{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:3PBW3HTVT4R67MCDL57QFQJXBG","short_pith_number":"pith:3PBW3HTV","canonical_record":{"source":{"id":"0906.2364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-12T15:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"e4897b1a13b537f150fdf5aa6ce467f8ecf437012ef5ff89de801acae09287b2","abstract_canon_sha256":"19f283d0f83a5257b1d9298a515d6c79ed56f5a812ce3b174ae7e3619b8cb170"},"schema_version":"1.0"},"canonical_sha256":"dbc36d9e759f23efb0435f7f02c13709af80c0d694b88a20431a84bcdc97fc66","source":{"kind":"arxiv","id":"0906.2364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2364","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2364v2","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2364","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"3PBW3HTVT4R6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PBW3HTVT4R67MCD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PBW3HTV","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:3PBW3HTVT4R67MCDL57QFQJXBG","target":"record","payload":{"canonical_record":{"source":{"id":"0906.2364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-12T15:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"e4897b1a13b537f150fdf5aa6ce467f8ecf437012ef5ff89de801acae09287b2","abstract_canon_sha256":"19f283d0f83a5257b1d9298a515d6c79ed56f5a812ce3b174ae7e3619b8cb170"},"schema_version":"1.0"},"canonical_sha256":"dbc36d9e759f23efb0435f7f02c13709af80c0d694b88a20431a84bcdc97fc66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:26.407648Z","signature_b64":"PQ7VAUx9u2e0q+ZR1PK5ZtdIsDx81/VVpGQIp4Gj5z1+AGinSHbzvUBpO+HiDRzG4Pn33A24F7bCcWYXp6IbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbc36d9e759f23efb0435f7f02c13709af80c0d694b88a20431a84bcdc97fc66","last_reissued_at":"2026-05-18T01:17:26.407204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:26.407204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.2364","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":"2026-05-18T01:17:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2LoOCI/pM8G3KGfuqd/gz4zdgK0ztDw4mauCqVn1UIrv20piPA6a3gHrvRHXsMa8rvIBi+tvvpgcHTDZF3aqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:42:37.045943Z"},"content_sha256":"d0289b696a8149cd4f3f707dfab20de3afc21136675228e4ecda835a19ea8b4d","schema_version":"1.0","event_id":"sha256:d0289b696a8149cd4f3f707dfab20de3afc21136675228e4ecda835a19ea8b4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:3PBW3HTVT4R67MCDL57QFQJXBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rationally connected varieties over the maximally unramified extension of p-adic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Amanda Knecht, Bradley Duesler","submitted_at":"2009-06-12T15:47:14Z","abstract_excerpt":"A result of Graber, Harris, and Starr shows that a rationally connected variety defined over the function field of a curve over the complex numbers always has a rational point. Similarly, a separably rationally connected variety over a finite field or the function field of a curve over any algebraically closed field will have a rational point. Here we show that rationally connected varieties over the maximally unramified extension of the p-adics usually, in a precise sense, have rational points. This result is in the spirit of Ax and Kochen's result saying that the p-adics are usually $C_{2}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2364","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":"2026-05-18T01:17:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VfEuBZQ98EmymA+JqGfb+i5Dqkah2+ZplkPoADLUtAkYHNx2AHiTyaiaC1v449J28GMTzql3gOqhmlYbG+cDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:42:37.046283Z"},"content_sha256":"21bc21b23e13858b96da7539964286ffff4bc8cb3be5038eb27d398a1c078fa1","schema_version":"1.0","event_id":"sha256:21bc21b23e13858b96da7539964286ffff4bc8cb3be5038eb27d398a1c078fa1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PBW3HTVT4R67MCDL57QFQJXBG/bundle.json","state_url":"https://pith.science/pith/3PBW3HTVT4R67MCDL57QFQJXBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PBW3HTVT4R67MCDL57QFQJXBG/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":"2026-06-29T15:42:37Z","links":{"resolver":"https://pith.science/pith/3PBW3HTVT4R67MCDL57QFQJXBG","bundle":"https://pith.science/pith/3PBW3HTVT4R67MCDL57QFQJXBG/bundle.json","state":"https://pith.science/pith/3PBW3HTVT4R67MCDL57QFQJXBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PBW3HTVT4R67MCDL57QFQJXBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3PBW3HTVT4R67MCDL57QFQJXBG","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":"19f283d0f83a5257b1d9298a515d6c79ed56f5a812ce3b174ae7e3619b8cb170","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-12T15:47:14Z","title_canon_sha256":"e4897b1a13b537f150fdf5aa6ce467f8ecf437012ef5ff89de801acae09287b2"},"schema_version":"1.0","source":{"id":"0906.2364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2364","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2364v2","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2364","created_at":"2026-05-18T01:17:26Z"},{"alias_kind":"pith_short_12","alias_value":"3PBW3HTVT4R6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PBW3HTVT4R67MCD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PBW3HTV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:21bc21b23e13858b96da7539964286ffff4bc8cb3be5038eb27d398a1c078fa1","target":"graph","created_at":"2026-05-18T01:17:26Z","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":"A result of Graber, Harris, and Starr shows that a rationally connected variety defined over the function field of a curve over the complex numbers always has a rational point. Similarly, a separably rationally connected variety over a finite field or the function field of a curve over any algebraically closed field will have a rational point. Here we show that rationally connected varieties over the maximally unramified extension of the p-adics usually, in a precise sense, have rational points. This result is in the spirit of Ax and Kochen's result saying that the p-adics are usually $C_{2}$ ","authors_text":"Amanda Knecht, Bradley Duesler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-12T15:47:14Z","title":"Rationally connected varieties over the maximally unramified extension of p-adic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2364","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:d0289b696a8149cd4f3f707dfab20de3afc21136675228e4ecda835a19ea8b4d","target":"record","created_at":"2026-05-18T01:17:26Z","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":"19f283d0f83a5257b1d9298a515d6c79ed56f5a812ce3b174ae7e3619b8cb170","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-06-12T15:47:14Z","title_canon_sha256":"e4897b1a13b537f150fdf5aa6ce467f8ecf437012ef5ff89de801acae09287b2"},"schema_version":"1.0","source":{"id":"0906.2364","kind":"arxiv","version":2}},"canonical_sha256":"dbc36d9e759f23efb0435f7f02c13709af80c0d694b88a20431a84bcdc97fc66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbc36d9e759f23efb0435f7f02c13709af80c0d694b88a20431a84bcdc97fc66","first_computed_at":"2026-05-18T01:17:26.407204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:26.407204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQ7VAUx9u2e0q+ZR1PK5ZtdIsDx81/VVpGQIp4Gj5z1+AGinSHbzvUBpO+HiDRzG4Pn33A24F7bCcWYXp6IbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:26.407648Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0289b696a8149cd4f3f707dfab20de3afc21136675228e4ecda835a19ea8b4d","sha256:21bc21b23e13858b96da7539964286ffff4bc8cb3be5038eb27d398a1c078fa1"],"state_sha256":"c165d5644d0a6eb05434c1ccdd6861749765caa9e2b6300f3df319f112efc61f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xn13UbeMI9aoaBHsJG9Nad2tmYb6Vj2qsEq4fJ+vZNmbVZ+KfBBI5cL+aR73borCh/zpIMNTty1vphmYrFYhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:42:37.048086Z","bundle_sha256":"91a2da0fa70f589b5bc7a38be77141d43acc9b6b409a290f247517f39c2c44fc"}}