{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EO6MM2YG54GRJLSVOVPVR4V6A2","short_pith_number":"pith:EO6MM2YG","schema_version":"1.0","canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","source":{"kind":"arxiv","id":"1504.06671","version":1},"attestation_state":"computed","paper":{"title":"Enumerating Extensions of $(\\pi)$-Adic Fields with Given Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brian Sinclair, Sebastian Pauli","submitted_at":"2015-04-24T23:53:57Z","abstract_excerpt":"We give an algorithm that constructs a minimal set of polynomials defining all extension of a $(\\pi)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon."},"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":"1504.06671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-24T23:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"c19da2c2c3436823e165a0b9a9104a9635d8b0d676be3386503aaea5b32bac09","abstract_canon_sha256":"dbe1f0c21d4c26e62ae2dfbef8a73e3fd00d9040e3f879b7487c1e5a85897b79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:20.729044Z","signature_b64":"HtfrppfIxdc3yWhsAdFNy1KB6Z8Q7xwkHO7BXJNqqo4sIvBdyuqg9UZu9VZpqfqogVfv3z3jZUvQYEgjNpITCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23bcc66b06ef0d14ae55755f58f2be069cf5f8659e6fa91d15ab32041ceb1748","last_reissued_at":"2026-05-18T00:48:20.728312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:20.728312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerating Extensions of $(\\pi)$-Adic Fields with Given Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brian Sinclair, Sebastian Pauli","submitted_at":"2015-04-24T23:53:57Z","abstract_excerpt":"We give an algorithm that constructs a minimal set of polynomials defining all extension of a $(\\pi)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of the ramification polygon."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06671","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":"1504.06671","created_at":"2026-05-18T00:48:20.728446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06671v1","created_at":"2026-05-18T00:48:20.728446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06671","created_at":"2026-05-18T00:48:20.728446+00:00"},{"alias_kind":"pith_short_12","alias_value":"EO6MM2YG54GR","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EO6MM2YG54GRJLSV","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EO6MM2YG","created_at":"2026-05-18T12:29:19.899920+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/EO6MM2YG54GRJLSVOVPVR4V6A2","json":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2.json","graph_json":"https://pith.science/api/pith-number/EO6MM2YG54GRJLSVOVPVR4V6A2/graph.json","events_json":"https://pith.science/api/pith-number/EO6MM2YG54GRJLSVOVPVR4V6A2/events.json","paper":"https://pith.science/paper/EO6MM2YG"},"agent_actions":{"view_html":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2","download_json":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2.json","view_paper":"https://pith.science/paper/EO6MM2YG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06671&json=true","fetch_graph":"https://pith.science/api/pith-number/EO6MM2YG54GRJLSVOVPVR4V6A2/graph.json","fetch_events":"https://pith.science/api/pith-number/EO6MM2YG54GRJLSVOVPVR4V6A2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/action/storage_attestation","attest_author":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/action/author_attestation","sign_citation":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/action/citation_signature","submit_replication":"https://pith.science/pith/EO6MM2YG54GRJLSVOVPVR4V6A2/action/replication_record"}},"created_at":"2026-05-18T00:48:20.728446+00:00","updated_at":"2026-05-18T00:48:20.728446+00:00"}