{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4EK3T55WAPHOC3COGWEJMQLWQU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4ff08562509631b8ba698e39ac329acbdf2321dbce2f30c9ae58f98b96d8b3b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-10T14:40:24Z","title_canon_sha256":"90a0c86b46ed087c3ffdf37bb1c02ae062f6a344a97f61d6a4bb4433d7ea9faa"},"schema_version":"1.0","source":{"id":"1804.03566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03566","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03566v1","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03566","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"4EK3T55WAPHO","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4EK3T55WAPHOC3CO","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4EK3T55W","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:009d2185ea6dc2b29075572aa04f78ef147474b8ff55316439c5d194a8d6d0bf","target":"graph","created_at":"2026-05-18T00:18:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let ${{\\bf F}}_q$ be a finite field of order a positive power $q$ of a prime number. We study the nonarchimedean quadratic Lagrange spectrum defined by Parkkonen and Paulin by considering the approximation by elements of the orbit of a given quadratic power series in ${{\\bf F}}_q((Y^{-1}))$, for the action by homographies and anti-homographies of ${\\rm PGL}_2({{\\bf F}}_q[Y])$ on ${{\\bf F}}_q((Y^{-1})) \\cup \\{\\infty\\}$. While their approach used geometric methods of group actions on Bruhat--Tits trees, ours is based on the theory of continued fractions in power series fields.","authors_text":"Yann Bugeaud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-10T14:40:24Z","title":"Nonarchimedean quadratic Lagrange spectra and continued fractions in power series fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03566","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:91c3f3b65e59b1fc92615a65035520c2ebcfc60931f6d93eace2ed7c132d0e01","target":"record","created_at":"2026-05-18T00:18:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4ff08562509631b8ba698e39ac329acbdf2321dbce2f30c9ae58f98b96d8b3b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-10T14:40:24Z","title_canon_sha256":"90a0c86b46ed087c3ffdf37bb1c02ae062f6a344a97f61d6a4bb4433d7ea9faa"},"schema_version":"1.0","source":{"id":"1804.03566","kind":"arxiv","version":1}},"canonical_sha256":"e115b9f7b603cee16c4e3588964176850608bc9929ec29333f2b82f18d34c15e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e115b9f7b603cee16c4e3588964176850608bc9929ec29333f2b82f18d34c15e","first_computed_at":"2026-05-18T00:18:47.712583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:47.712583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"An7LTvJ182CXB3wfplAibFQ4tyAzJavdcDXcb70VAkQVcrB39VLVZESQa+K91HTldu4tsipgMZ13kJtRgHazDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:47.713213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91c3f3b65e59b1fc92615a65035520c2ebcfc60931f6d93eace2ed7c132d0e01","sha256:009d2185ea6dc2b29075572aa04f78ef147474b8ff55316439c5d194a8d6d0bf"],"state_sha256":"a60868adfe9601e03f9bdaae9e388ff9bce9cc50c5cbe953a8a09ad6ba2233fa"}