{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:P32PTN6QRP7QHQC4KCQHI7BXS4","short_pith_number":"pith:P32PTN6Q","schema_version":"1.0","canonical_sha256":"7ef4f9b7d08bff03c05c50a0747c379705344315c31b718bfce712898013290e","source":{"kind":"arxiv","id":"1903.06736","version":1},"attestation_state":"computed","paper":{"title":"Defectless polynomials over henselian fields and inductive valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Enric Nart, Nath\\'alia Moraes de Oliveira","submitted_at":"2019-03-15T18:29:49Z","abstract_excerpt":"Let $(K,v)$ be a henselian valued field. Let $\\mathbb{P}^{dless}\\subset K[x]$ be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation $\\,\\approx\\,$ on $\\,\\mathbb{P}^{dless}$, we establish a canonical bijection $\\mathbb{M}\\to \\mathbb{P}^{dless}/\\!\\!\\approx$, where $\\mathbb{M}$ is a discrete MacLane space, constructed in terms of inductive valuations on $K[x]$ extending $v$."},"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":"1903.06736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-03-15T18:29:49Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"aaa947d5664ebff129bc45ba7c77c03417f9109d33ed213c8db3983cdf53011d","abstract_canon_sha256":"2d85bd6645fe978f28aa34ec13b2aae2c8113d6193ca33a80d5c91cc1eb337b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:09.179783Z","signature_b64":"A7iIM8QZSOqrklOsQYCAdfpFRqHkxmfZcGSrWBvPzhsVTZg3czuD/Ph4iFoek9Q/BPbFxZknhRIU0ByAF6t+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ef4f9b7d08bff03c05c50a0747c379705344315c31b718bfce712898013290e","last_reissued_at":"2026-05-17T23:51:09.179187Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:09.179187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Defectless polynomials over henselian fields and inductive valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Enric Nart, Nath\\'alia Moraes de Oliveira","submitted_at":"2019-03-15T18:29:49Z","abstract_excerpt":"Let $(K,v)$ be a henselian valued field. Let $\\mathbb{P}^{dless}\\subset K[x]$ be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation $\\,\\approx\\,$ on $\\,\\mathbb{P}^{dless}$, we establish a canonical bijection $\\mathbb{M}\\to \\mathbb{P}^{dless}/\\!\\!\\approx$, where $\\mathbb{M}$ is a discrete MacLane space, constructed in terms of inductive valuations on $K[x]$ extending $v$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06736","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":"1903.06736","created_at":"2026-05-17T23:51:09.179267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.06736v1","created_at":"2026-05-17T23:51:09.179267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06736","created_at":"2026-05-17T23:51:09.179267+00:00"},{"alias_kind":"pith_short_12","alias_value":"P32PTN6QRP7Q","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"P32PTN6QRP7QHQC4","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"P32PTN6Q","created_at":"2026-05-18T12:33:24.271573+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/P32PTN6QRP7QHQC4KCQHI7BXS4","json":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4.json","graph_json":"https://pith.science/api/pith-number/P32PTN6QRP7QHQC4KCQHI7BXS4/graph.json","events_json":"https://pith.science/api/pith-number/P32PTN6QRP7QHQC4KCQHI7BXS4/events.json","paper":"https://pith.science/paper/P32PTN6Q"},"agent_actions":{"view_html":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4","download_json":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4.json","view_paper":"https://pith.science/paper/P32PTN6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.06736&json=true","fetch_graph":"https://pith.science/api/pith-number/P32PTN6QRP7QHQC4KCQHI7BXS4/graph.json","fetch_events":"https://pith.science/api/pith-number/P32PTN6QRP7QHQC4KCQHI7BXS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4/action/storage_attestation","attest_author":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4/action/author_attestation","sign_citation":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4/action/citation_signature","submit_replication":"https://pith.science/pith/P32PTN6QRP7QHQC4KCQHI7BXS4/action/replication_record"}},"created_at":"2026-05-17T23:51:09.179267+00:00","updated_at":"2026-05-17T23:51:09.179267+00:00"}