"},"content_sha256":"67cb8c39256b528ee831b2efbb6f78389c7e0abeb828b373942a5271a8ad0195","schema_version":"1.0","event_id":"sha256:67cb8c39256b528ee831b2efbb6f78389c7e0abeb828b373942a5271a8ad0195"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:A7O2WHHNIS7OS4MQRCFAEQU6VW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogeneous Fibrations over Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yi Zhu","submitted_at":"2011-11-12T20:37:11Z","abstract_excerpt":"By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface, a projective homogeneous space admits a rational point if the elementary obstruction vanishes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2963","kind":"arxiv","version":3},"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":"2026-05-18T00:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gpKeMX5iXmMjbp6u0s3lLyNSvQIAKWuqg+DfaPsX8G4chKd9WD27v8HbNEMpMKskQwj6WIh6yvm3mvDLvWttDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:06:26.781563Z"},"content_sha256":"05cc6ef063af1ba3c72b7964c5bac6bc670e4019dc3da44f2011192421b75fe8","schema_version":"1.0","event_id":"sha256:05cc6ef063af1ba3c72b7964c5bac6bc670e4019dc3da44f2011192421b75fe8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW/bundle.json","state_url":"https://pith.science/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW/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":"2026-06-01T15:06:26Z","links":{"resolver":"https://pith.science/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW","bundle":"https://pith.science/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW/bundle.json","state":"https://pith.science/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7O2WHHNIS7OS4MQRCFAEQU6VW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A7O2WHHNIS7OS4MQRCFAEQU6VW","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":"60967f0acd8c24d61e2e06bae443ac231cda559fca63ffd4f65a2cf04da52d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-12T20:37:11Z","title_canon_sha256":"b0b410cf869d46c0fde3b4f225ad3aabf52e15e2df94db482a073f57d5506ab0"},"schema_version":"1.0","source":{"id":"1111.2963","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2963","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2963v3","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2963","created_at":"2026-05-18T00:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"A7O2WHHNIS7O","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A7O2WHHNIS7OS4MQ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A7O2WHHN","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:05cc6ef063af1ba3c72b7964c5bac6bc670e4019dc3da44f2011192421b75fe8","target":"graph","created_at":"2026-05-18T00:52:42Z","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":"By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface, a projective homogeneous space admits a rational point if the elementary obstruction vanishes.","authors_text":"Yi Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-12T20:37:11Z","title":"Homogeneous Fibrations over Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2963","kind":"arxiv","version":3},"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":"sha256:67cb8c39256b528ee831b2efbb6f78389c7e0abeb828b373942a5271a8ad0195","target":"record","created_at":"2026-05-18T00:52:42Z","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":"60967f0acd8c24d61e2e06bae443ac231cda559fca63ffd4f65a2cf04da52d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-12T20:37:11Z","title_canon_sha256":"b0b410cf869d46c0fde3b4f225ad3aabf52e15e2df94db482a073f57d5506ab0"},"schema_version":"1.0","source":{"id":"1111.2963","kind":"arxiv","version":3}},"canonical_sha256":"07ddab1ced44bee97190888a02429ead946ab0ba0c508f238b07d65c47ea1164","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07ddab1ced44bee97190888a02429ead946ab0ba0c508f238b07d65c47ea1164","first_computed_at":"2026-05-18T00:52:42.254468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:42.254468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"isqYoaXuL5fngJYoeC4zPD7hEc8wIcnd/53cl5f9OqQLMAoCfy6FTofSGMQC4ZRK+RBTLheG5Tb7di09gXXDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:42.255190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2963","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67cb8c39256b528ee831b2efbb6f78389c7e0abeb828b373942a5271a8ad0195","sha256:05cc6ef063af1ba3c72b7964c5bac6bc670e4019dc3da44f2011192421b75fe8"],"state_sha256":"b957efcb1a622ab83c9895b9bfa722c7191d5b6ad6340126d667e476be46be10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RQRciepmVXtMAlNeHWKpyfLRP4hz3YnNsQmMkGYfuS3ecXOSMeSFApJpmZHFo9hakRcXSKrfoJXt8yNwxRkxBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:06:26.783545Z","bundle_sha256":"062a7b81be53b7ac61651b9771c1a2b798100beaf04426b3bcf559919bc31590"}}