{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7KPBX5NL26DTBLMOFSDBRGI7GO","short_pith_number":"pith:7KPBX5NL","schema_version":"1.0","canonical_sha256":"fa9e1bf5abd78730ad8e2c8618991f33891be01724668c2a59d70f92b44d5c02","source":{"kind":"arxiv","id":"1509.02454","version":2},"attestation_state":"computed","paper":{"title":"Ergodic properties of folding maps on spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Almut Burchard, Anne Dranovski, Gregory R. Chambers","submitted_at":"2015-09-08T17:21:23Z","abstract_excerpt":"We consider the trajectories of points on $\\mathbb{S}^{d - 1}$ under sequences of certain folding maps associated with reflections. The main result characterizes collections of folding maps that produce dense trajectories. The minimal number of maps in such a collection is $d+1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.02454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-08T17:21:23Z","cross_cats_sorted":[],"title_canon_sha256":"5f2dc7671c1e25877252292f12cfcf3a173693d1e9a71b731ae8a7746b363a44","abstract_canon_sha256":"8283da7650d219a097ddab8bddbabf264df4ba6f7221c844e1bd9a55ed0359d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:01.085359Z","signature_b64":"2a7UTY+LMVva0YB40ZUlbgUEH+FrqMLpdU2ALqSvpJsLUXsS/rnJk1s166yty+Ili/Vp2vUBb5Ru8gVUEA27DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa9e1bf5abd78730ad8e2c8618991f33891be01724668c2a59d70f92b44d5c02","last_reissued_at":"2026-05-18T00:12:01.084657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:01.084657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic properties of folding maps on spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Almut Burchard, Anne Dranovski, Gregory R. Chambers","submitted_at":"2015-09-08T17:21:23Z","abstract_excerpt":"We consider the trajectories of points on $\\mathbb{S}^{d - 1}$ under sequences of certain folding maps associated with reflections. The main result characterizes collections of folding maps that produce dense trajectories. The minimal number of maps in such a collection is $d+1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02454","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.02454","created_at":"2026-05-18T00:12:01.084744+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02454v2","created_at":"2026-05-18T00:12:01.084744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02454","created_at":"2026-05-18T00:12:01.084744+00:00"},{"alias_kind":"pith_short_12","alias_value":"7KPBX5NL26DT","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7KPBX5NL26DTBLMO","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7KPBX5NL","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO","json":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO.json","graph_json":"https://pith.science/api/pith-number/7KPBX5NL26DTBLMOFSDBRGI7GO/graph.json","events_json":"https://pith.science/api/pith-number/7KPBX5NL26DTBLMOFSDBRGI7GO/events.json","paper":"https://pith.science/paper/7KPBX5NL"},"agent_actions":{"view_html":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO","download_json":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO.json","view_paper":"https://pith.science/paper/7KPBX5NL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02454&json=true","fetch_graph":"https://pith.science/api/pith-number/7KPBX5NL26DTBLMOFSDBRGI7GO/graph.json","fetch_events":"https://pith.science/api/pith-number/7KPBX5NL26DTBLMOFSDBRGI7GO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO/action/storage_attestation","attest_author":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO/action/author_attestation","sign_citation":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO/action/citation_signature","submit_replication":"https://pith.science/pith/7KPBX5NL26DTBLMOFSDBRGI7GO/action/replication_record"}},"created_at":"2026-05-18T00:12:01.084744+00:00","updated_at":"2026-05-18T00:12:01.084744+00:00"}