{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T5N4S5NVZPDZ555PX4TVSRCUJG","short_pith_number":"pith:T5N4S5NV","schema_version":"1.0","canonical_sha256":"9f5bc975b5cbc79ef7afbf2759445449922b0707bf0c80918611bbdfae05573d","source":{"kind":"arxiv","id":"1703.07010","version":1},"attestation_state":"computed","paper":{"title":"On Frobenius and Fibers of Arithmetic Jet Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arnab Saha, James Borger","submitted_at":"2017-03-21T00:11:58Z","abstract_excerpt":"In this article, given a scheme $X$ we show the existence of canonical lifts of Frobenius maps in an inverse system of schemes obtained from the fiber product of the canonical prolongation sequence of arithmetic jet spaces $J^*X$ and a prolongation sequence $S^*$ over the scheme $X$. As a consequence, for any smooth group scheme $E$, if $N^n$ denote the kernel of the canonical projection map of the $n$-th jet space $J^nE \\rightarrow E$, then the inverse system $\\{N^n\\}_n$ is a prolongation sequence."},"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":"1703.07010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-21T00:11:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ac6dea39b8e3ed2675f8723e7526d19f69915062415ab9d9cd493a505c3accb7","abstract_canon_sha256":"40407969020c023c06de8ed8a9c7262a6d9174b1e457898dc0c682991d4ecacc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:11.628796Z","signature_b64":"LMqqPTVsB2dtEf9SQkDHHCZ0pWWlmdSI84Ci7QTHYpreMPfoi0MbZLKQb8me8v+0bK0Jo8QzqnnmGyC7U9CaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f5bc975b5cbc79ef7afbf2759445449922b0707bf0c80918611bbdfae05573d","last_reissued_at":"2026-05-18T00:48:11.628027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:11.628027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Frobenius and Fibers of Arithmetic Jet Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arnab Saha, James Borger","submitted_at":"2017-03-21T00:11:58Z","abstract_excerpt":"In this article, given a scheme $X$ we show the existence of canonical lifts of Frobenius maps in an inverse system of schemes obtained from the fiber product of the canonical prolongation sequence of arithmetic jet spaces $J^*X$ and a prolongation sequence $S^*$ over the scheme $X$. As a consequence, for any smooth group scheme $E$, if $N^n$ denote the kernel of the canonical projection map of the $n$-th jet space $J^nE \\rightarrow E$, then the inverse system $\\{N^n\\}_n$ is a prolongation sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07010","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":"1703.07010","created_at":"2026-05-18T00:48:11.628150+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07010v1","created_at":"2026-05-18T00:48:11.628150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07010","created_at":"2026-05-18T00:48:11.628150+00:00"},{"alias_kind":"pith_short_12","alias_value":"T5N4S5NVZPDZ","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"T5N4S5NVZPDZ555P","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"T5N4S5NV","created_at":"2026-05-18T12:31:43.269735+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/T5N4S5NVZPDZ555PX4TVSRCUJG","json":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG.json","graph_json":"https://pith.science/api/pith-number/T5N4S5NVZPDZ555PX4TVSRCUJG/graph.json","events_json":"https://pith.science/api/pith-number/T5N4S5NVZPDZ555PX4TVSRCUJG/events.json","paper":"https://pith.science/paper/T5N4S5NV"},"agent_actions":{"view_html":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG","download_json":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG.json","view_paper":"https://pith.science/paper/T5N4S5NV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07010&json=true","fetch_graph":"https://pith.science/api/pith-number/T5N4S5NVZPDZ555PX4TVSRCUJG/graph.json","fetch_events":"https://pith.science/api/pith-number/T5N4S5NVZPDZ555PX4TVSRCUJG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG/action/storage_attestation","attest_author":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG/action/author_attestation","sign_citation":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG/action/citation_signature","submit_replication":"https://pith.science/pith/T5N4S5NVZPDZ555PX4TVSRCUJG/action/replication_record"}},"created_at":"2026-05-18T00:48:11.628150+00:00","updated_at":"2026-05-18T00:48:11.628150+00:00"}