{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KY3BHHGLOZ42NU43DEYLPHAYMW","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":"f11b22fe79262b0e4c6bf3ef096bf79fbdad53e6dd014c06435a69f2ca4a1e12","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-09T17:01:00Z","title_canon_sha256":"8f10ef947164775c2726b8449eba08c43a3297f294bf75f064b1a226c720f320"},"schema_version":"1.0","source":{"id":"1407.2563","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2563","created_at":"2026-05-17T23:57:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2563v1","created_at":"2026-05-17T23:57:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2563","created_at":"2026-05-17T23:57:08Z"},{"alias_kind":"pith_short_12","alias_value":"KY3BHHGLOZ42","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KY3BHHGLOZ42NU43","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KY3BHHGL","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:f152c11b0693b219d8a29fc7970d95699a4dde8bcc41f949ec9a9874e3bcd7e1","target":"graph","created_at":"2026-05-17T23:57:08Z","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 study the connectedness locus N for the family of iterated function systems of pairs of affine-linear maps in the plane (the non-self-similar case). First results on the set N were obtained in joint work with P. Shmerkin (2006). Here we establish rigorous bounds for the set N based on the study of power series of special form. We also derive some bounds for the region of \"*-transversality\" which have applications to the computation of Hausdorff measure of the self-affine attractor. We prove that a large portion of the set N is connected and locally connected, and conjecture that the entire ","authors_text":"Boris Solomyak","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-09T17:01:00Z","title":"Connectedness locus for pairs of affine maps and zeros of power series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2563","kind":"arxiv","version":1},"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:da7e22dbd9c934b4be3eaf5b90ba35adb99df7971999a4fc63ea1adc059aa1a0","target":"record","created_at":"2026-05-17T23:57:08Z","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":"f11b22fe79262b0e4c6bf3ef096bf79fbdad53e6dd014c06435a69f2ca4a1e12","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-09T17:01:00Z","title_canon_sha256":"8f10ef947164775c2726b8449eba08c43a3297f294bf75f064b1a226c720f320"},"schema_version":"1.0","source":{"id":"1407.2563","kind":"arxiv","version":1}},"canonical_sha256":"5636139ccb7679a6d39b1930b79c186592939b9bfa755248830b7763b74404b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5636139ccb7679a6d39b1930b79c186592939b9bfa755248830b7763b74404b9","first_computed_at":"2026-05-17T23:57:08.034847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:08.034847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5kOFz/fNGAa1qF2fL0wZumHYEKdvirj8DBYLWkVxjfrUZCeaMlyZvuN+2VnTfN0/6OWcCfX8ywAjmab03yqwBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:08.035352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2563","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7e22dbd9c934b4be3eaf5b90ba35adb99df7971999a4fc63ea1adc059aa1a0","sha256:f152c11b0693b219d8a29fc7970d95699a4dde8bcc41f949ec9a9874e3bcd7e1"],"state_sha256":"2e2afb86fd9c843adc31ae867cc74e196bad54c71b27447d51d3e28795897ca4"}