{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PPKXTJMAKHXJHJZAW2MW6LFOZ5","short_pith_number":"pith:PPKXTJMA","canonical_record":{"source":{"id":"1507.08149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-29T14:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"57c0db6a2d99de1cea33ef3c3e2f411fbf117852de4c0f2b15071d07d88a292f","abstract_canon_sha256":"f4aa2f99da85aed817c9a6deed437349376f2d39e8f073b660824ca3f82f7859"},"schema_version":"1.0"},"canonical_sha256":"7bd579a58051ee93a720b6996f2caecf658c78e68c82fa2a3dddb7a6871fbf9d","source":{"kind":"arxiv","id":"1507.08149","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08149","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08149v3","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08149","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"PPKXTJMAKHXJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPKXTJMAKHXJHJZA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPKXTJMA","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PPKXTJMAKHXJHJZAW2MW6LFOZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-29T14:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"57c0db6a2d99de1cea33ef3c3e2f411fbf117852de4c0f2b15071d07d88a292f","abstract_canon_sha256":"f4aa2f99da85aed817c9a6deed437349376f2d39e8f073b660824ca3f82f7859"},"schema_version":"1.0"},"canonical_sha256":"7bd579a58051ee93a720b6996f2caecf658c78e68c82fa2a3dddb7a6871fbf9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:44.623722Z","signature_b64":"WxV7/eEna+BJI4PEx0G7Zo6QPuUfVwdfjPMelJ4nRPV7Dyj+zr8I+zrOU6zkj/PGdocob4ldE3II4ywP5b3bAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bd579a58051ee93a720b6996f2caecf658c78e68c82fa2a3dddb7a6871fbf9d","last_reissued_at":"2026-05-18T01:23:44.623130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:44.623130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08149","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAJ/EcPyfATFhmrONee3yjK94tjejvgCMLpQkFgqChdhnEv4RX3oZnasSD3M1TOlL0yIl7tFZZrojZ3z096jDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:46:59.427414Z"},"content_sha256":"0ede49cc601bf83bb6ba90e30739a652f9cf2a07d5e7792b613db09b8d71d79b","schema_version":"1.0","event_id":"sha256:0ede49cc601bf83bb6ba90e30739a652f9cf2a07d5e7792b613db09b8d71d79b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PPKXTJMAKHXJHJZAW2MW6LFOZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On non-dense orbits of certain non-algebraic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weisheng Wu","submitted_at":"2015-07-29T14:10:15Z","abstract_excerpt":"In this paper, we manage to apply Schmidt games to certain non-algebraic dynamical systems. More precisely, we show that the set of points with non-dense forward orbit under a $C^2$-Anosov diffeomorphism with conformality on unstable manifolds is a winning set for Schmidt games. It is also proved that for a $C^{1+\\theta}$-expanding endomorphism the set of points with non-dense forward orbit is a winning set for certain variants of Schmidt games."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08149","kind":"arxiv","version":3},"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":"2026-05-18T01:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PY2rC7gX8SzRPeSizYKPiqX4Ttc+QRAOiG3CGsjDrVEFJP4+tuQ5QLLIHHYNRxFN4I2QWg7UPjL6rU6pVbj0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:46:59.427753Z"},"content_sha256":"b3a36df3a12a07f0a3eef5981138832242690415893764dc0e812c5f7eabedf0","schema_version":"1.0","event_id":"sha256:b3a36df3a12a07f0a3eef5981138832242690415893764dc0e812c5f7eabedf0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5/bundle.json","state_url":"https://pith.science/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5/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":"2026-06-27T11:46:59Z","links":{"resolver":"https://pith.science/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5","bundle":"https://pith.science/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5/bundle.json","state":"https://pith.science/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPKXTJMAKHXJHJZAW2MW6LFOZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PPKXTJMAKHXJHJZAW2MW6LFOZ5","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":"f4aa2f99da85aed817c9a6deed437349376f2d39e8f073b660824ca3f82f7859","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-29T14:10:15Z","title_canon_sha256":"57c0db6a2d99de1cea33ef3c3e2f411fbf117852de4c0f2b15071d07d88a292f"},"schema_version":"1.0","source":{"id":"1507.08149","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08149","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08149v3","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08149","created_at":"2026-05-18T01:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"PPKXTJMAKHXJ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPKXTJMAKHXJHJZA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPKXTJMA","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:b3a36df3a12a07f0a3eef5981138832242690415893764dc0e812c5f7eabedf0","target":"graph","created_at":"2026-05-18T01:23:44Z","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 manage to apply Schmidt games to certain non-algebraic dynamical systems. More precisely, we show that the set of points with non-dense forward orbit under a $C^2$-Anosov diffeomorphism with conformality on unstable manifolds is a winning set for Schmidt games. It is also proved that for a $C^{1+\\theta}$-expanding endomorphism the set of points with non-dense forward orbit is a winning set for certain variants of Schmidt games.","authors_text":"Weisheng Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-29T14:10:15Z","title":"On non-dense orbits of certain non-algebraic dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08149","kind":"arxiv","version":3},"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":"sha256:0ede49cc601bf83bb6ba90e30739a652f9cf2a07d5e7792b613db09b8d71d79b","target":"record","created_at":"2026-05-18T01:23:44Z","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":"f4aa2f99da85aed817c9a6deed437349376f2d39e8f073b660824ca3f82f7859","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-29T14:10:15Z","title_canon_sha256":"57c0db6a2d99de1cea33ef3c3e2f411fbf117852de4c0f2b15071d07d88a292f"},"schema_version":"1.0","source":{"id":"1507.08149","kind":"arxiv","version":3}},"canonical_sha256":"7bd579a58051ee93a720b6996f2caecf658c78e68c82fa2a3dddb7a6871fbf9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bd579a58051ee93a720b6996f2caecf658c78e68c82fa2a3dddb7a6871fbf9d","first_computed_at":"2026-05-18T01:23:44.623130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:44.623130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WxV7/eEna+BJI4PEx0G7Zo6QPuUfVwdfjPMelJ4nRPV7Dyj+zr8I+zrOU6zkj/PGdocob4ldE3II4ywP5b3bAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:44.623722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08149","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ede49cc601bf83bb6ba90e30739a652f9cf2a07d5e7792b613db09b8d71d79b","sha256:b3a36df3a12a07f0a3eef5981138832242690415893764dc0e812c5f7eabedf0"],"state_sha256":"49e7b93301c641e4af7a780f1d752fc7778ca1e4ebd7c470c8c0a12b7dd97f18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UADRuHwRYApdixo7vAYTg2Mu2iBqWXPVMKU8hSKS5FGf4NvSa1xeI7hxjOb2q6kMze8RU6atzh27V5g8idQoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:46:59.429560Z","bundle_sha256":"6dd4b6db087c80b215c2cbbc2fe64226232652ff50e3176c93754cf51eb63e94"}}