{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NZTXMGMKGGZ3MNJQ7TQMI2F23I","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":"1c9293c491e979957b4ea90b78aa5ff388957eb9492f3d21d44d39d7f4f6f658","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-02-21T19:30:46Z","title_canon_sha256":"c52afdccbf1fb846b7b70bfa2768efacf513bf6e9eb2e8993be70fee06819eb0"},"schema_version":"1.0","source":{"id":"2002.09520","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.09520","created_at":"2026-07-05T00:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"2002.09520v1","created_at":"2026-07-05T00:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09520","created_at":"2026-07-05T00:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"NZTXMGMKGGZ3","created_at":"2026-07-05T00:43:08Z"},{"alias_kind":"pith_short_16","alias_value":"NZTXMGMKGGZ3MNJQ","created_at":"2026-07-05T00:43:08Z"},{"alias_kind":"pith_short_8","alias_value":"NZTXMGMK","created_at":"2026-07-05T00:43:08Z"}],"graph_snapshots":[{"event_id":"sha256:c5fe97d8dc5f539ed28c855f6b9d6f1eeeba661d4649bb58b4eebf116a6e7435","target":"graph","created_at":"2026-07-05T00:43:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.09520/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Ilia Smilga, Jeffrey Danciger, Todd A. Drumm, William M. Goldman","cross_cats":["math.DG","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-02-21T19:30:46Z","title":"Proper actions of discrete groups of affine transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09520","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":"sha256:715a8ff675992e041bfee531fa641c67f9098dac18cf1304a204746d5bffe892","target":"record","created_at":"2026-07-05T00:43:08Z","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":"1c9293c491e979957b4ea90b78aa5ff388957eb9492f3d21d44d39d7f4f6f658","cross_cats_sorted":["math.DG","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2020-02-21T19:30:46Z","title_canon_sha256":"c52afdccbf1fb846b7b70bfa2768efacf513bf6e9eb2e8993be70fee06819eb0"},"schema_version":"1.0","source":{"id":"2002.09520","kind":"arxiv","version":1}},"canonical_sha256":"6e6776198a31b3b63530fce0c468bada3a86ab999ef6cba328bf0dceebba5268","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e6776198a31b3b63530fce0c468bada3a86ab999ef6cba328bf0dceebba5268","first_computed_at":"2026-07-05T00:43:08.586295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:43:08.586295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rkp7edbFvhw3N89jydjr0LPgRcyHnkNpRC++rrPSoPFaYajUM+iV7xZKxE7nmxVJ8QPevGy1k1GcTBAC0ZrlBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:43:08.586790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.09520","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:715a8ff675992e041bfee531fa641c67f9098dac18cf1304a204746d5bffe892","sha256:c5fe97d8dc5f539ed28c855f6b9d6f1eeeba661d4649bb58b4eebf116a6e7435"],"state_sha256":"a7dbfaaca3bcb29543cf9197ac9fe396b502c28b80d87d566ac505962e85aaae"}