{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CWMPWKGWURURTZED2YFZF4FYXG","short_pith_number":"pith:CWMPWKGW","canonical_record":{"source":{"id":"1605.01119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-04T00:17:20Z","cross_cats_sorted":[],"title_canon_sha256":"a334d585258cd1b433fe13205539e7ab4ca0c9c9e6aa189206ad299f2ec2d0f9","abstract_canon_sha256":"387818505291abc3b92f506565a616182a691319c73d189f00034600c483a400"},"schema_version":"1.0"},"canonical_sha256":"1598fb28d6a46919e483d60b92f0b8b98df839d1b93f595110bafa7a068a2010","source":{"kind":"arxiv","id":"1605.01119","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01119","created_at":"2026-05-18T00:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01119v2","created_at":"2026-05-18T00:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01119","created_at":"2026-05-18T00:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"CWMPWKGWURUR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CWMPWKGWURURTZED","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CWMPWKGW","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CWMPWKGWURURTZED2YFZF4FYXG","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01119","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-04T00:17:20Z","cross_cats_sorted":[],"title_canon_sha256":"a334d585258cd1b433fe13205539e7ab4ca0c9c9e6aa189206ad299f2ec2d0f9","abstract_canon_sha256":"387818505291abc3b92f506565a616182a691319c73d189f00034600c483a400"},"schema_version":"1.0"},"canonical_sha256":"1598fb28d6a46919e483d60b92f0b8b98df839d1b93f595110bafa7a068a2010","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:58.449250Z","signature_b64":"X7UHooRxYwTdy/My8pK7w3n36MRM59wb+L1oFJlwQnFx0Xjt3kMxv8rEJxlhqYuxW1/7+8U8qn0nke36Ep6/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1598fb28d6a46919e483d60b92f0b8b98df839d1b93f595110bafa7a068a2010","last_reissued_at":"2026-05-18T00:59:58.448770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:58.448770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01119","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BtNz9sBMiGp7K9cG47XSs2CTiw6bx7C4+ueDuxpDdIz4NNA314F+U64g1WKkvPtDT6SBiEdo+oeULTbJPsrHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:45:00.595277Z"},"content_sha256":"779426603e11bd18d9dfad9f7c278569fae392280f3f7be20f86bbc33ffa20e5","schema_version":"1.0","event_id":"sha256:779426603e11bd18d9dfad9f7c278569fae392280f3f7be20f86bbc33ffa20e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CWMPWKGWURURTZED2YFZF4FYXG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sensitivity, proximal extension and higher order almost automorphy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Tao Yu, Xiangdong Ye","submitted_at":"2016-05-04T00:17:20Z","abstract_excerpt":"Let $(X,T)$ be a topological dynamical system, and $\\mathcal{F}$ be a family of subsets of $\\mathbb{Z}_+$. $(X,T)$ is strongly $\\mathcal{F}$-sensitive, if there is $\\delta>0$ such that for each non-empty open subset $U$, there are $x,y\\in U$ with $\\{n\\in\\mathbb{Z}_+: d(T^nx,T^ny)>\\delta\\}\\in\\mathcal{F}$. Let $\\mathcal{F}_t$ (resp. $\\mathcal{F}_{ip}$, $\\mathcal{F}_{fip}$) be consisting of thick sets (resp. IP-sets, subsets containing arbitrarily long finite IP-sets).\n  The following Auslander-Yorke's type dichotomy theorems are obtained: (1) a minimal system is either strongly $\\mathcal{F}_{fip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01119","kind":"arxiv","version":2},"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":"2026-05-18T00:59:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BtCrZI8goN7JOwinrPuO7vSjyYjuFhLpyETipC4VMylNAVIkL3Axxxy4XeGwmhXs+lxYh6rv0e/Evog8QC/nCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:45:00.595661Z"},"content_sha256":"1b37cc6ce59f5aadaace27fb13a9a23409e54f90273f544f171b67a688d3523d","schema_version":"1.0","event_id":"sha256:1b37cc6ce59f5aadaace27fb13a9a23409e54f90273f544f171b67a688d3523d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWMPWKGWURURTZED2YFZF4FYXG/bundle.json","state_url":"https://pith.science/pith/CWMPWKGWURURTZED2YFZF4FYXG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWMPWKGWURURTZED2YFZF4FYXG/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":"2026-06-24T11:45:00Z","links":{"resolver":"https://pith.science/pith/CWMPWKGWURURTZED2YFZF4FYXG","bundle":"https://pith.science/pith/CWMPWKGWURURTZED2YFZF4FYXG/bundle.json","state":"https://pith.science/pith/CWMPWKGWURURTZED2YFZF4FYXG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWMPWKGWURURTZED2YFZF4FYXG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CWMPWKGWURURTZED2YFZF4FYXG","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":"387818505291abc3b92f506565a616182a691319c73d189f00034600c483a400","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-04T00:17:20Z","title_canon_sha256":"a334d585258cd1b433fe13205539e7ab4ca0c9c9e6aa189206ad299f2ec2d0f9"},"schema_version":"1.0","source":{"id":"1605.01119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01119","created_at":"2026-05-18T00:59:58Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01119v2","created_at":"2026-05-18T00:59:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01119","created_at":"2026-05-18T00:59:58Z"},{"alias_kind":"pith_short_12","alias_value":"CWMPWKGWURUR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CWMPWKGWURURTZED","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CWMPWKGW","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:1b37cc6ce59f5aadaace27fb13a9a23409e54f90273f544f171b67a688d3523d","target":"graph","created_at":"2026-05-18T00:59:58Z","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 $(X,T)$ be a topological dynamical system, and $\\mathcal{F}$ be a family of subsets of $\\mathbb{Z}_+$. $(X,T)$ is strongly $\\mathcal{F}$-sensitive, if there is $\\delta>0$ such that for each non-empty open subset $U$, there are $x,y\\in U$ with $\\{n\\in\\mathbb{Z}_+: d(T^nx,T^ny)>\\delta\\}\\in\\mathcal{F}$. Let $\\mathcal{F}_t$ (resp. $\\mathcal{F}_{ip}$, $\\mathcal{F}_{fip}$) be consisting of thick sets (resp. IP-sets, subsets containing arbitrarily long finite IP-sets).\n  The following Auslander-Yorke's type dichotomy theorems are obtained: (1) a minimal system is either strongly $\\mathcal{F}_{fip","authors_text":"Tao Yu, Xiangdong Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-04T00:17:20Z","title":"Sensitivity, proximal extension and higher order almost automorphy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01119","kind":"arxiv","version":2},"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":"sha256:779426603e11bd18d9dfad9f7c278569fae392280f3f7be20f86bbc33ffa20e5","target":"record","created_at":"2026-05-18T00:59:58Z","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":"387818505291abc3b92f506565a616182a691319c73d189f00034600c483a400","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-04T00:17:20Z","title_canon_sha256":"a334d585258cd1b433fe13205539e7ab4ca0c9c9e6aa189206ad299f2ec2d0f9"},"schema_version":"1.0","source":{"id":"1605.01119","kind":"arxiv","version":2}},"canonical_sha256":"1598fb28d6a46919e483d60b92f0b8b98df839d1b93f595110bafa7a068a2010","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1598fb28d6a46919e483d60b92f0b8b98df839d1b93f595110bafa7a068a2010","first_computed_at":"2026-05-18T00:59:58.448770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:58.448770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7UHooRxYwTdy/My8pK7w3n36MRM59wb+L1oFJlwQnFx0Xjt3kMxv8rEJxlhqYuxW1/7+8U8qn0nke36Ep6/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:58.449250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:779426603e11bd18d9dfad9f7c278569fae392280f3f7be20f86bbc33ffa20e5","sha256:1b37cc6ce59f5aadaace27fb13a9a23409e54f90273f544f171b67a688d3523d"],"state_sha256":"337eb3e0d337b24ad72986d21b452eacf71c59dfed7ea82012583cf4916a0c7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9V9HmpxtPNsAGkAD02pm/7DGQTXYOfTOQ37c4gq/g6NyyvK4UrHlk9CDTjymmRiRaeBzTCVyIgKkrif+C88Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:45:00.597543Z","bundle_sha256":"17d32be4137c4a9eef6ac6dcb9b651e0214158948be1e8c3ce1a1d70d2a058da"}}