{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K3EXK3H7EWQ2MU7B2MBMK5MM4C","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":"22ebdb4fbba59a2fbd33cfa4e69485e70c6e92cc05c5e64e9db91d065260570a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-12T17:12:48Z","title_canon_sha256":"7f0df2f5656faf7dd0878e3bf1b15eb7c5c58b0f79aa1f6b33696fac0b2376fc"},"schema_version":"1.0","source":{"id":"1203.2555","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2555","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2555v2","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2555","created_at":"2026-05-18T03:46:45Z"},{"alias_kind":"pith_short_12","alias_value":"K3EXK3H7EWQ2","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K3EXK3H7EWQ2MU7B","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K3EXK3H7","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:e3c06cae59b9edc86cb60f636d3c9f36a6c9c020191382b23cb295c70b7a6fe1","target":"graph","created_at":"2026-05-18T03:46:45Z","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 prove the finiteness of the Zsigmondy set associated to the critical orbit of f(z) = z^d+c for rational values of c by finding an effective bound on the size of the set. For non-recurrent critical orbits, the Zsigmondy set is explicitly computed by utilizing effective dynamical height bounds. In the general case, we use Thue-style Diophantine approximation methods to bound the size of the Zsigmondy set when d >2, and complex-analytic methods when d=2.","authors_text":"Holly Krieger","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-12T17:12:48Z","title":"Primitive prime divisors in the critical orbit of z^d+c"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2555","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":"sha256:5d961537976464946f9c230d5fe5236355138042e6b40081a14f497482542c23","target":"record","created_at":"2026-05-18T03:46:45Z","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":"22ebdb4fbba59a2fbd33cfa4e69485e70c6e92cc05c5e64e9db91d065260570a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-12T17:12:48Z","title_canon_sha256":"7f0df2f5656faf7dd0878e3bf1b15eb7c5c58b0f79aa1f6b33696fac0b2376fc"},"schema_version":"1.0","source":{"id":"1203.2555","kind":"arxiv","version":2}},"canonical_sha256":"56c9756cff25a1a653e1d302c5758ce08e01f93ec733903657d9884ffabe42eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56c9756cff25a1a653e1d302c5758ce08e01f93ec733903657d9884ffabe42eb","first_computed_at":"2026-05-18T03:46:45.231796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:45.231796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rT9abUNYQzMvATPbPDyrCkvdcAE6at1qiHMYyxLVuc96CUpAl3dF07hvnp3Onzy8lO0GUPHSVlJL9jk2H1WMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:45.232602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2555","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d961537976464946f9c230d5fe5236355138042e6b40081a14f497482542c23","sha256:e3c06cae59b9edc86cb60f636d3c9f36a6c9c020191382b23cb295c70b7a6fe1"],"state_sha256":"dc5a2a252389a73d4e844965111978beb840028dfd047ef9a7d107c7372ee4b4"}