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Relying on Hopkins-Morel-Hoyois isomorphism of the 0th slice $s_0MGL_S$ for Voevodsky's slice tower with $MGL_S/(x_1, x_2,\\ldots)$ (after inverting the characteristic of $k$), Spitzweck computes the remaining slices of $MGL_S$ as $s_nMGL_S=\\Sigma^n_TH\\mathbb{Z}\\otimes \\mathbb{L}^{-n}$ (again, after inverting the"},"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":"1501.02436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-11T10:25:03Z","cross_cats_sorted":[],"title_canon_sha256":"2663b4fe4c5138c6e9848a78e05b8fb63f71a383d20d2a91375b960ebe36c501","abstract_canon_sha256":"c5b36b359759c90c504641ca3c1b17806a9891cb4dd1ad932711c46e419f8737"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:37.964515Z","signature_b64":"tZA1w9m/BewzSXMtOUhaDe34ud53Np4RvYnGPCOgNjp9OZVcJOa0w+xua4nPAP5Dn5Hf5a5Zguj65XRnI9MHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84f7c53b6c8f32f6eda420ef8dc4d36f3cdd9b00a116897854fa7a5749aff8da","last_reissued_at":"2026-05-18T02:29:37.964036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:37.964036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quotients of MGL, their slices and their geometric parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Girja Shanker Tripathi, Marc Levine","submitted_at":"2015-01-11T10:25:03Z","abstract_excerpt":"Let $x_1, x_2,\\ldots$ be a system of homogeneous polynomial generators for the Lazard ring $\\mathbb{L}^*=MU^{2*}$ and let $MGL_S$ denote Voevodsky's algebraic cobordism spectrum in the motivic stable homotopy category over a base-scheme $S$.Take $S$ essentially smooth over a field $k$. Relying on Hopkins-Morel-Hoyois isomorphism of the 0th slice $s_0MGL_S$ for Voevodsky's slice tower with $MGL_S/(x_1, x_2,\\ldots)$ (after inverting the characteristic of $k$), Spitzweck computes the remaining slices of $MGL_S$ as $s_nMGL_S=\\Sigma^n_TH\\mathbb{Z}\\otimes \\mathbb{L}^{-n}$ (again, after inverting the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02436","kind":"arxiv","version":1},"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":"1501.02436","created_at":"2026-05-18T02:29:37.964122+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02436v1","created_at":"2026-05-18T02:29:37.964122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02436","created_at":"2026-05-18T02:29:37.964122+00:00"},{"alias_kind":"pith_short_12","alias_value":"QT34KO3MR4ZP","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QT34KO3MR4ZPN3NE","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QT34KO3M","created_at":"2026-05-18T12:29:37.295048+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/QT34KO3MR4ZPN3NEEDXY3RGTN4","json":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4.json","graph_json":"https://pith.science/api/pith-number/QT34KO3MR4ZPN3NEEDXY3RGTN4/graph.json","events_json":"https://pith.science/api/pith-number/QT34KO3MR4ZPN3NEEDXY3RGTN4/events.json","paper":"https://pith.science/paper/QT34KO3M"},"agent_actions":{"view_html":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4","download_json":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4.json","view_paper":"https://pith.science/paper/QT34KO3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02436&json=true","fetch_graph":"https://pith.science/api/pith-number/QT34KO3MR4ZPN3NEEDXY3RGTN4/graph.json","fetch_events":"https://pith.science/api/pith-number/QT34KO3MR4ZPN3NEEDXY3RGTN4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4/action/storage_attestation","attest_author":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4/action/author_attestation","sign_citation":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4/action/citation_signature","submit_replication":"https://pith.science/pith/QT34KO3MR4ZPN3NEEDXY3RGTN4/action/replication_record"}},"created_at":"2026-05-18T02:29:37.964122+00:00","updated_at":"2026-05-18T02:29:37.964122+00:00"}