{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:E56GH3BBHMIXTM4EFCLOOYAJK4","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":"1d172ffe6481b6d7bac2e9ae798e9e53e16707448f417e063acd90939d3d8e08","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2007-04-12T15:37:46Z","title_canon_sha256":"649c23b6accadd8f8b98fede72f230a61b405e8be0c3eaca48f99dcdff04c010"},"schema_version":"1.0","source":{"id":"0704.1599","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.1599","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"arxiv_version","alias_value":"0704.1599v4","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.1599","created_at":"2026-05-18T04:35:46Z"},{"alias_kind":"pith_short_12","alias_value":"E56GH3BBHMIX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"E56GH3BBHMIXTM4E","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"E56GH3BB","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:07bf1f2f89cb41053b98603960df175153f7dab286557e9be8198b1524eb5cfd","target":"graph","created_at":"2026-05-18T04:35:46Z","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 an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in H\\'enon-like families in the plane. To bypass a huge inductive argument, we introduce an induction-free explicit definition of dynamically critical points. The argument is sufficiently general and in particular applies to the case of non-invertible maps as well. It naturally raises the question of an intrinsic characterization of dynamically critical points for dissipative surface maps.","authors_text":"Hiroki Takahasi","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2007-04-12T15:37:46Z","title":"Critical points for surface maps and the Benedicks-Carleson theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.1599","kind":"arxiv","version":4},"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":"sha256:732b57b37e7de0578dc53717d0c4cca1aeafea6611e16b0cb3b86aeb947152ae","target":"record","created_at":"2026-05-18T04:35:46Z","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":"1d172ffe6481b6d7bac2e9ae798e9e53e16707448f417e063acd90939d3d8e08","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2007-04-12T15:37:46Z","title_canon_sha256":"649c23b6accadd8f8b98fede72f230a61b405e8be0c3eaca48f99dcdff04c010"},"schema_version":"1.0","source":{"id":"0704.1599","kind":"arxiv","version":4}},"canonical_sha256":"277c63ec213b1179b3842896e760095739ea507f488ac1b684440f8406dd9867","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"277c63ec213b1179b3842896e760095739ea507f488ac1b684440f8406dd9867","first_computed_at":"2026-05-18T04:35:46.431775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:46.431775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JhhYcA7QcceK0wxinM28vUjBjd57f8KGESnEkHaZgo9DdABF+kEeLNOATMry4UFrqIOKthpww5ESC4pOmud2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:46.432364Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.1599","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:732b57b37e7de0578dc53717d0c4cca1aeafea6611e16b0cb3b86aeb947152ae","sha256:07bf1f2f89cb41053b98603960df175153f7dab286557e9be8198b1524eb5cfd"],"state_sha256":"195a97da4f1fddf97752b615db9d95071c4c5f6d7365d9b3dfe187e65a74be3c"}