{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:27YJ5OHKLDAHJMLCXBYILNP5OE","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":"2e14a99e9d45478d17f90c22f55f31fe8b19531bf9aeecfa6a8c9baa36426cd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-07T09:18:15Z","title_canon_sha256":"bedd04a3ea40c379b655a15d44637a570c8c30b14b09761b9230378e3213628d"},"schema_version":"1.0","source":{"id":"1404.1702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1702","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1702v1","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1702","created_at":"2026-05-18T02:54:40Z"},{"alias_kind":"pith_short_12","alias_value":"27YJ5OHKLDAH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"27YJ5OHKLDAHJMLC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"27YJ5OHK","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:e1d0f16dbfb2a9c2a3ec9bee5b8abea7d9068c416a403b0766ee00656b7247dc","target":"graph","created_at":"2026-05-18T02:54:40Z","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 $f: \\mathbb{T}^3\\to\\mathbb{T}^3$ be a partially hyperbolic diffeomorphism on the 3-torus $\\mathbb{T}^3$. In his thesis, Hammerlindl proved that for lifted center foliation $\\mathcal{F}^c_f$, there exists $R>0$, such that for any $x\\in \\mathbb{R}^3$, ${\\cal F}^c_f(x)\\subset B_R (x+E^c)$, where $\\mathbb{R}^3=E^s\\oplus E^c\\oplus E^u$ is the partially hyperbolic splitting of the linear model of $f$. The same is true for the lifted center-stable and center-unstable foliations. Then he asked if the this property is true for strong stable and strong unstable foliations. In this note, we give a ne","authors_text":"Pengfei Zhang, Shaobo Gan, Yan Ren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-07T09:18:15Z","title":"An answer to Hammerlindl's question on strong unstable foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1702","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:c830401d7cd851ef59c75d4a2d09b00dcd781f100a3707757dd96ea31a2efafd","target":"record","created_at":"2026-05-18T02:54:40Z","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":"2e14a99e9d45478d17f90c22f55f31fe8b19531bf9aeecfa6a8c9baa36426cd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-07T09:18:15Z","title_canon_sha256":"bedd04a3ea40c379b655a15d44637a570c8c30b14b09761b9230378e3213628d"},"schema_version":"1.0","source":{"id":"1404.1702","kind":"arxiv","version":1}},"canonical_sha256":"d7f09eb8ea58c074b162b87085b5fd7103ca562dd7f8aea116a42157cb743b77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7f09eb8ea58c074b162b87085b5fd7103ca562dd7f8aea116a42157cb743b77","first_computed_at":"2026-05-18T02:54:40.355189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:40.355189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5LRA3wdx1wODyNbvYZ0nLvtxyeGyY6/44W14RHIWm7/aGQaFttYNebRnPGhoPic9TU2jVGZ7NUd34FOIhuaeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:40.355569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c830401d7cd851ef59c75d4a2d09b00dcd781f100a3707757dd96ea31a2efafd","sha256:e1d0f16dbfb2a9c2a3ec9bee5b8abea7d9068c416a403b0766ee00656b7247dc"],"state_sha256":"213e68b7740a0272658356e81ae38d501d38d7d8fdb0a30e891724c2a35db0d8"}