{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GOCNEQKUDHSW5GUQLYO6THL4MZ","short_pith_number":"pith:GOCNEQKU","schema_version":"1.0","canonical_sha256":"3384d2415419e56e9a905e1de99d7c6645faafdd3ba4133f1a88fcffd7374c95","source":{"kind":"arxiv","id":"1205.1340","version":1},"attestation_state":"computed","paper":{"title":"Local computation of differents and discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Nart","submitted_at":"2012-05-07T10:54:05Z","abstract_excerpt":"We obtain several results on the computation of different and discriminant ideals of finite extensions of local fields. As an application, we deduce routines to compute the $\\p$-adic valuation of the discriminant $\\dsc(f)$, and the resultant $\\res(f,g)$, for polynomials $f(x),g(x)\\in A[x]$, where $A$ is a Dedekind domain and $\\p$ is a non-zero prime ideal of $A$ with finite residue field. These routines do not require the computation of neither $\\dsc(f)$ nor $\\res(f,g)$; hence, they are useful in cases where this latter computation is inefficient because the polynomials have a large degree or "},"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":"1205.1340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-07T10:54:05Z","cross_cats_sorted":[],"title_canon_sha256":"67846ebdc31845d745e8c3af669c42a3b3dbcbca485942635e348fa565a21c65","abstract_canon_sha256":"210a1c95aaf90957a341f4748d7b66c7a30cb0ce7c0403b3af75bc1230878db1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:11.438201Z","signature_b64":"6O0veG6QbZJNVE0s3uBIYCDhFqvBhn5o7TSd/oHbHt26LKqWu58oSB00XcO4TWz2iUvtE4B+b6t9Hm+mcEUFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3384d2415419e56e9a905e1de99d7c6645faafdd3ba4133f1a88fcffd7374c95","last_reissued_at":"2026-05-18T03:56:11.437367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:11.437367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local computation of differents and discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Nart","submitted_at":"2012-05-07T10:54:05Z","abstract_excerpt":"We obtain several results on the computation of different and discriminant ideals of finite extensions of local fields. As an application, we deduce routines to compute the $\\p$-adic valuation of the discriminant $\\dsc(f)$, and the resultant $\\res(f,g)$, for polynomials $f(x),g(x)\\in A[x]$, where $A$ is a Dedekind domain and $\\p$ is a non-zero prime ideal of $A$ with finite residue field. These routines do not require the computation of neither $\\dsc(f)$ nor $\\res(f,g)$; hence, they are useful in cases where this latter computation is inefficient because the polynomials have a large degree or "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1340","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":"1205.1340","created_at":"2026-05-18T03:56:11.437506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1340v1","created_at":"2026-05-18T03:56:11.437506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1340","created_at":"2026-05-18T03:56:11.437506+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOCNEQKUDHSW","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOCNEQKUDHSW5GUQ","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOCNEQKU","created_at":"2026-05-18T12:27:06.952714+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/GOCNEQKUDHSW5GUQLYO6THL4MZ","json":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ.json","graph_json":"https://pith.science/api/pith-number/GOCNEQKUDHSW5GUQLYO6THL4MZ/graph.json","events_json":"https://pith.science/api/pith-number/GOCNEQKUDHSW5GUQLYO6THL4MZ/events.json","paper":"https://pith.science/paper/GOCNEQKU"},"agent_actions":{"view_html":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ","download_json":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ.json","view_paper":"https://pith.science/paper/GOCNEQKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1340&json=true","fetch_graph":"https://pith.science/api/pith-number/GOCNEQKUDHSW5GUQLYO6THL4MZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GOCNEQKUDHSW5GUQLYO6THL4MZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ/action/storage_attestation","attest_author":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ/action/author_attestation","sign_citation":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ/action/citation_signature","submit_replication":"https://pith.science/pith/GOCNEQKUDHSW5GUQLYO6THL4MZ/action/replication_record"}},"created_at":"2026-05-18T03:56:11.437506+00:00","updated_at":"2026-05-18T03:56:11.437506+00:00"}