{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HIPUXHTKD4XBPWSGGYBS7PC2ZC","short_pith_number":"pith:HIPUXHTK","schema_version":"1.0","canonical_sha256":"3a1f4b9e6a1f2e17da4636032fbc5ac89ffd75de0507bf73f05605aeeb340949","source":{"kind":"arxiv","id":"1208.6220","version":3},"attestation_state":"computed","paper":{"title":"Points on Elliptic Curves Parametrizing Dynamical Galois Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wade Hindes","submitted_at":"2012-08-30T16:11:52Z","abstract_excerpt":"We show how rational points on certain varieties parametrize phenomena arising in the Galois theory of iterates of quadratic polynomials. As an example, we characterize completely the set of quadratic polynomials $x^2+c$ whose third iterate has a \"small\" Galois group by determining the rational points on some elliptic curves. It follows as a corollary that the only such integer value with this property is $c=3$, answering a question of Rafe Jones. Furthermore, using a result of Granville's on the rational points on quadratic twists of a hyperelliptic curve, we indicate how the ABC conjecture i"},"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":"1208.6220","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-30T16:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"8200c1561458d479694c3a49748b0a867e470c6e6e96ea5caa82cb2a2d43a460","abstract_canon_sha256":"ba27ebe6ecc83314195056e93434d66f7cdb51ba78de7bb460edb13e2ad57111"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:33.273728Z","signature_b64":"KQYCbRbbPNDT7QqLYcfaP+FubxcTWUpE57vx7jqiwFUg6LaF9G7lUqCvu1pu3FW/aDp2j6Jkx9Imi+2HOVXVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a1f4b9e6a1f2e17da4636032fbc5ac89ffd75de0507bf73f05605aeeb340949","last_reissued_at":"2026-05-18T03:44:33.272891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:33.272891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Points on Elliptic Curves Parametrizing Dynamical Galois Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wade Hindes","submitted_at":"2012-08-30T16:11:52Z","abstract_excerpt":"We show how rational points on certain varieties parametrize phenomena arising in the Galois theory of iterates of quadratic polynomials. As an example, we characterize completely the set of quadratic polynomials $x^2+c$ whose third iterate has a \"small\" Galois group by determining the rational points on some elliptic curves. It follows as a corollary that the only such integer value with this property is $c=3$, answering a question of Rafe Jones. Furthermore, using a result of Granville's on the rational points on quadratic twists of a hyperelliptic curve, we indicate how the ABC conjecture i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6220","kind":"arxiv","version":3},"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":"1208.6220","created_at":"2026-05-18T03:44:33.273042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6220v3","created_at":"2026-05-18T03:44:33.273042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6220","created_at":"2026-05-18T03:44:33.273042+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIPUXHTKD4XB","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIPUXHTKD4XBPWSG","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIPUXHTK","created_at":"2026-05-18T12:27:09.501522+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/HIPUXHTKD4XBPWSGGYBS7PC2ZC","json":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC.json","graph_json":"https://pith.science/api/pith-number/HIPUXHTKD4XBPWSGGYBS7PC2ZC/graph.json","events_json":"https://pith.science/api/pith-number/HIPUXHTKD4XBPWSGGYBS7PC2ZC/events.json","paper":"https://pith.science/paper/HIPUXHTK"},"agent_actions":{"view_html":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC","download_json":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC.json","view_paper":"https://pith.science/paper/HIPUXHTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6220&json=true","fetch_graph":"https://pith.science/api/pith-number/HIPUXHTKD4XBPWSGGYBS7PC2ZC/graph.json","fetch_events":"https://pith.science/api/pith-number/HIPUXHTKD4XBPWSGGYBS7PC2ZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC/action/storage_attestation","attest_author":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC/action/author_attestation","sign_citation":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC/action/citation_signature","submit_replication":"https://pith.science/pith/HIPUXHTKD4XBPWSGGYBS7PC2ZC/action/replication_record"}},"created_at":"2026-05-18T03:44:33.273042+00:00","updated_at":"2026-05-18T03:44:33.273042+00:00"}