{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WICARREKTQMDWTQQMGLNXV622I","short_pith_number":"pith:WICARREK","canonical_record":{"source":{"id":"1612.03358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-11T00:11:47Z","cross_cats_sorted":[],"title_canon_sha256":"00f36be9f0c396bc9341ae65f796331ecee9be8648eff79f3e94c4a8c22123e6","abstract_canon_sha256":"de164e5677ae1fc6eb22efc047c91820037c9e01870cb3e556bee0904d7f665f"},"schema_version":"1.0"},"canonical_sha256":"b20408c48a9c183b4e106196dbd7dad23387bbc79761ad2f4684f1c0f3df6576","source":{"kind":"arxiv","id":"1612.03358","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03358","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03358v2","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03358","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"WICARREKTQMD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WICARREKTQMDWTQQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WICARREK","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WICARREKTQMDWTQQMGLNXV622I","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-11T00:11:47Z","cross_cats_sorted":[],"title_canon_sha256":"00f36be9f0c396bc9341ae65f796331ecee9be8648eff79f3e94c4a8c22123e6","abstract_canon_sha256":"de164e5677ae1fc6eb22efc047c91820037c9e01870cb3e556bee0904d7f665f"},"schema_version":"1.0"},"canonical_sha256":"b20408c48a9c183b4e106196dbd7dad23387bbc79761ad2f4684f1c0f3df6576","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:30.593466Z","signature_b64":"toSimMWE2Kr5kNX4vLA8QCFqGR5SUUGP7s4QJn62k7slAiBn8SaJr5TIy1GBeKDSe0rTBZSN6zELFzTL+lzZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b20408c48a9c183b4e106196dbd7dad23387bbc79761ad2f4684f1c0f3df6576","last_reissued_at":"2026-05-18T00:27:30.592540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:30.592540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03358","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":"2026-05-18T00:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9VQlmrljNcpdVlod9M4Py/qZpxb7Tahw+8f8A75CtDNCfTk4V8ABSOsFNxsdPhxvpLdn8UqUqJf6HDg/ce5YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:21:19.184574Z"},"content_sha256":"ee82b90f738dc015b449eb4bc61aac9c3aff11900df3b4f9f45917c2cf0b6a7e","schema_version":"1.0","event_id":"sha256:ee82b90f738dc015b449eb4bc61aac9c3aff11900df3b4f9f45917c2cf0b6a7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WICARREKTQMDWTQQMGLNXV622I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A large arboreal Galois representation for a cubic postcritically finite polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Benjamin Hutz, Jamie Juul, Robert L. Benedetto, Xander Faber, Yu Yasufuku","submitted_at":"2016-12-11T00:11:47Z","abstract_excerpt":"We give a complete description of the arboreal Galois representation of a certain postcritically finite cubic polynomial over a large class of number fields and for a large class of basepoints. This is the first such example that is not conjugate to a power map, Chebyshev polynomial, or Latt\\`es map. The associated Galois action on an infinite ternary rooted tree has Hausdorff dimension bounded strictly between that of the infinite wreath product of cyclic groups and that of the infinite wreath product of symmetric groups. We deduce a zero-density result for prime divisors in an orbit under th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03358","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":"2026-05-18T00:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aWStdqgJ4YhJdSFbFQNtHvQgqF9ljc3sYKBKDkLGpbVqDSASlBeuWsmEcIvQuJPNc8BxvpC4yEGyJg20TFZgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:21:19.184928Z"},"content_sha256":"73874c66bb08505b227642bf7205de21e0a4687e64644f44819db53f89539ddd","schema_version":"1.0","event_id":"sha256:73874c66bb08505b227642bf7205de21e0a4687e64644f44819db53f89539ddd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WICARREKTQMDWTQQMGLNXV622I/bundle.json","state_url":"https://pith.science/pith/WICARREKTQMDWTQQMGLNXV622I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WICARREKTQMDWTQQMGLNXV622I/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":"2026-05-30T07:21:19Z","links":{"resolver":"https://pith.science/pith/WICARREKTQMDWTQQMGLNXV622I","bundle":"https://pith.science/pith/WICARREKTQMDWTQQMGLNXV622I/bundle.json","state":"https://pith.science/pith/WICARREKTQMDWTQQMGLNXV622I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WICARREKTQMDWTQQMGLNXV622I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WICARREKTQMDWTQQMGLNXV622I","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":"de164e5677ae1fc6eb22efc047c91820037c9e01870cb3e556bee0904d7f665f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-11T00:11:47Z","title_canon_sha256":"00f36be9f0c396bc9341ae65f796331ecee9be8648eff79f3e94c4a8c22123e6"},"schema_version":"1.0","source":{"id":"1612.03358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03358","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03358v2","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03358","created_at":"2026-05-18T00:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"WICARREKTQMD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WICARREKTQMDWTQQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WICARREK","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:73874c66bb08505b227642bf7205de21e0a4687e64644f44819db53f89539ddd","target":"graph","created_at":"2026-05-18T00:27:30Z","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 give a complete description of the arboreal Galois representation of a certain postcritically finite cubic polynomial over a large class of number fields and for a large class of basepoints. This is the first such example that is not conjugate to a power map, Chebyshev polynomial, or Latt\\`es map. The associated Galois action on an infinite ternary rooted tree has Hausdorff dimension bounded strictly between that of the infinite wreath product of cyclic groups and that of the infinite wreath product of symmetric groups. We deduce a zero-density result for prime divisors in an orbit under th","authors_text":"Benjamin Hutz, Jamie Juul, Robert L. Benedetto, Xander Faber, Yu Yasufuku","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-11T00:11:47Z","title":"A large arboreal Galois representation for a cubic postcritically finite polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03358","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:ee82b90f738dc015b449eb4bc61aac9c3aff11900df3b4f9f45917c2cf0b6a7e","target":"record","created_at":"2026-05-18T00:27:30Z","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":"de164e5677ae1fc6eb22efc047c91820037c9e01870cb3e556bee0904d7f665f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-11T00:11:47Z","title_canon_sha256":"00f36be9f0c396bc9341ae65f796331ecee9be8648eff79f3e94c4a8c22123e6"},"schema_version":"1.0","source":{"id":"1612.03358","kind":"arxiv","version":2}},"canonical_sha256":"b20408c48a9c183b4e106196dbd7dad23387bbc79761ad2f4684f1c0f3df6576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b20408c48a9c183b4e106196dbd7dad23387bbc79761ad2f4684f1c0f3df6576","first_computed_at":"2026-05-18T00:27:30.592540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:30.592540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"toSimMWE2Kr5kNX4vLA8QCFqGR5SUUGP7s4QJn62k7slAiBn8SaJr5TIy1GBeKDSe0rTBZSN6zELFzTL+lzZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:30.593466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee82b90f738dc015b449eb4bc61aac9c3aff11900df3b4f9f45917c2cf0b6a7e","sha256:73874c66bb08505b227642bf7205de21e0a4687e64644f44819db53f89539ddd"],"state_sha256":"32c6b7e44c6c2dd506224db0c330d77048e55465e866dfed69ec80168a273bea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAXNN3svFqkHl3RXfzbQRJrrBJnTC1c+6jwfCr2lswai+bZWDntyWy+483Zs1JJal/0WxMVM8Xc9wMrtGD1CBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:21:19.187034Z","bundle_sha256":"257bd9dd0fa4311eb98f217d66ce1d4e90b07c3eef7b052dae1f114528237ea4"}}