{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZSXOGSOR2Y2GPJ7ALWENBLNTMW","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":"af6ffc1cb377495e7a1e832ebb0bf417afb5d9e702e73e60de91676cec71fb59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-26T15:43:49Z","title_canon_sha256":"a35837d9121f6db8a40e10f380dcbaa11dc8a2ac86c930038c045f723c1d6648"},"schema_version":"1.0","source":{"id":"1108.5330","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5330","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5330v5","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5330","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZSXOGSOR2Y2G","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZSXOGSOR2Y2GPJ7A","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZSXOGSOR","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:768d9cb9268f738c9636b2972743b4ef8dce7cb3e2cdab7eebbb0653d0241ea6","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":"For a smooth manifold of any dimension greater than one, we present an open set of smooth endomorphisms such that any of them has a transitive attractor with a non-empty interior. These maps are $m$-fold non-branched coverings, $m \\ge 3$. The construction applies to any manifold of the form $S^1 \\times M$, where $S^1$ is the standard circle and $M$ is an arbitrary manifold.","authors_text":"Denis Volk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-26T15:43:49Z","title":"Persistent massive attractors of smooth maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5330","kind":"arxiv","version":5},"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":"sha256:1d06b348486194f24abf468f5756cedc4221ae81180ba22186b5344697799c96","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":"af6ffc1cb377495e7a1e832ebb0bf417afb5d9e702e73e60de91676cec71fb59","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-26T15:43:49Z","title_canon_sha256":"a35837d9121f6db8a40e10f380dcbaa11dc8a2ac86c930038c045f723c1d6648"},"schema_version":"1.0","source":{"id":"1108.5330","kind":"arxiv","version":5}},"canonical_sha256":"ccaee349d1d63467a7e05d88d0adb365989e788b83aba7f24d66e8c4ca2f1bd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccaee349d1d63467a7e05d88d0adb365989e788b83aba7f24d66e8c4ca2f1bd8","first_computed_at":"2026-05-17T23:53:19.270851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:19.270851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKwCs0o4jSSE79HTrblbLWbc6yqm36uG7EnrqrIX/s2+u3untt8ojqM4jowJxHbapAtLRRlQcQD1aeFXpgaSBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:19.271390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5330","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d06b348486194f24abf468f5756cedc4221ae81180ba22186b5344697799c96","sha256:768d9cb9268f738c9636b2972743b4ef8dce7cb3e2cdab7eebbb0653d0241ea6"],"state_sha256":"0b7f19410f2d87e6f0db9aadad96b267b07eded0889021f15587e83fa0df7c3e"}