{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YYFEWWRSYZ32N3BI4ERFLOI5OF","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":"3b2aa1ac27dd6a81ee6ea63239ffaf7ffd1c84fd90d4a7e67670bbfff0cfbf39","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-07T17:42:49Z","title_canon_sha256":"442d70a7ac44ec1aaca2e2dbcaa7965d50b67e11fa07cb1cf336ee89b4f4c051"},"schema_version":"1.0","source":{"id":"1702.02115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02115","created_at":"2026-05-18T00:39:28Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02115v2","created_at":"2026-05-18T00:39:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02115","created_at":"2026-05-18T00:39:28Z"},{"alias_kind":"pith_short_12","alias_value":"YYFEWWRSYZ32","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YYFEWWRSYZ32N3BI","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YYFEWWRS","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:3cfd6a5dd46d0ae2b0ed29a873cd08181a583a31ef1bea9fc483cfe29de811fa","target":"graph","created_at":"2026-05-18T00:39:28Z","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":"In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types : repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets : the bifurcation locus of $H_d(\\mathbb P^2)$ and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of H\\'enon maps to obtain examples of attr","authors_text":"Johan Taflin","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-07T17:42:49Z","title":"Blenders near polynomial product maps of $\\mathbb C^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02115","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":"sha256:6e0c33f481275c9849e19868695e7860bf46b9fb771eedb7b93c7347d4354996","target":"record","created_at":"2026-05-18T00:39:28Z","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":"3b2aa1ac27dd6a81ee6ea63239ffaf7ffd1c84fd90d4a7e67670bbfff0cfbf39","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-07T17:42:49Z","title_canon_sha256":"442d70a7ac44ec1aaca2e2dbcaa7965d50b67e11fa07cb1cf336ee89b4f4c051"},"schema_version":"1.0","source":{"id":"1702.02115","kind":"arxiv","version":2}},"canonical_sha256":"c60a4b5a32c677a6ec28e12255b91d7176d1868168b91d2726c0053803766907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c60a4b5a32c677a6ec28e12255b91d7176d1868168b91d2726c0053803766907","first_computed_at":"2026-05-18T00:39:28.712281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:28.712281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nzCaG6VIT6su/abR84MpIcFqUerH+F6ZWTQYJDrRBlGatYiVBdjvj2DaHuI4/evUbTY/QTfoKRX+6DMeLzuyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:28.712874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e0c33f481275c9849e19868695e7860bf46b9fb771eedb7b93c7347d4354996","sha256:3cfd6a5dd46d0ae2b0ed29a873cd08181a583a31ef1bea9fc483cfe29de811fa"],"state_sha256":"13c69911ee7453836ab1725d4f0c89f6f77ef11ce303f6a083e0a1d55b64dd9a"}