{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BLT5AYHMCZKP5IL4SDSAAVP4AM","short_pith_number":"pith:BLT5AYHM","schema_version":"1.0","canonical_sha256":"0ae7d060ec1654fea17c90e40055fc031ec8dcb7db76ee025089ff5c17642b53","source":{"kind":"arxiv","id":"1607.00523","version":1},"attestation_state":"computed","paper":{"title":"On the arithmetic of Z_p-extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Daqing Wan, Michiel Kosters","submitted_at":"2016-07-02T15:39:33Z","abstract_excerpt":"This paper contains three parts.\n  In the first part, we give a thorough overview of the theory of Artin-Schreier-Witt extensions: this theory allows one to understand the $\\mathbf{Z}/p^n\\mathbf{Z}$-extensions of any field $K$ of characteristic $p$ via $p$-typical Witt vectors. Let $W_n(K)$ be the ring of $p$-typical Witt vectors of $K$ of length $n$ and let $\\wp = F-\\mathrm{id}: W_n(K)\\longrightarrow W_n(K)$, where $F$ is the Frobenius map and $\\mathrm{id}$ is the identity map. Artin-Schreier-Witt theory tells us that the abelian group $W_n(K)/\\wp W_n(K)$ represents the set of $\\mathbf{Z}/p^n"},"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":"1607.00523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-02T15:39:33Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"479b0bb37c8577226737de1fb44ee7b5125c2121ef0cfa648f66afdee8a5ecc1","abstract_canon_sha256":"c32671682d712b74769b30e106accf000177d346b7f29ef1e5c7660cf86b91ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:36.857987Z","signature_b64":"xS2juS/Yy/Ye+moUSVmFtfNDHHWt4sZKzkQEIOtP9KpJCaRGxXV8H6u2IQRCWOZsb9VPTbotp4lDTKRphvMPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ae7d060ec1654fea17c90e40055fc031ec8dcb7db76ee025089ff5c17642b53","last_reissued_at":"2026-05-18T01:11:36.857637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:36.857637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the arithmetic of Z_p-extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Daqing Wan, Michiel Kosters","submitted_at":"2016-07-02T15:39:33Z","abstract_excerpt":"This paper contains three parts.\n  In the first part, we give a thorough overview of the theory of Artin-Schreier-Witt extensions: this theory allows one to understand the $\\mathbf{Z}/p^n\\mathbf{Z}$-extensions of any field $K$ of characteristic $p$ via $p$-typical Witt vectors. Let $W_n(K)$ be the ring of $p$-typical Witt vectors of $K$ of length $n$ and let $\\wp = F-\\mathrm{id}: W_n(K)\\longrightarrow W_n(K)$, where $F$ is the Frobenius map and $\\mathrm{id}$ is the identity map. Artin-Schreier-Witt theory tells us that the abelian group $W_n(K)/\\wp W_n(K)$ represents the set of $\\mathbf{Z}/p^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00523","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":"1607.00523","created_at":"2026-05-18T01:11:36.857699+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.00523v1","created_at":"2026-05-18T01:11:36.857699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00523","created_at":"2026-05-18T01:11:36.857699+00:00"},{"alias_kind":"pith_short_12","alias_value":"BLT5AYHMCZKP","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BLT5AYHMCZKP5IL4","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BLT5AYHM","created_at":"2026-05-18T12:30:07.202191+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/BLT5AYHMCZKP5IL4SDSAAVP4AM","json":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM.json","graph_json":"https://pith.science/api/pith-number/BLT5AYHMCZKP5IL4SDSAAVP4AM/graph.json","events_json":"https://pith.science/api/pith-number/BLT5AYHMCZKP5IL4SDSAAVP4AM/events.json","paper":"https://pith.science/paper/BLT5AYHM"},"agent_actions":{"view_html":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM","download_json":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM.json","view_paper":"https://pith.science/paper/BLT5AYHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.00523&json=true","fetch_graph":"https://pith.science/api/pith-number/BLT5AYHMCZKP5IL4SDSAAVP4AM/graph.json","fetch_events":"https://pith.science/api/pith-number/BLT5AYHMCZKP5IL4SDSAAVP4AM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM/action/storage_attestation","attest_author":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM/action/author_attestation","sign_citation":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM/action/citation_signature","submit_replication":"https://pith.science/pith/BLT5AYHMCZKP5IL4SDSAAVP4AM/action/replication_record"}},"created_at":"2026-05-18T01:11:36.857699+00:00","updated_at":"2026-05-18T01:11:36.857699+00:00"}