{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X7AUULVTC64SKRUCGKR5IS56Q5","short_pith_number":"pith:X7AUULVT","canonical_record":{"source":{"id":"1409.4449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-15T21:02:16Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"6872828d7c0c77142e883de0630d4d5f637475f47f18d5da71e60965494cf3f1","abstract_canon_sha256":"4683b07f65cb154a794b8b85263e7c9ba25529f55ecda8e298dab8109701f1b4"},"schema_version":"1.0"},"canonical_sha256":"bfc14a2eb317b925468232a3d44bbe8767695ee4d28f7483ec0eb1240407940f","source":{"kind":"arxiv","id":"1409.4449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4449","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4449v1","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4449","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"X7AUULVTC64S","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7AUULVTC64SKRUC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7AUULVT","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X7AUULVTC64SKRUCGKR5IS56Q5","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-15T21:02:16Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"6872828d7c0c77142e883de0630d4d5f637475f47f18d5da71e60965494cf3f1","abstract_canon_sha256":"4683b07f65cb154a794b8b85263e7c9ba25529f55ecda8e298dab8109701f1b4"},"schema_version":"1.0"},"canonical_sha256":"bfc14a2eb317b925468232a3d44bbe8767695ee4d28f7483ec0eb1240407940f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:45.533250Z","signature_b64":"n71m1XZaQ1ic9AZpxGwDeLdnkDZHsSob+9YGnjse9M9LjR1Urr/PMgAombTnFuBFqD4RqdpA+ZUfF0qKeRIhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfc14a2eb317b925468232a3d44bbe8767695ee4d28f7483ec0eb1240407940f","last_reissued_at":"2026-05-18T02:42:45.532793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:45.532793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4449","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOKg0uhj34QyoZZ3FBtrqZJDj6JeYwDunpkc+PhmboEoKLhZMLHtIJ7uqXnQTPaYpQ03MHGdBtTjlfiyIrDbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:26:58.825136Z"},"content_sha256":"fbddf88bb15dd0b53ee42a239e4bece24fff8875bb9c240e76bf84e0f8ae8276","schema_version":"1.0","event_id":"sha256:fbddf88bb15dd0b53ee42a239e4bece24fff8875bb9c240e76bf84e0f8ae8276"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X7AUULVTC64SKRUCGKR5IS56Q5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On stability and hyperbolicity for polynomial automorphisms of C^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Pierre Berger, Romain Dujardin","submitted_at":"2014-09-15T21:02:16Z","abstract_excerpt":"Let $(f_\\lambda)_{\\lambda\\in \\Lambda}$ be a holomorphic family of polynomial automorphisms of $\\mathbb{C}^2$. Following previous work of Dujardin and Lyubich, we say that such a family is weakly stable if saddle periodic orbits do not bifurcate. It is an open question whether this property is equivalent to structural stability on the Julia set $J^*$ (that is, the closure of the set of saddle periodic points).\n  In this paper we introduce a notion of regular point for a polynomial automorphism, inspired by Pesin theory, and prove that in a weakly stable family, the set of regular points moves h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4449","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMfSTnz1rcRXL0kBy7s1BxjMVOXs1qUGtkjpRTsb6sEOaVy3QR/4d+DcfVqwW99tIAfpACEq4zc++IPto4VFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:26:58.825506Z"},"content_sha256":"ebdb66daf035344593068a6bde1fc07debb53506e9f57fade3ebfb9e78537445","schema_version":"1.0","event_id":"sha256:ebdb66daf035344593068a6bde1fc07debb53506e9f57fade3ebfb9e78537445"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7AUULVTC64SKRUCGKR5IS56Q5/bundle.json","state_url":"https://pith.science/pith/X7AUULVTC64SKRUCGKR5IS56Q5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7AUULVTC64SKRUCGKR5IS56Q5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T20:26:58Z","links":{"resolver":"https://pith.science/pith/X7AUULVTC64SKRUCGKR5IS56Q5","bundle":"https://pith.science/pith/X7AUULVTC64SKRUCGKR5IS56Q5/bundle.json","state":"https://pith.science/pith/X7AUULVTC64SKRUCGKR5IS56Q5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7AUULVTC64SKRUCGKR5IS56Q5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X7AUULVTC64SKRUCGKR5IS56Q5","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":"4683b07f65cb154a794b8b85263e7c9ba25529f55ecda8e298dab8109701f1b4","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-15T21:02:16Z","title_canon_sha256":"6872828d7c0c77142e883de0630d4d5f637475f47f18d5da71e60965494cf3f1"},"schema_version":"1.0","source":{"id":"1409.4449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4449","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4449v1","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4449","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"X7AUULVTC64S","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7AUULVTC64SKRUC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7AUULVT","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:ebdb66daf035344593068a6bde1fc07debb53506e9f57fade3ebfb9e78537445","target":"graph","created_at":"2026-05-18T02:42:45Z","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":"Let $(f_\\lambda)_{\\lambda\\in \\Lambda}$ be a holomorphic family of polynomial automorphisms of $\\mathbb{C}^2$. Following previous work of Dujardin and Lyubich, we say that such a family is weakly stable if saddle periodic orbits do not bifurcate. It is an open question whether this property is equivalent to structural stability on the Julia set $J^*$ (that is, the closure of the set of saddle periodic points).\n  In this paper we introduce a notion of regular point for a polynomial automorphism, inspired by Pesin theory, and prove that in a weakly stable family, the set of regular points moves h","authors_text":"Pierre Berger, Romain Dujardin","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-15T21:02:16Z","title":"On stability and hyperbolicity for polynomial automorphisms of C^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4449","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:fbddf88bb15dd0b53ee42a239e4bece24fff8875bb9c240e76bf84e0f8ae8276","target":"record","created_at":"2026-05-18T02:42:45Z","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":"4683b07f65cb154a794b8b85263e7c9ba25529f55ecda8e298dab8109701f1b4","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-15T21:02:16Z","title_canon_sha256":"6872828d7c0c77142e883de0630d4d5f637475f47f18d5da71e60965494cf3f1"},"schema_version":"1.0","source":{"id":"1409.4449","kind":"arxiv","version":1}},"canonical_sha256":"bfc14a2eb317b925468232a3d44bbe8767695ee4d28f7483ec0eb1240407940f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfc14a2eb317b925468232a3d44bbe8767695ee4d28f7483ec0eb1240407940f","first_computed_at":"2026-05-18T02:42:45.532793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:45.532793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n71m1XZaQ1ic9AZpxGwDeLdnkDZHsSob+9YGnjse9M9LjR1Urr/PMgAombTnFuBFqD4RqdpA+ZUfF0qKeRIhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:45.533250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbddf88bb15dd0b53ee42a239e4bece24fff8875bb9c240e76bf84e0f8ae8276","sha256:ebdb66daf035344593068a6bde1fc07debb53506e9f57fade3ebfb9e78537445"],"state_sha256":"0d663653f3dc1a8364f24d6cc6f0133a2799f0413419179848bb20139d1bb89b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NB+WCJy6n0tT+qDVrJnCChtXMv9AiTDZddDYIA77A451bSiDos9fCw6NXawpRtWNGMGsrC8chw2S1g2umYJkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T20:26:58.827458Z","bundle_sha256":"c28320ddb96fc4d25d1e0504c5d045f2872acb646693548b047d6dfdad693445"}}