{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WSHMNWSIDCJVOI6BTEDMBSUAKN","short_pith_number":"pith:WSHMNWSI","schema_version":"1.0","canonical_sha256":"b48ec6da4818935723c19906c0ca80536ae4ca654f7baf04fcb92a4e2ab3389e","source":{"kind":"arxiv","id":"1704.03842","version":3},"attestation_state":"computed","paper":{"title":"Tropical Newton-Puiseux polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dima Grigoriev","submitted_at":"2017-04-12T17:00:04Z","abstract_excerpt":"We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a tropical curve is designed. The complexity of resolubility of tropical prevarieties of arbitrary codimensions is studied. Tropical Newton-Puiseux rational functions are introduced, and we prove that any tropical polynomial has a resolution in tropical Newton-Puiseux rational functions (this can be treated as a tropical analog of the algebraic closedness of the f"},"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":"1704.03842","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-12T17:00:04Z","cross_cats_sorted":[],"title_canon_sha256":"5f5f41f95919f406420123efff39b43c733084384167d2c3d018d9abab2bcc4e","abstract_canon_sha256":"a5411f804d20078e251aa390935fe219849de4c4e2f300e11502500b013e623d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:23.644407Z","signature_b64":"Fn3x/t/bcAo5e5iNWHg8C0huvhzjjPZlzaKjL2wR+gqNn7JpbHyp1MBvic9KAYYb6WPcpEOjMM92J29Ipr4+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b48ec6da4818935723c19906c0ca80536ae4ca654f7baf04fcb92a4e2ab3389e","last_reissued_at":"2026-05-18T00:01:23.643913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:23.643913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tropical Newton-Puiseux polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dima Grigoriev","submitted_at":"2017-04-12T17:00:04Z","abstract_excerpt":"We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a tropical curve is designed. The complexity of resolubility of tropical prevarieties of arbitrary codimensions is studied. Tropical Newton-Puiseux rational functions are introduced, and we prove that any tropical polynomial has a resolution in tropical Newton-Puiseux rational functions (this can be treated as a tropical analog of the algebraic closedness of the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03842","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":"1704.03842","created_at":"2026-05-18T00:01:23.643979+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.03842v3","created_at":"2026-05-18T00:01:23.643979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03842","created_at":"2026-05-18T00:01:23.643979+00:00"},{"alias_kind":"pith_short_12","alias_value":"WSHMNWSIDCJV","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WSHMNWSIDCJVOI6B","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WSHMNWSI","created_at":"2026-05-18T12:31:53.515858+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/WSHMNWSIDCJVOI6BTEDMBSUAKN","json":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN.json","graph_json":"https://pith.science/api/pith-number/WSHMNWSIDCJVOI6BTEDMBSUAKN/graph.json","events_json":"https://pith.science/api/pith-number/WSHMNWSIDCJVOI6BTEDMBSUAKN/events.json","paper":"https://pith.science/paper/WSHMNWSI"},"agent_actions":{"view_html":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN","download_json":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN.json","view_paper":"https://pith.science/paper/WSHMNWSI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.03842&json=true","fetch_graph":"https://pith.science/api/pith-number/WSHMNWSIDCJVOI6BTEDMBSUAKN/graph.json","fetch_events":"https://pith.science/api/pith-number/WSHMNWSIDCJVOI6BTEDMBSUAKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN/action/storage_attestation","attest_author":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN/action/author_attestation","sign_citation":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN/action/citation_signature","submit_replication":"https://pith.science/pith/WSHMNWSIDCJVOI6BTEDMBSUAKN/action/replication_record"}},"created_at":"2026-05-18T00:01:23.643979+00:00","updated_at":"2026-05-18T00:01:23.643979+00:00"}