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In particular, c induces an isomorphism {\\pi}_n(E)-> {\\pi}_{n,0}c(E) for all spectra E.\n  Fix an embedding of k into the complex numbers and let Re:SH(k) -> SH be the associated Betti realization. We show that the slice tower for the motivic sphere spectrum has Betti realizatio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.0283","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-31T16:27:51Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"bf749909704e121ee0019892773a49824d420222b6971bfce9cde30941a164ae","abstract_canon_sha256":"313d6182d3375ebf2dcd205ab4c5db557db39052f9d655ff434d82b22282c33c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.937525Z","signature_b64":"EQvFokpD5jp1Sl21y5wFMjPG46YGzz4nzgu/rFsUi0NWvTBWdOwNHf8zXkrYunJXjSRhPyncYAZsINi0/RXkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90b58f469f3360ecc8e7f84846c96b18717786ee47198aceeff8d09ad7d0bf94","last_reissued_at":"2026-05-18T02:57:53.936842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.936842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A comparison of motivic and classical homotopy theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Marc Levine","submitted_at":"2011-12-31T16:27:51Z","abstract_excerpt":"Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a space to the constant presheaf of spaces on Sm/k. We show that c is fully faithful. In particular, c induces an isomorphism {\\pi}_n(E)-> {\\pi}_{n,0}c(E) for all spectra E.\n  Fix an embedding of k into the complex numbers and let Re:SH(k) -> SH be the associated Betti realization. We show that the slice tower for the motivic sphere spectrum has Betti realizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0283","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.0283","created_at":"2026-05-18T02:57:53.936941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0283v4","created_at":"2026-05-18T02:57:53.936941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0283","created_at":"2026-05-18T02:57:53.936941+00:00"},{"alias_kind":"pith_short_12","alias_value":"SC2Y6RU7GNQO","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SC2Y6RU7GNQOZSHH","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SC2Y6RU7","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB","json":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB.json","graph_json":"https://pith.science/api/pith-number/SC2Y6RU7GNQOZSHH7BEENSLLDB/graph.json","events_json":"https://pith.science/api/pith-number/SC2Y6RU7GNQOZSHH7BEENSLLDB/events.json","paper":"https://pith.science/paper/SC2Y6RU7"},"agent_actions":{"view_html":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB","download_json":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB.json","view_paper":"https://pith.science/paper/SC2Y6RU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0283&json=true","fetch_graph":"https://pith.science/api/pith-number/SC2Y6RU7GNQOZSHH7BEENSLLDB/graph.json","fetch_events":"https://pith.science/api/pith-number/SC2Y6RU7GNQOZSHH7BEENSLLDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/action/storage_attestation","attest_author":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/action/author_attestation","sign_citation":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/action/citation_signature","submit_replication":"https://pith.science/pith/SC2Y6RU7GNQOZSHH7BEENSLLDB/action/replication_record"}},"created_at":"2026-05-18T02:57:53.936941+00:00","updated_at":"2026-05-18T02:57:53.936941+00:00"}