{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KIQQWBE3U4UFI6IOFXOTQI25I7","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":"c4245ac52250e1461d60d4cfaeae0b3f751753cc0a55f8c163bb7dfc7e00c078","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-01T15:16:16Z","title_canon_sha256":"dd050478716f8bbbc2879c605f6c2163f6288e4d0fb668194ac460b485f66d09"},"schema_version":"1.0","source":{"id":"1803.00434","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00434","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00434v2","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00434","created_at":"2026-05-18T00:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"KIQQWBE3U4UF","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KIQQWBE3U4UFI6IO","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KIQQWBE3","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:c6184cc17746c38c73f1c23c3d2e491ed1a5e2f48b8fea8912d98f99c23b6f8d","target":"graph","created_at":"2026-05-18T00:21:34Z","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~$E$ be a Hilbertian field of characteristic~$0$. R.W.K. Odoni conjectured that for every positive integer~$n$ there exists a polynomial~$f\\in E[X]$ of degree~$n$ such that each iterate~$f^{\\circ{k}}$ of~$f$ is irreducible and the Galois group of the splitting field of~$f^{\\circ k}$ is isomorphic to the automorphism group of a regular,~$n$-branching tree of height~$k.$ We prove this conjecture when~$E$ is a number field.","authors_text":"Joel Specter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-01T15:16:16Z","title":"Polynomials with Surjective Arboreal Galois Representations Exist in Every Degree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00434","kind":"arxiv","version":2},"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":"sha256:9643897ac615c1f8b934356eb4980861c4190ec5c29eb173682c76e5458a9043","target":"record","created_at":"2026-05-18T00:21:34Z","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":"c4245ac52250e1461d60d4cfaeae0b3f751753cc0a55f8c163bb7dfc7e00c078","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-01T15:16:16Z","title_canon_sha256":"dd050478716f8bbbc2879c605f6c2163f6288e4d0fb668194ac460b485f66d09"},"schema_version":"1.0","source":{"id":"1803.00434","kind":"arxiv","version":2}},"canonical_sha256":"52210b049ba72854790e2ddd38235d47c7e8c2d5c3aca7b1ab2bc49537406f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52210b049ba72854790e2ddd38235d47c7e8c2d5c3aca7b1ab2bc49537406f78","first_computed_at":"2026-05-18T00:21:34.052399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:34.052399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jKSOrrQQuyvRiAgpIBqK6TLgljp4hngphH6d45Q4gEWdaeuuFr85qpmaR3ejUIku2DhfnEbcIeVGpJXQbSTwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:34.052863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00434","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9643897ac615c1f8b934356eb4980861c4190ec5c29eb173682c76e5458a9043","sha256:c6184cc17746c38c73f1c23c3d2e491ed1a5e2f48b8fea8912d98f99c23b6f8d"],"state_sha256":"c0802ab50a5edef8fa2bfd849f9d23c7075fa6fa29005cd627725cabec3316ef"}