{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:NZTXMGMKGGZ3MNJQ7TQMI2F23I","short_pith_number":"pith:NZTXMGMK","schema_version":"1.0","canonical_sha256":"6e6776198a31b3b63530fce0c468bada3a86ab999ef6cba328bf0dceebba5268","source":{"kind":"arxiv","id":"2002.09520","version":1},"attestation_state":"computed","paper":{"title":"Proper actions of discrete groups of affine transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"Ilia Smilga, Jeffrey Danciger, Todd A. Drumm, William M. Goldman","submitted_at":"2020-02-21T19:30:46Z","abstract_excerpt":"In the early 1980's Margulis startled the world by showing the existence of proper affine actions of free groups on 3-space, answering a provocative and suggestive question Milnor posed in 1977. In this paper we discuss the historical background motivating this question, recent progress on this subject, and future directions inspired by this discovery."},"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":"2002.09520","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-02-21T19:30:46Z","cross_cats_sorted":["math.DG","math.GT"],"title_canon_sha256":"c52afdccbf1fb846b7b70bfa2768efacf513bf6e9eb2e8993be70fee06819eb0","abstract_canon_sha256":"1c9293c491e979957b4ea90b78aa5ff388957eb9492f3d21d44d39d7f4f6f658"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:43:08.586790Z","signature_b64":"Rkp7edbFvhw3N89jydjr0LPgRcyHnkNpRC++rrPSoPFaYajUM+iV7xZKxE7nmxVJ8QPevGy1k1GcTBAC0ZrlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e6776198a31b3b63530fce0c468bada3a86ab999ef6cba328bf0dceebba5268","last_reissued_at":"2026-07-05T00:43:08.586295Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:43:08.586295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proper actions of discrete groups of affine transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GT"],"primary_cat":"math.GR","authors_text":"Ilia Smilga, Jeffrey Danciger, Todd A. Drumm, William M. Goldman","submitted_at":"2020-02-21T19:30:46Z","abstract_excerpt":"In the early 1980's Margulis startled the world by showing the existence of proper affine actions of free groups on 3-space, answering a provocative and suggestive question Milnor posed in 1977. In this paper we discuss the historical background motivating this question, recent progress on this subject, and future directions inspired by this discovery."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09520","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.09520/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2002.09520","created_at":"2026-07-05T00:43:08.586372+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.09520v1","created_at":"2026-07-05T00:43:08.586372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09520","created_at":"2026-07-05T00:43:08.586372+00:00"},{"alias_kind":"pith_short_12","alias_value":"NZTXMGMKGGZ3","created_at":"2026-07-05T00:43:08.586372+00:00"},{"alias_kind":"pith_short_16","alias_value":"NZTXMGMKGGZ3MNJQ","created_at":"2026-07-05T00:43:08.586372+00:00"},{"alias_kind":"pith_short_8","alias_value":"NZTXMGMK","created_at":"2026-07-05T00:43:08.586372+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.00599","citing_title":"Entropy and affine actions for surface groups","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I","json":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I.json","graph_json":"https://pith.science/api/pith-number/NZTXMGMKGGZ3MNJQ7TQMI2F23I/graph.json","events_json":"https://pith.science/api/pith-number/NZTXMGMKGGZ3MNJQ7TQMI2F23I/events.json","paper":"https://pith.science/paper/NZTXMGMK"},"agent_actions":{"view_html":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I","download_json":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I.json","view_paper":"https://pith.science/paper/NZTXMGMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.09520&json=true","fetch_graph":"https://pith.science/api/pith-number/NZTXMGMKGGZ3MNJQ7TQMI2F23I/graph.json","fetch_events":"https://pith.science/api/pith-number/NZTXMGMKGGZ3MNJQ7TQMI2F23I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I/action/storage_attestation","attest_author":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I/action/author_attestation","sign_citation":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I/action/citation_signature","submit_replication":"https://pith.science/pith/NZTXMGMKGGZ3MNJQ7TQMI2F23I/action/replication_record"}},"created_at":"2026-07-05T00:43:08.586372+00:00","updated_at":"2026-07-05T00:43:08.586372+00:00"}