{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OLF2VSODX6MG2V554YSXY4GIDI","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":"5b2edee6fbc266dd6bb19ee7530679f0cf8e91dc0576fcfd1a5741b913647f44","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-18T20:51:14Z","title_canon_sha256":"44890f2b95794a8319b794aa084fd23664c73846f185e2badba1251b6f7732fb"},"schema_version":"1.0","source":{"id":"1108.3854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3854","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3854v1","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3854","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"OLF2VSODX6MG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OLF2VSODX6MG2V55","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OLF2VSOD","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:2232e91f3a339e09ee4b0e08443d939098b1c64e9dde494349a1b14bda5da2d6","target":"graph","created_at":"2026-05-18T04:15:06Z","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 study the 0-th stable A^1-homotopy sheaf of a smooth proper variety over a field k assumed to be infinite, perfect and to have characteristic unequal to 2. We provide an explicit description of this sheaf in terms of the theory of (twisted) Chow-Witt groups as defined by Barge-Morel and developed by Fasel. We study the notion of rational point up to stable A^1-homotopy, defined in terms of the stable A^1-homotopy sheaf of groups mentioned above. We show that, for a smooth proper k-variety X, existence of a rational point up to stable A^1-homotopy is equivalent to existence of a 0-cycle of d","authors_text":"Aravind Asok, Christian Haesemeyer","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-18T20:51:14Z","title":"The 0-th stable A^1-homotopy sheaf and quadratic zero cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3854","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:b4d5bc66a50f0348f364dfd1f3b9137c5db62b49f37b2cde438951b2c57c7bca","target":"record","created_at":"2026-05-18T04:15:06Z","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":"5b2edee6fbc266dd6bb19ee7530679f0cf8e91dc0576fcfd1a5741b913647f44","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-18T20:51:14Z","title_canon_sha256":"44890f2b95794a8319b794aa084fd23664c73846f185e2badba1251b6f7732fb"},"schema_version":"1.0","source":{"id":"1108.3854","kind":"arxiv","version":1}},"canonical_sha256":"72cbaac9c3bf986d57bde6257c70c81a0e7593c1421c3e62d3170c287ad427e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72cbaac9c3bf986d57bde6257c70c81a0e7593c1421c3e62d3170c287ad427e2","first_computed_at":"2026-05-18T04:15:06.235379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:06.235379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xiz56OLWBtSRtxwGyaUsgLZF8EaUDmsVMzRorUqeHIEhBAu+9XK3dYGDJYkEuFCATKhHtve+sDTDUzVKi7BbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:06.236146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4d5bc66a50f0348f364dfd1f3b9137c5db62b49f37b2cde438951b2c57c7bca","sha256:2232e91f3a339e09ee4b0e08443d939098b1c64e9dde494349a1b14bda5da2d6"],"state_sha256":"dccc4300c247395b8b21a002281eec0c7f3015f47084458653457180f8b06a87"}