{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QHXSFVRWK36KAZBGP7KPAKHG3D","short_pith_number":"pith:QHXSFVRW","canonical_record":{"source":{"id":"1107.0438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-03T08:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"712301f2f01058f7449efabfbb7f755b1abda7ef4bf58263a176d84b6a76f385","abstract_canon_sha256":"bd45c41e3bb3c8a7093a19b3ea5c5bb0fac16eaa2706c54e2d29c807c04ef145"},"schema_version":"1.0"},"canonical_sha256":"81ef22d63656fca064267fd4f028e6d8ddf4c308d4f69e7179f32c036e7622bd","source":{"kind":"arxiv","id":"1107.0438","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0438","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0438v2","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0438","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"QHXSFVRWK36K","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHXSFVRWK36KAZBG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHXSFVRW","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QHXSFVRWK36KAZBGP7KPAKHG3D","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-03T08:58:42Z","cross_cats_sorted":[],"title_canon_sha256":"712301f2f01058f7449efabfbb7f755b1abda7ef4bf58263a176d84b6a76f385","abstract_canon_sha256":"bd45c41e3bb3c8a7093a19b3ea5c5bb0fac16eaa2706c54e2d29c807c04ef145"},"schema_version":"1.0"},"canonical_sha256":"81ef22d63656fca064267fd4f028e6d8ddf4c308d4f69e7179f32c036e7622bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:17.724095Z","signature_b64":"9oWh2tPO5II03jdxzimeAuz+yeHdAxHPf8VGrKQe9a4i2qMOSQWzHjpfqWtLYUL45nkybiMLZsr1s8t2Z+XnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ef22d63656fca064267fd4f028e6d8ddf4c308d4f69e7179f32c036e7622bd","last_reissued_at":"2026-05-18T04:11:17.723539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:17.723539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0438","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stshGvrWxm3EBuImjn+Edo4q29V2cMoxdaRFhNEtq7dz7ILAHEeQAIU3zY20yfQvVpT3/sfWUHR2rruPjRopCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:06:33.190095Z"},"content_sha256":"d6c15727b21e950e61cb597d10888ea0afb6bbb0cfdaa4111dc9ecb70801c0d3","schema_version":"1.0","event_id":"sha256:d6c15727b21e950e61cb597d10888ea0afb6bbb0cfdaa4111dc9ecb70801c0d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QHXSFVRWK36KAZBGP7KPAKHG3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incompressibility of orthogonal grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nikita A. Karpenko","submitted_at":"2011-07-03T08:58:42Z","abstract_excerpt":"We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer in the interval [1, (\\dim q)/2]). If the degree of each closed point on Q is divisible by 2^i and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-incompressible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0438","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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UNnTmHwOT7eaekD3A0FgARoIM7gTWHBj5IQkeBlG+cqIENvJtsCCll9NuTEcR4L7RhCzPLTX9QmZ0lIZ7d6aCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:06:33.190470Z"},"content_sha256":"567e743365ac8c918e4be4753e921ff7390a4f79bc9c9a21b707d24045a53967","schema_version":"1.0","event_id":"sha256:567e743365ac8c918e4be4753e921ff7390a4f79bc9c9a21b707d24045a53967"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHXSFVRWK36KAZBGP7KPAKHG3D/bundle.json","state_url":"https://pith.science/pith/QHXSFVRWK36KAZBGP7KPAKHG3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHXSFVRWK36KAZBGP7KPAKHG3D/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":"2026-06-02T05:06:33Z","links":{"resolver":"https://pith.science/pith/QHXSFVRWK36KAZBGP7KPAKHG3D","bundle":"https://pith.science/pith/QHXSFVRWK36KAZBGP7KPAKHG3D/bundle.json","state":"https://pith.science/pith/QHXSFVRWK36KAZBGP7KPAKHG3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHXSFVRWK36KAZBGP7KPAKHG3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QHXSFVRWK36KAZBGP7KPAKHG3D","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":"bd45c41e3bb3c8a7093a19b3ea5c5bb0fac16eaa2706c54e2d29c807c04ef145","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-03T08:58:42Z","title_canon_sha256":"712301f2f01058f7449efabfbb7f755b1abda7ef4bf58263a176d84b6a76f385"},"schema_version":"1.0","source":{"id":"1107.0438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0438","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0438v2","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0438","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"QHXSFVRWK36K","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHXSFVRWK36KAZBG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHXSFVRW","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:567e743365ac8c918e4be4753e921ff7390a4f79bc9c9a21b707d24045a53967","target":"graph","created_at":"2026-05-18T04:11:17Z","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 the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer in the interval [1, (\\dim q)/2]). If the degree of each closed point on Q is divisible by 2^i and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-incompressible.","authors_text":"Nikita A. Karpenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-03T08:58:42Z","title":"Incompressibility of orthogonal grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0438","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:d6c15727b21e950e61cb597d10888ea0afb6bbb0cfdaa4111dc9ecb70801c0d3","target":"record","created_at":"2026-05-18T04:11:17Z","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":"bd45c41e3bb3c8a7093a19b3ea5c5bb0fac16eaa2706c54e2d29c807c04ef145","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-03T08:58:42Z","title_canon_sha256":"712301f2f01058f7449efabfbb7f755b1abda7ef4bf58263a176d84b6a76f385"},"schema_version":"1.0","source":{"id":"1107.0438","kind":"arxiv","version":2}},"canonical_sha256":"81ef22d63656fca064267fd4f028e6d8ddf4c308d4f69e7179f32c036e7622bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81ef22d63656fca064267fd4f028e6d8ddf4c308d4f69e7179f32c036e7622bd","first_computed_at":"2026-05-18T04:11:17.723539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:17.723539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9oWh2tPO5II03jdxzimeAuz+yeHdAxHPf8VGrKQe9a4i2qMOSQWzHjpfqWtLYUL45nkybiMLZsr1s8t2Z+XnAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:17.724095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6c15727b21e950e61cb597d10888ea0afb6bbb0cfdaa4111dc9ecb70801c0d3","sha256:567e743365ac8c918e4be4753e921ff7390a4f79bc9c9a21b707d24045a53967"],"state_sha256":"5982e7a4f38beefffe46b6b65a54d81d4a5e39a2440691274ccd9c982db3b21c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82LI/MrztFxPXqAsePfZBJl8aERqEf7PUxPMquZMa7FO0iiatuNp9Xr1SYconIdOUfZaNh9mZ6rJNG37UyttBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:06:33.192408Z","bundle_sha256":"35d1fd558611c0b8da2281f5204e1e5d089a8dffcf72a8b5c0f9e547ee49ec91"}}