{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:A42V5QFVU5JWCIOVF6L4IS6ETL","short_pith_number":"pith:A42V5QFV","canonical_record":{"source":{"id":"1705.08353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-23T15:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"4aa05ca83b8d18bc58caa1ae046b1c25cd21151afad868a57bf20095c478216e","abstract_canon_sha256":"96d1ae7f8b98a7f30cc02c804b6af8d51c0cd55a2d27ed229e7f741a5a65c54f"},"schema_version":"1.0"},"canonical_sha256":"07355ec0b5a7536121d52f97c44bc49afb09cf4fd38eb1553af5d9e8adab8a3e","source":{"kind":"arxiv","id":"1705.08353","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08353","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08353v2","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08353","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"pith_short_12","alias_value":"A42V5QFVU5JW","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A42V5QFVU5JWCIOV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A42V5QFV","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:A42V5QFVU5JWCIOVF6L4IS6ETL","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-23T15:15:44Z","cross_cats_sorted":[],"title_canon_sha256":"4aa05ca83b8d18bc58caa1ae046b1c25cd21151afad868a57bf20095c478216e","abstract_canon_sha256":"96d1ae7f8b98a7f30cc02c804b6af8d51c0cd55a2d27ed229e7f741a5a65c54f"},"schema_version":"1.0"},"canonical_sha256":"07355ec0b5a7536121d52f97c44bc49afb09cf4fd38eb1553af5d9e8adab8a3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:22.560671Z","signature_b64":"697yeQW9o8CmhTdSTq/7awsJjGFbRWjPck8zjjcBXPJV1dG2MQAU//Ns2RO8cqCn8NVmUP/Y5RMwautvmy3dCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07355ec0b5a7536121d52f97c44bc49afb09cf4fd38eb1553af5d9e8adab8a3e","last_reissued_at":"2026-05-18T00:34:22.560209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:22.560209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08353","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFTcrE39cLfRjqGrcJMR4yKnK2XjuXMplsUaQumebjEqU+7J5K6DJ9rJ6E6siCMgk1vIAHrpqWmiMmgW9njOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T01:36:52.562525Z"},"content_sha256":"8dc51db31e1d0352573ce61ad4c0b07f312892ee244795242be81fd6d3e100d2","schema_version":"1.0","event_id":"sha256:8dc51db31e1d0352573ce61ad4c0b07f312892ee244795242be81fd6d3e100d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:A42V5QFVU5JWCIOVF6L4IS6ETL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying Galois groups of small iterates via rational points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wade Hindes","submitted_at":"2017-05-23T15:15:44Z","abstract_excerpt":"We establish several surjectivity theorems regarding the Galois groups of small iterates of $\\phi_c(x)=x^2+c$ for $c\\in\\mathbb{Q}$. To do this, we use explicit techniques from the theory of rational points on curves, including the method of Chabauty-Coleman and the Mordell-Weil sieve. For example, we succeed in finding all rational points on a hyperelliptic curve of genus $7$, with rank $5$ Jacobian, whose points parametrize quadratic polynomials with a \"newly small\" Galois group at the fifth stage of iteration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08353","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGe93PPc4nY/wfcpKFRAfzXtk7HgBtenaRrjKKgGeSBcH//u3g0on2ZuCXGLF7D+3vITdGQ4AW6K71HvDSBaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T01:36:52.562869Z"},"content_sha256":"1a220ac03f9f24697aab657b42b7018df856e573f1a8aaf14d59d214eee1b6fe","schema_version":"1.0","event_id":"sha256:1a220ac03f9f24697aab657b42b7018df856e573f1a8aaf14d59d214eee1b6fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A42V5QFVU5JWCIOVF6L4IS6ETL/bundle.json","state_url":"https://pith.science/pith/A42V5QFVU5JWCIOVF6L4IS6ETL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A42V5QFVU5JWCIOVF6L4IS6ETL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T01:36:52Z","links":{"resolver":"https://pith.science/pith/A42V5QFVU5JWCIOVF6L4IS6ETL","bundle":"https://pith.science/pith/A42V5QFVU5JWCIOVF6L4IS6ETL/bundle.json","state":"https://pith.science/pith/A42V5QFVU5JWCIOVF6L4IS6ETL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A42V5QFVU5JWCIOVF6L4IS6ETL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A42V5QFVU5JWCIOVF6L4IS6ETL","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":"96d1ae7f8b98a7f30cc02c804b6af8d51c0cd55a2d27ed229e7f741a5a65c54f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-23T15:15:44Z","title_canon_sha256":"4aa05ca83b8d18bc58caa1ae046b1c25cd21151afad868a57bf20095c478216e"},"schema_version":"1.0","source":{"id":"1705.08353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08353","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08353v2","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08353","created_at":"2026-05-18T00:34:22Z"},{"alias_kind":"pith_short_12","alias_value":"A42V5QFVU5JW","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A42V5QFVU5JWCIOV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A42V5QFV","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:1a220ac03f9f24697aab657b42b7018df856e573f1a8aaf14d59d214eee1b6fe","target":"graph","created_at":"2026-05-18T00:34:22Z","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":"We establish several surjectivity theorems regarding the Galois groups of small iterates of $\\phi_c(x)=x^2+c$ for $c\\in\\mathbb{Q}$. To do this, we use explicit techniques from the theory of rational points on curves, including the method of Chabauty-Coleman and the Mordell-Weil sieve. For example, we succeed in finding all rational points on a hyperelliptic curve of genus $7$, with rank $5$ Jacobian, whose points parametrize quadratic polynomials with a \"newly small\" Galois group at the fifth stage of iteration.","authors_text":"Wade Hindes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-23T15:15:44Z","title":"Classifying Galois groups of small iterates via rational points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08353","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":"sha256:8dc51db31e1d0352573ce61ad4c0b07f312892ee244795242be81fd6d3e100d2","target":"record","created_at":"2026-05-18T00:34:22Z","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":"96d1ae7f8b98a7f30cc02c804b6af8d51c0cd55a2d27ed229e7f741a5a65c54f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-23T15:15:44Z","title_canon_sha256":"4aa05ca83b8d18bc58caa1ae046b1c25cd21151afad868a57bf20095c478216e"},"schema_version":"1.0","source":{"id":"1705.08353","kind":"arxiv","version":2}},"canonical_sha256":"07355ec0b5a7536121d52f97c44bc49afb09cf4fd38eb1553af5d9e8adab8a3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07355ec0b5a7536121d52f97c44bc49afb09cf4fd38eb1553af5d9e8adab8a3e","first_computed_at":"2026-05-18T00:34:22.560209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:22.560209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"697yeQW9o8CmhTdSTq/7awsJjGFbRWjPck8zjjcBXPJV1dG2MQAU//Ns2RO8cqCn8NVmUP/Y5RMwautvmy3dCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:22.560671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dc51db31e1d0352573ce61ad4c0b07f312892ee244795242be81fd6d3e100d2","sha256:1a220ac03f9f24697aab657b42b7018df856e573f1a8aaf14d59d214eee1b6fe"],"state_sha256":"3ba98a33bd7736f5499ecec8c1cbbc1b91cde9c6e6e1a951ef6ffec39ae42de0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/6gqfFxueh2t9AasVA9bvZFIISp1Fu6bHW1hppqiMWvdhpmVPfbUwKpvrQAIC9JF3vX72BqhdNWwvxPCgC2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T01:36:52.564793Z","bundle_sha256":"040b7949d2b6ced0899312c0c27f682f9299a28b85b3cd8dfeaeedbb5fc05037"}}