{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AARJD4WZILSE2UC5KRBJF7DFHY","short_pith_number":"pith:AARJD4WZ","schema_version":"1.0","canonical_sha256":"002291f2d942e44d505d544292fc653e230f10fe8cead5799355c743944d7e2a","source":{"kind":"arxiv","id":"1712.09487","version":1},"attestation_state":"computed","paper":{"title":"Total $p$-differentials on schemes over $Z/p^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"David Zureick-Brown, Eric Katz, Joseph Rabinoff, Taylor Dupuy","submitted_at":"2017-12-27T04:21:35Z","abstract_excerpt":"For a scheme $X$ defined over the length $2$ $p$-typical Witt vectors $W_2(k)$ of a characteristic $p$ field, we introduce total $p$-differentials which interpolate between Frobenius-twisted differentials and Buium's $p$-differentials. They form a sheaf over the reduction $X_0$, and behave as if they were the sheaf of differentials of $X$ over a deeper base below $W_2(k)$. This allows us to construct the analogues of Gauss-Manin connections and Kodaira-Spencer classes as in the Katz-Oda formalism. We make connections to Frobenius lifts, Borger-Weiland's biring formalism, and Deligne--Illusie c"},"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":"1712.09487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-27T04:21:35Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a1c62bcc7b859c08fa7621dda8b3656db79173bb3510340cd57d8549c1684c89","abstract_canon_sha256":"47231841795520ba44701da58851158df4417d6c32c79d0c257fba6626a1d3e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:08.240206Z","signature_b64":"W2ztR/7Nb/iVnaVVgyulhe83QXmbPTsD+WQlIMqKtumwagHzsU/sygG5lV9h2oPN8khtmVuWIDWD96zNUYu+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"002291f2d942e44d505d544292fc653e230f10fe8cead5799355c743944d7e2a","last_reissued_at":"2026-05-18T00:27:08.239577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:08.239577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Total $p$-differentials on schemes over $Z/p^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"David Zureick-Brown, Eric Katz, Joseph Rabinoff, Taylor Dupuy","submitted_at":"2017-12-27T04:21:35Z","abstract_excerpt":"For a scheme $X$ defined over the length $2$ $p$-typical Witt vectors $W_2(k)$ of a characteristic $p$ field, we introduce total $p$-differentials which interpolate between Frobenius-twisted differentials and Buium's $p$-differentials. They form a sheaf over the reduction $X_0$, and behave as if they were the sheaf of differentials of $X$ over a deeper base below $W_2(k)$. This allows us to construct the analogues of Gauss-Manin connections and Kodaira-Spencer classes as in the Katz-Oda formalism. We make connections to Frobenius lifts, Borger-Weiland's biring formalism, and Deligne--Illusie c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09487","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":"1712.09487","created_at":"2026-05-18T00:27:08.239665+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09487v1","created_at":"2026-05-18T00:27:08.239665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09487","created_at":"2026-05-18T00:27:08.239665+00:00"},{"alias_kind":"pith_short_12","alias_value":"AARJD4WZILSE","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AARJD4WZILSE2UC5","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AARJD4WZ","created_at":"2026-05-18T12:31:05.417338+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/AARJD4WZILSE2UC5KRBJF7DFHY","json":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY.json","graph_json":"https://pith.science/api/pith-number/AARJD4WZILSE2UC5KRBJF7DFHY/graph.json","events_json":"https://pith.science/api/pith-number/AARJD4WZILSE2UC5KRBJF7DFHY/events.json","paper":"https://pith.science/paper/AARJD4WZ"},"agent_actions":{"view_html":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY","download_json":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY.json","view_paper":"https://pith.science/paper/AARJD4WZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09487&json=true","fetch_graph":"https://pith.science/api/pith-number/AARJD4WZILSE2UC5KRBJF7DFHY/graph.json","fetch_events":"https://pith.science/api/pith-number/AARJD4WZILSE2UC5KRBJF7DFHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY/action/storage_attestation","attest_author":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY/action/author_attestation","sign_citation":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY/action/citation_signature","submit_replication":"https://pith.science/pith/AARJD4WZILSE2UC5KRBJF7DFHY/action/replication_record"}},"created_at":"2026-05-18T00:27:08.239665+00:00","updated_at":"2026-05-18T00:27:08.239665+00:00"}