{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QUZP35JUMUQKVXZYHMEM2J6KPG","short_pith_number":"pith:QUZP35JU","schema_version":"1.0","canonical_sha256":"8532fdf5346520aadf383b08cd27ca79aa834a2f8e707bca655b1ec1ae2d70f8","source":{"kind":"arxiv","id":"1305.0775","version":3},"attestation_state":"computed","paper":{"title":"Residual ideals of MacLane valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Nart, Jes\\'us Montes, Jordi Gu\\`ardia, Julio Fern\\'andez","submitted_at":"2013-05-03T16:54:34Z","abstract_excerpt":"Let $K$ be a field equipped with a discrete valuation $v$. In a pioneering work, S. MacLane determined all valuations on $K(x)$ extending $v$. His work was recently reviewed and generalized by M. Vaqui\\'e, by using the graded algebra of a valuation. We extend Vaqui\\'e's approach by studying residual ideals of the graded algebra of a valuation as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of the theory. As a consequence, we determine the structure of the graded algebra of the discrete valuations on $K(x)$ and we show how these"},"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":"1305.0775","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-03T16:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"64abe9037b55a3845b196815b431a2eedd5da298cdb699b0fc7cdcb6c5c6e3f5","abstract_canon_sha256":"32717cd364ec31140c5d3db8bb143ac6427719e4096e91e6b448632a4389f13d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:33.834126Z","signature_b64":"8kILTBawSFAlIoEmPt/XZH5/IZBd8+btr+J+lbUExzorauZlAsrFg8p0/jmHBrn7J9wKbFUfimFtMI0UxAgeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8532fdf5346520aadf383b08cd27ca79aa834a2f8e707bca655b1ec1ae2d70f8","last_reissued_at":"2026-05-18T03:17:33.833618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:33.833618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Residual ideals of MacLane valuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Nart, Jes\\'us Montes, Jordi Gu\\`ardia, Julio Fern\\'andez","submitted_at":"2013-05-03T16:54:34Z","abstract_excerpt":"Let $K$ be a field equipped with a discrete valuation $v$. In a pioneering work, S. MacLane determined all valuations on $K(x)$ extending $v$. His work was recently reviewed and generalized by M. Vaqui\\'e, by using the graded algebra of a valuation. We extend Vaqui\\'e's approach by studying residual ideals of the graded algebra of a valuation as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of the theory. As a consequence, we determine the structure of the graded algebra of the discrete valuations on $K(x)$ and we show how these"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0775","kind":"arxiv","version":3},"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":"1305.0775","created_at":"2026-05-18T03:17:33.833702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0775v3","created_at":"2026-05-18T03:17:33.833702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0775","created_at":"2026-05-18T03:17:33.833702+00:00"},{"alias_kind":"pith_short_12","alias_value":"QUZP35JUMUQK","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QUZP35JUMUQKVXZY","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QUZP35JU","created_at":"2026-05-18T12:27:57.521954+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/QUZP35JUMUQKVXZYHMEM2J6KPG","json":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG.json","graph_json":"https://pith.science/api/pith-number/QUZP35JUMUQKVXZYHMEM2J6KPG/graph.json","events_json":"https://pith.science/api/pith-number/QUZP35JUMUQKVXZYHMEM2J6KPG/events.json","paper":"https://pith.science/paper/QUZP35JU"},"agent_actions":{"view_html":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG","download_json":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG.json","view_paper":"https://pith.science/paper/QUZP35JU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0775&json=true","fetch_graph":"https://pith.science/api/pith-number/QUZP35JUMUQKVXZYHMEM2J6KPG/graph.json","fetch_events":"https://pith.science/api/pith-number/QUZP35JUMUQKVXZYHMEM2J6KPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG/action/storage_attestation","attest_author":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG/action/author_attestation","sign_citation":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG/action/citation_signature","submit_replication":"https://pith.science/pith/QUZP35JUMUQKVXZYHMEM2J6KPG/action/replication_record"}},"created_at":"2026-05-18T03:17:33.833702+00:00","updated_at":"2026-05-18T03:17:33.833702+00:00"}