{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ITJOZ2WNN354M25F6N2FLDZPBR","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":"bf97ee7058fd7b5fc342ed394421af2b98ec8f768bafbdfdf3f5f1ffc0e8df17","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-28T11:03:38Z","title_canon_sha256":"3b41b8487dbfd56a808be379ac5849fef7845076ffb0658f19bb517936afe944"},"schema_version":"1.0","source":{"id":"1301.6513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6513","created_at":"2026-05-18T03:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6513v1","created_at":"2026-05-18T03:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6513","created_at":"2026-05-18T03:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"ITJOZ2WNN354","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"ITJOZ2WNN354M25F","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"ITJOZ2WN","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:79e6badcf6ef67a5c869afdd4f4e6ad25b1e82ec547d44755afcec168959991c","target":"graph","created_at":"2026-05-18T03:35:15Z","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":"We look at group actions on metric spaces, particularly at group actions on geodesic hyperbolic spaces. We classify the types of automorphisms on these spaces and prove several results about the density of the hyperbolic limit set of the group in the whole limit set of the group. In the case of graphs, our theorems hold also when the graphs are not hyperbolic.","authors_text":"Matthias Hamann","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-28T11:03:38Z","title":"Group actions on metric spaces: fixed points and free subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6513","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":"sha256:378dd67d315269b733d5346bc55cc75eb27f3cf30e83926f2a14191325e978a5","target":"record","created_at":"2026-05-18T03:35:15Z","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":"bf97ee7058fd7b5fc342ed394421af2b98ec8f768bafbdfdf3f5f1ffc0e8df17","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-28T11:03:38Z","title_canon_sha256":"3b41b8487dbfd56a808be379ac5849fef7845076ffb0658f19bb517936afe944"},"schema_version":"1.0","source":{"id":"1301.6513","kind":"arxiv","version":1}},"canonical_sha256":"44d2eceacd6efbc66ba5f374558f2f0c5eb5bbaebf9869152786beeaefa1dc2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44d2eceacd6efbc66ba5f374558f2f0c5eb5bbaebf9869152786beeaefa1dc2e","first_computed_at":"2026-05-18T03:35:15.148651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:15.148651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DdL9YinZZkDWsnBZnLuuEOLL1E/bzUo6hPPJpyE5ZRA0PaKgBgcRTWX9qlA3T/WgicB81H9IoOIMXWef0fR4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:15.149371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:378dd67d315269b733d5346bc55cc75eb27f3cf30e83926f2a14191325e978a5","sha256:79e6badcf6ef67a5c869afdd4f4e6ad25b1e82ec547d44755afcec168959991c"],"state_sha256":"1acf517b108ad26ae953bdaa1adde2bd7b8ebd2dd2ec4afff6b25a4fcacc6e4a"}