{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZSXOGSOR2Y2GPJ7ALWENBLNTMW","short_pith_number":"pith:ZSXOGSOR","canonical_record":{"source":{"id":"1108.5330","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-26T15:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"a35837d9121f6db8a40e10f380dcbaa11dc8a2ac86c930038c045f723c1d6648","abstract_canon_sha256":"af6ffc1cb377495e7a1e832ebb0bf417afb5d9e702e73e60de91676cec71fb59"},"schema_version":"1.0"},"canonical_sha256":"ccaee349d1d63467a7e05d88d0adb365989e788b83aba7f24d66e8c4ca2f1bd8","source":{"kind":"arxiv","id":"1108.5330","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZSXOGSOR2Y2GPJ7ALWENBLNTMW","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5330","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-26T15:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"a35837d9121f6db8a40e10f380dcbaa11dc8a2ac86c930038c045f723c1d6648","abstract_canon_sha256":"af6ffc1cb377495e7a1e832ebb0bf417afb5d9e702e73e60de91676cec71fb59"},"schema_version":"1.0"},"canonical_sha256":"ccaee349d1d63467a7e05d88d0adb365989e788b83aba7f24d66e8c4ca2f1bd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.271390Z","signature_b64":"LKwCs0o4jSSE79HTrblbLWbc6yqm36uG7EnrqrIX/s2+u3untt8ojqM4jowJxHbapAtLRRlQcQD1aeFXpgaSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccaee349d1d63467a7e05d88d0adb365989e788b83aba7f24d66e8c4ca2f1bd8","last_reissued_at":"2026-05-17T23:53:19.270851Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.270851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5330","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RF4AFwQtH6dhP5PV97ADChoBG86hsIi6Gx9gUVGim+g8Mfu2xdzprvsII2Ryh6oIUrrHbW9aqQ3hQbrmtuu9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:47:31.407648Z"},"content_sha256":"1d06b348486194f24abf468f5756cedc4221ae81180ba22186b5344697799c96","schema_version":"1.0","event_id":"sha256:1d06b348486194f24abf468f5756cedc4221ae81180ba22186b5344697799c96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZSXOGSOR2Y2GPJ7ALWENBLNTMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistent massive attractors of smooth maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Denis Volk","submitted_at":"2011-08-26T15:43:49Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5330","kind":"arxiv","version":5},"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":"2026-05-17T23:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cmg1eMr9w7NcCfQLj+oW2FyBF3ONB1qqelkpZMb01TauseUWz9GeNk61VQzo7CoIhDGl22Qbx3XymYw5VnQKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:47:31.408287Z"},"content_sha256":"768d9cb9268f738c9636b2972743b4ef8dce7cb3e2cdab7eebbb0653d0241ea6","schema_version":"1.0","event_id":"sha256:768d9cb9268f738c9636b2972743b4ef8dce7cb3e2cdab7eebbb0653d0241ea6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW/bundle.json","state_url":"https://pith.science/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW/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":"2026-06-05T20:47:31Z","links":{"resolver":"https://pith.science/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW","bundle":"https://pith.science/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW/bundle.json","state":"https://pith.science/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSXOGSOR2Y2GPJ7ALWENBLNTMW/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VIs9gsJYY9hQP2seeeUyXKTNSXMY3qZjlJhAfGbQgtWmXDbJZq8iWIZ4Nd63Lc6zdGdOJS00XpV5PsyzyVP1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:47:31.411707Z","bundle_sha256":"612d4877ce179d4a3579a2b0515da40c4a55fc82d29b3bfdbf31bb456ce80d88"}}