{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4UGEOUCTRFH25STXDNR2RVFMFL","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":"8698ce89711b243d13a39211ef335b3bd6862b09e234da757ba819754e37fee1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-26T13:42:27Z","title_canon_sha256":"c30b190496cec7f2f3745da836e3548bebaf55e2c6d9559596d509f61fd00d02"},"schema_version":"1.0","source":{"id":"2401.14862","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.14862","created_at":"2026-07-05T10:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"2401.14862v3","created_at":"2026-07-05T10:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.14862","created_at":"2026-07-05T10:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"4UGEOUCTRFH2","created_at":"2026-07-05T10:50:41Z"},{"alias_kind":"pith_short_16","alias_value":"4UGEOUCTRFH25STX","created_at":"2026-07-05T10:50:41Z"},{"alias_kind":"pith_short_8","alias_value":"4UGEOUCT","created_at":"2026-07-05T10:50:41Z"}],"graph_snapshots":[{"event_id":"sha256:331ef3a01aa6bd3c8d5313bdf60a73bced10aeb6869e64f68f246cbe9bba750d","target":"graph","created_at":"2026-07-05T10:50:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.14862/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a number field $k$, and a quadratic rational function $f(x) \\in k(x)$, the associated arboreal representation of the absolute Galois group of $k$ is a subgroup of the automorphism group of a regular rooted binary tree. Boston and Jones conjectured that the image of such a representation for $f \\in \\mathbb{Z}[x]$ contains a dense set of settled elements. An automorphism is settled if the number of its orbits on the $n\\text{th}$ level of the tree remains small as $n$ goes to infinity.\n  In this article, we exhibit many quadratic rational functions whose associated Arboreal Galois groups ar","authors_text":"\\\"Ozlem Ejder","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-26T13:42:27Z","title":"Galois theory of quadratic rational functions with periodic critical points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14862","kind":"arxiv","version":3},"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":"sha256:95ae82f2d384cf11a8670a8f49e5756846e2efb44ab8b5620dbed73445ddf69b","target":"record","created_at":"2026-07-05T10:50:41Z","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":"8698ce89711b243d13a39211ef335b3bd6862b09e234da757ba819754e37fee1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-26T13:42:27Z","title_canon_sha256":"c30b190496cec7f2f3745da836e3548bebaf55e2c6d9559596d509f61fd00d02"},"schema_version":"1.0","source":{"id":"2401.14862","kind":"arxiv","version":3}},"canonical_sha256":"e50c475053894faeca771b63a8d4ac2ad61d19d38bed7fd15271f0ff956593d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e50c475053894faeca771b63a8d4ac2ad61d19d38bed7fd15271f0ff956593d5","first_computed_at":"2026-07-05T10:50:41.372519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:41.372519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NFRcOGqFIQ7JQMHJSkpmjukOnlS6XvzMWSAqaSIJySjLElmniDkBCxkh21NYYtmekbUk4RqNZXYh8sHW8EEWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:41.372997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.14862","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95ae82f2d384cf11a8670a8f49e5756846e2efb44ab8b5620dbed73445ddf69b","sha256:331ef3a01aa6bd3c8d5313bdf60a73bced10aeb6869e64f68f246cbe9bba750d"],"state_sha256":"279b006bbf955361a1609c76898fe5699514734b30e0a6d2d320e920a52f5419"}