{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:THVADWUGQN6O4AOWWYZJDYUTQU","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":"0f4d4e653ba8997690a2f597c7368befd841424f00d2b5500b2f674ade0f5b39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-14T23:15:54Z","title_canon_sha256":"72396235a5c0eefc2bf07294788615d541df81d1fbd618177f14495c5c5dea49"},"schema_version":"1.0","source":{"id":"1109.3226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3226","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3226v2","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3226","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"THVADWUGQN6O","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"THVADWUGQN6O4AOW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"THVADWUG","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6d239bbbbb2764364b67673a47f4c8b82f973779164d2efccef973c894c7ff72","target":"graph","created_at":"2026-05-17T23:53:19Z","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":"Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich's theorem for elliptic curves. We also define the minimal critical discriminant, a global object which can be viewed as a measure of arithmetic complexity of a rational map. We formulate a conjectural bound on the minimal critical discriminant, which is analogous to Szpiro's co","authors_text":"Clayton Petsche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-14T23:15:54Z","title":"Critically separable rational maps in families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3226","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":"sha256:99d2242cfc589c190cbd310a5520c740eaa10fd39d0811783b1af987ca818c93","target":"record","created_at":"2026-05-17T23:53:19Z","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":"0f4d4e653ba8997690a2f597c7368befd841424f00d2b5500b2f674ade0f5b39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-14T23:15:54Z","title_canon_sha256":"72396235a5c0eefc2bf07294788615d541df81d1fbd618177f14495c5c5dea49"},"schema_version":"1.0","source":{"id":"1109.3226","kind":"arxiv","version":2}},"canonical_sha256":"99ea01da86837cee01d6b63291e29385327e0a8ff6b70a4fec20095d349a1bf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ea01da86837cee01d6b63291e29385327e0a8ff6b70a4fec20095d349a1bf0","first_computed_at":"2026-05-17T23:53:19.249869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:19.249869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xIfhNqq7qtazlaWY3NiQ0Mb5tBBP48yexcKn9srY2/dp654ehsqkjScQhpkY+rLCaAFUpfJDvo47huTPsQ7GAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:19.250492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99d2242cfc589c190cbd310a5520c740eaa10fd39d0811783b1af987ca818c93","sha256:6d239bbbbb2764364b67673a47f4c8b82f973779164d2efccef973c894c7ff72"],"state_sha256":"a331c9eab6d0337e00af638fedbdc1b8c79a39b0c331d1fe7fb57b3128ca24b3"}