{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PV6AL4WBWHCZ7USCWY4V3YZGJT","short_pith_number":"pith:PV6AL4WB","schema_version":"1.0","canonical_sha256":"7d7c05f2c1b1c59fd242b6395de3264cf1177bd2ed7d1a0a7d19fd45ebbe3c55","source":{"kind":"arxiv","id":"1306.4141","version":1},"attestation_state":"computed","paper":{"title":"Minimum Degree of the Difference of Two Polynomials over Q, and Weighted Plane Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Zvonkin, F. Pakovich","submitted_at":"2013-06-18T11:15:17Z","abstract_excerpt":"A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins d'enfants, which studies the action of the absolute Galois group on graphs embedded into Riemann surfaces, we show that a weighted plane tree is a graphical representation of a pair of coprime complex polynomials A,B such that: (a) deg A = deg B, and A and B have the same leading coefficient; (b) the multiplicities of the roots of A (respectively, of B) are "},"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":"1306.4141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-06-18T11:15:17Z","cross_cats_sorted":[],"title_canon_sha256":"39bd568e5ff0b0bf63da84242cb115eddc0c50848ac709bfa17b00e29839f476","abstract_canon_sha256":"7e41e77b4d0678f5bbaab8ead86c7d4769b5175f83f28425514aaecf3807ea22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:37.011569Z","signature_b64":"A1AvWeZFIwL9pFh4M3cVfqb8bachXVGdGomr1IWwVnezKqFgIbiuykNAQAV7Q5y0GGBnso6itUIVRoL/mPT9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d7c05f2c1b1c59fd242b6395de3264cf1177bd2ed7d1a0a7d19fd45ebbe3c55","last_reissued_at":"2026-05-18T03:20:37.010827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:37.010827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum Degree of the Difference of Two Polynomials over Q, and Weighted Plane Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"A. Zvonkin, F. Pakovich","submitted_at":"2013-06-18T11:15:17Z","abstract_excerpt":"A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins d'enfants, which studies the action of the absolute Galois group on graphs embedded into Riemann surfaces, we show that a weighted plane tree is a graphical representation of a pair of coprime complex polynomials A,B such that: (a) deg A = deg B, and A and B have the same leading coefficient; (b) the multiplicities of the roots of A (respectively, of B) are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4141","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":"1306.4141","created_at":"2026-05-18T03:20:37.010937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.4141v1","created_at":"2026-05-18T03:20:37.010937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4141","created_at":"2026-05-18T03:20:37.010937+00:00"},{"alias_kind":"pith_short_12","alias_value":"PV6AL4WBWHCZ","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"PV6AL4WBWHCZ7USC","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"PV6AL4WB","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/PV6AL4WBWHCZ7USCWY4V3YZGJT","json":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT.json","graph_json":"https://pith.science/api/pith-number/PV6AL4WBWHCZ7USCWY4V3YZGJT/graph.json","events_json":"https://pith.science/api/pith-number/PV6AL4WBWHCZ7USCWY4V3YZGJT/events.json","paper":"https://pith.science/paper/PV6AL4WB"},"agent_actions":{"view_html":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT","download_json":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT.json","view_paper":"https://pith.science/paper/PV6AL4WB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.4141&json=true","fetch_graph":"https://pith.science/api/pith-number/PV6AL4WBWHCZ7USCWY4V3YZGJT/graph.json","fetch_events":"https://pith.science/api/pith-number/PV6AL4WBWHCZ7USCWY4V3YZGJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT/action/storage_attestation","attest_author":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT/action/author_attestation","sign_citation":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT/action/citation_signature","submit_replication":"https://pith.science/pith/PV6AL4WBWHCZ7USCWY4V3YZGJT/action/replication_record"}},"created_at":"2026-05-18T03:20:37.010937+00:00","updated_at":"2026-05-18T03:20:37.010937+00:00"}