{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U3WY2FXX5QFNUKUBZHODPPMBLH","short_pith_number":"pith:U3WY2FXX","canonical_record":{"source":{"id":"1507.06490","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T13:38:54Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"34cc389c516fe63445303669a5d423cdac5559f359f8b2ffb481768b0d6dfc1c","abstract_canon_sha256":"088b0cc5dfa4fdaf7a0b83fc8bd50930421b0a0ed5424e815baa17518466e884"},"schema_version":"1.0"},"canonical_sha256":"a6ed8d16f7ec0ada2a81c9dc37bd8159e659ecf4a839fe8ec191c1b5e4e5ed2a","source":{"kind":"arxiv","id":"1507.06490","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06490","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06490v3","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06490","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"U3WY2FXX5QFN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3WY2FXX5QFNUKUB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3WY2FXX","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U3WY2FXX5QFNUKUBZHODPPMBLH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06490","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T13:38:54Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"34cc389c516fe63445303669a5d423cdac5559f359f8b2ffb481768b0d6dfc1c","abstract_canon_sha256":"088b0cc5dfa4fdaf7a0b83fc8bd50930421b0a0ed5424e815baa17518466e884"},"schema_version":"1.0"},"canonical_sha256":"a6ed8d16f7ec0ada2a81c9dc37bd8159e659ecf4a839fe8ec191c1b5e4e5ed2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:23.019827Z","signature_b64":"o5+z3PfzjjJ6HwBIc2weCj6FsT0HAxjp45toLwmY/xK1aj6B0NHHQWx+aWDeBvVymnD/75wDfx0TbUzaOLZ0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6ed8d16f7ec0ada2a81c9dc37bd8159e659ecf4a839fe8ec191c1b5e4e5ed2a","last_reissued_at":"2026-05-18T00:50:23.019007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:23.019007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06490","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":"2026-05-18T00:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8MWPNuF/2H8NdPIcuIxDuHmdj5zsz3NbLXoerlGbNsG/RA421Wfe7oI8/XrsloRbOu1i8+bU7Gt6AM8EuwFCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:47:21.430967Z"},"content_sha256":"e0fb92108e14a9562797985b2235135fe7e00923894b858c5a3c7c0cbcc74322","schema_version":"1.0","event_id":"sha256:e0fb92108e14a9562797985b2235135fe7e00923894b858c5a3c7c0cbcc74322"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U3WY2FXX5QFNUKUBZHODPPMBLH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projectivity of the Witt vector affine Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Bhargav Bhatt, Peter Scholze","submitted_at":"2015-07-23T13:38:54Z","abstract_excerpt":"We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in W(k)[1/p]^n for a perfect field k of charactristic p, is representable by an ind-(perfect scheme) over k. This improves on previous results of Zhu by constructing a natural ample line bundle. Along the way, we establish various foundational results on perfect schemes, notably h-descent results for vector bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06490","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":"2026-05-18T00:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pynFgg2lNRarV2Qhefw1lOVUni6onGtiq+kxoHIwsbEFPIA2W8kGBkpzP/23PcxVrn0r4uLZuOtKi5cPGENwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:47:21.431465Z"},"content_sha256":"ebc4c4cee057ae11071fe542d40ded42d3ae4a80e62d60ef309d60dfbfeeeaab","schema_version":"1.0","event_id":"sha256:ebc4c4cee057ae11071fe542d40ded42d3ae4a80e62d60ef309d60dfbfeeeaab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3WY2FXX5QFNUKUBZHODPPMBLH/bundle.json","state_url":"https://pith.science/pith/U3WY2FXX5QFNUKUBZHODPPMBLH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3WY2FXX5QFNUKUBZHODPPMBLH/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":"2026-06-04T04:47:21Z","links":{"resolver":"https://pith.science/pith/U3WY2FXX5QFNUKUBZHODPPMBLH","bundle":"https://pith.science/pith/U3WY2FXX5QFNUKUBZHODPPMBLH/bundle.json","state":"https://pith.science/pith/U3WY2FXX5QFNUKUBZHODPPMBLH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3WY2FXX5QFNUKUBZHODPPMBLH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U3WY2FXX5QFNUKUBZHODPPMBLH","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":"088b0cc5dfa4fdaf7a0b83fc8bd50930421b0a0ed5424e815baa17518466e884","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T13:38:54Z","title_canon_sha256":"34cc389c516fe63445303669a5d423cdac5559f359f8b2ffb481768b0d6dfc1c"},"schema_version":"1.0","source":{"id":"1507.06490","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06490","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06490v3","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06490","created_at":"2026-05-18T00:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"U3WY2FXX5QFN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U3WY2FXX5QFNUKUB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U3WY2FXX","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:ebc4c4cee057ae11071fe542d40ded42d3ae4a80e62d60ef309d60dfbfeeeaab","target":"graph","created_at":"2026-05-18T00:50:23Z","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":"We prove that the Witt vector affine Grassmannian, which parametrizes W(k)-lattices in W(k)[1/p]^n for a perfect field k of charactristic p, is representable by an ind-(perfect scheme) over k. This improves on previous results of Zhu by constructing a natural ample line bundle. Along the way, we establish various foundational results on perfect schemes, notably h-descent results for vector bundles.","authors_text":"Bhargav Bhatt, Peter Scholze","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T13:38:54Z","title":"Projectivity of the Witt vector affine Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06490","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:e0fb92108e14a9562797985b2235135fe7e00923894b858c5a3c7c0cbcc74322","target":"record","created_at":"2026-05-18T00:50:23Z","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":"088b0cc5dfa4fdaf7a0b83fc8bd50930421b0a0ed5424e815baa17518466e884","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-23T13:38:54Z","title_canon_sha256":"34cc389c516fe63445303669a5d423cdac5559f359f8b2ffb481768b0d6dfc1c"},"schema_version":"1.0","source":{"id":"1507.06490","kind":"arxiv","version":3}},"canonical_sha256":"a6ed8d16f7ec0ada2a81c9dc37bd8159e659ecf4a839fe8ec191c1b5e4e5ed2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6ed8d16f7ec0ada2a81c9dc37bd8159e659ecf4a839fe8ec191c1b5e4e5ed2a","first_computed_at":"2026-05-18T00:50:23.019007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:23.019007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o5+z3PfzjjJ6HwBIc2weCj6FsT0HAxjp45toLwmY/xK1aj6B0NHHQWx+aWDeBvVymnD/75wDfx0TbUzaOLZ0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:23.019827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06490","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0fb92108e14a9562797985b2235135fe7e00923894b858c5a3c7c0cbcc74322","sha256:ebc4c4cee057ae11071fe542d40ded42d3ae4a80e62d60ef309d60dfbfeeeaab"],"state_sha256":"dc0219fcfbb3a0c397a9f8184727e3beea2f13856f6f92ded59f27d8f6fb2e56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JDoB6P4V3Rs98AgZS6H/fvoH582qWqtoCMbrx++7C8LCzV89ivxh2RoyHdlrQJIbeWtTSoxaLh0NvmZWf+QDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:47:21.434617Z","bundle_sha256":"ff3a61357a414e26c4cc110597cf686f9ec580acc9bd43b0ae8c96d1d8919e37"}}