{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YFXUOFQDNQ6UBFLUUKYDM5GVW5","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":"dfcd3a82ab9adaf7395e5bd77624b9380c675c58c0ab004198f8299500029aee","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-24T19:47:46Z","title_canon_sha256":"19c96daecd69a0502e4525b49b9c23c9e9522c139536fe6af5101d75bab8d820"},"schema_version":"1.0","source":{"id":"1510.07179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07179","created_at":"2026-05-18T01:29:19Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07179v1","created_at":"2026-05-18T01:29:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07179","created_at":"2026-05-18T01:29:19Z"},{"alias_kind":"pith_short_12","alias_value":"YFXUOFQDNQ6U","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YFXUOFQDNQ6UBFLU","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YFXUOFQD","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:d9eaefac6006c67d96defcbbc3423d91e621e4d381fa0cbc8351c7e2aa5b2cb0","target":"graph","created_at":"2026-05-18T01:29:19Z","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":"Considering the space of closed subsets of $\\mathbb{R}^d$, endowed with the Chabauty-Fell topology, and the affine action of $SL_d(\\mathbb{R})\\ltimes\\mathbb{R}^d$, we prove that the only minimal subsystems are the fixed points $\\{\\varnothing\\}$ and $\\{\\mathbb{R}^d\\}$. As a consequence we resolve a question of Gowers concerning the existence of certain Danzer sets: there is no set $Y \\subset \\mathbb{R}^d$ such that for every convex set $\\mathcal{C} \\subset \\mathbb{R}^d$ of volume one, the cardinality of $\\mathcal{C} \\cap Y$ is bounded above and below by nonzero contants independent of $\\mathcal","authors_text":"Barak Weiss, Omri Solan, Yaar Solomon","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-24T19:47:46Z","title":"On problems of Danzer and Gowers and dynamics on the space of closed subsets of $\\mathbb{R}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07179","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":"sha256:8cc08696cd077a9633ba5cafc8562a6dd38925e400cb6912b2218b60d3c18110","target":"record","created_at":"2026-05-18T01:29:19Z","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":"dfcd3a82ab9adaf7395e5bd77624b9380c675c58c0ab004198f8299500029aee","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-24T19:47:46Z","title_canon_sha256":"19c96daecd69a0502e4525b49b9c23c9e9522c139536fe6af5101d75bab8d820"},"schema_version":"1.0","source":{"id":"1510.07179","kind":"arxiv","version":1}},"canonical_sha256":"c16f4716036c3d409574a2b03674d5b7757939b1fb2ab8344e42a390d4ce8139","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c16f4716036c3d409574a2b03674d5b7757939b1fb2ab8344e42a390d4ce8139","first_computed_at":"2026-05-18T01:29:19.765812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:19.765812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XWuTahICXmGzqr6Vpr6EqbBZ3MNSAczvoF8BRrwhEMphZhRJdvPA3LxE2WjKyNdCPqEa21N5tR3bdIRq+OC5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:19.766514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cc08696cd077a9633ba5cafc8562a6dd38925e400cb6912b2218b60d3c18110","sha256:d9eaefac6006c67d96defcbbc3423d91e621e4d381fa0cbc8351c7e2aa5b2cb0"],"state_sha256":"fe6cd87de971559dde88f19d9cc34cf0c6bf0a1c91c4020596b27c82d53418bf"}