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We construct an explicit list of polynomials $g_d^{(1)},\\dots,g_d^{(t_d)}\\in\\mathbb{Z}[A_0,\\dots,A_{d-1}]$ such that the valuations $\\mathrm{ord}(g_{d}^{(i)}(a_0,\\dots,a_{d-1}))$ for $i=1,\\dots,t_d$ uniquely determine this set of distances for the polynomi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17148","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.17148/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2410.17148","created_at":"2026-07-05T10:28:24.834767+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.17148v2","created_at":"2026-07-05T10:28:24.834767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17148","created_at":"2026-07-05T10:28:24.834767+00:00"},{"alias_kind":"pith_short_12","alias_value":"6FNDSWCDIULM","created_at":"2026-07-05T10:28:24.834767+00:00"},{"alias_kind":"pith_short_16","alias_value":"6FNDSWCDIULMLC7E","created_at":"2026-07-05T10:28:24.834767+00:00"},{"alias_kind":"pith_short_8","alias_value":"6FNDSWCD","created_at":"2026-07-05T10:28:24.834767+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.08487","citing_title":"Invariants recovering the reduction type of a hyperelliptic curve","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT","json":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT.json","graph_json":"https://pith.science/api/pith-number/6FNDSWCDIULMLC7EO7PKIUXJVT/graph.json","events_json":"https://pith.science/api/pith-number/6FNDSWCDIULMLC7EO7PKIUXJVT/events.json","paper":"https://pith.science/paper/6FNDSWCD"},"agent_actions":{"view_html":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT","download_json":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT.json","view_paper":"https://pith.science/paper/6FNDSWCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.17148&json=true","fetch_graph":"https://pith.science/api/pith-number/6FNDSWCDIULMLC7EO7PKIUXJVT/graph.json","fetch_events":"https://pith.science/api/pith-number/6FNDSWCDIULMLC7EO7PKIUXJVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT/action/storage_attestation","attest_author":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT/action/author_attestation","sign_citation":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT/action/citation_signature","submit_replication":"https://pith.science/pith/6FNDSWCDIULMLC7EO7PKIUXJVT/action/replication_record"}},"created_at":"2026-07-05T10:28:24.834767+00:00","updated_at":"2026-07-05T10:28:24.834767+00:00"}