{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7BIKZMFKJQCI2626R4UE5OZA3I","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":"f13b65558d8064bdf4d47c75ab796fb4d42b0d0559596928fe7da457ead94783","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-24T14:18:56Z","title_canon_sha256":"807aac1f1cddc616243127621e7536800dc8ead9a013f0e990477e9d13f7f709"},"schema_version":"1.0","source":{"id":"1506.07375","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07375","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07375v3","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07375","created_at":"2026-05-18T00:10:32Z"},{"alias_kind":"pith_short_12","alias_value":"7BIKZMFKJQCI","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7BIKZMFKJQCI2626","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7BIKZMFK","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:25abebe11886d74ea4e5d57c3e9154f84c98285856c5c7468b993183b5cd0432","target":"graph","created_at":"2026-05-18T00:10:32Z","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":"Given a 0-connective motivic spectrum $E \\in SH(k)$ over a perfect field k, we determine $h_0$ of the associated motive $M E \\in DM(k)$ in terms of $\\pi_0 (E)$. Using this we show that if k has finite 2-\\'etale cohomological dimension, then the functor M is conservative when restricted to the subcategory of compact spectra, and induces an injection on Picard groups. We extend the conservativity result to fields of finite virtual 2-\\'etale cohomological dimension by considering what we call \"real motives\".\n  As a by-product we reprove a variant of a rigidity Theorem of R\\\"ondings-{\\O}stv{\\ae}r.","authors_text":"Tom Bachmann","cross_cats":["math.AG","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-24T14:18:56Z","title":"On the Conservativity of the Functor Assigning to a Motivic Spectrum its Motive"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07375","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:e7445d847a4109bcf0b4df30dd719933eefea0e1b35bc8b071bb835574552c6c","target":"record","created_at":"2026-05-18T00:10:32Z","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":"f13b65558d8064bdf4d47c75ab796fb4d42b0d0559596928fe7da457ead94783","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-24T14:18:56Z","title_canon_sha256":"807aac1f1cddc616243127621e7536800dc8ead9a013f0e990477e9d13f7f709"},"schema_version":"1.0","source":{"id":"1506.07375","kind":"arxiv","version":3}},"canonical_sha256":"f850acb0aa4c048d7b5e8f284ebb20da1f8801c35572a667beb62fbfe1fb1cbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f850acb0aa4c048d7b5e8f284ebb20da1f8801c35572a667beb62fbfe1fb1cbf","first_computed_at":"2026-05-18T00:10:32.534235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:32.534235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DuNTf1NlQDibi2HDoSm+NT10s83yz359UwxusigWgeKaB4YBEp1khdjsZNk4vuP3WvafW6j0+5feXhxGQvt7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:32.534900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07375","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7445d847a4109bcf0b4df30dd719933eefea0e1b35bc8b071bb835574552c6c","sha256:25abebe11886d74ea4e5d57c3e9154f84c98285856c5c7468b993183b5cd0432"],"state_sha256":"badbc3572cc9dd2772e611ca712d48eab6ea4ceba8a09489d85172196283417a"}