{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FGLLWTAL2F7ONY5S4QATEORUSU","short_pith_number":"pith:FGLLWTAL","canonical_record":{"source":{"id":"1310.7255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-27T21:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"3da58154732e814d29e86d8f6d9050a6de6923f6e7401137afd509ee1f336d3e","abstract_canon_sha256":"28caee3c7caf9adfa59718262693ed4113194cb907607d45d24050bb3a1b73f3"},"schema_version":"1.0"},"canonical_sha256":"2996bb4c0bd17ee6e3b2e401323a3495267fb08bce1f7adc6e5a82a45f4de373","source":{"kind":"arxiv","id":"1310.7255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7255","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7255v1","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7255","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"FGLLWTAL2F7O","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FGLLWTAL2F7ONY5S","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FGLLWTAL","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FGLLWTAL2F7ONY5S4QATEORUSU","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-27T21:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"3da58154732e814d29e86d8f6d9050a6de6923f6e7401137afd509ee1f336d3e","abstract_canon_sha256":"28caee3c7caf9adfa59718262693ed4113194cb907607d45d24050bb3a1b73f3"},"schema_version":"1.0"},"canonical_sha256":"2996bb4c0bd17ee6e3b2e401323a3495267fb08bce1f7adc6e5a82a45f4de373","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:45.828741Z","signature_b64":"MjA7UQIXpWZY6wPh3j5GbFNMtiqNv0F/83aJ3Brjl7dARsPoudgHOMX+tR/FJrIOCWqboaXJVN5H834Fl+F0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2996bb4c0bd17ee6e3b2e401323a3495267fb08bce1f7adc6e5a82a45f4de373","last_reissued_at":"2026-05-18T03:08:45.828128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:45.828128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7255","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b77AKKkRqn/HxKFHjb7jWUdy8/lnEjfvYRA7xzXMiJU2LH3epeC9REHv70w0bI8EnHdEvmsFhe/tTshusj3NCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:11:43.620574Z"},"content_sha256":"12a610cc36a98f7b6262b9298f9241587a28b5f3a4c9d8e1af46a57916764647","schema_version":"1.0","event_id":"sha256:12a610cc36a98f7b6262b9298f9241587a28b5f3a4c9d8e1af46a57916764647"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FGLLWTAL2F7ONY5S4QATEORUSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On groups with locally compact asymptotic cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark Sapir","submitted_at":"2013-10-27T21:38:11Z","abstract_excerpt":"We show how a recent result of Hrushovsky implies that if an asymptotic cone of a finitely generated group is locally compact, then the group is virtually nilpotent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7255","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JzQFpb0jwclDlj0tsc1Is6p1+Qctqi2CtE/b0vzLSgjkb8tvHs5XFrPSlofeljpATabjQTiIEMovAlG9A1qNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:11:43.620919Z"},"content_sha256":"dd7d3b73dc2048ec63e2347fcff33e5416555212ebf3d7aed03b7cc9677152d0","schema_version":"1.0","event_id":"sha256:dd7d3b73dc2048ec63e2347fcff33e5416555212ebf3d7aed03b7cc9677152d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGLLWTAL2F7ONY5S4QATEORUSU/bundle.json","state_url":"https://pith.science/pith/FGLLWTAL2F7ONY5S4QATEORUSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGLLWTAL2F7ONY5S4QATEORUSU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T21:11:43Z","links":{"resolver":"https://pith.science/pith/FGLLWTAL2F7ONY5S4QATEORUSU","bundle":"https://pith.science/pith/FGLLWTAL2F7ONY5S4QATEORUSU/bundle.json","state":"https://pith.science/pith/FGLLWTAL2F7ONY5S4QATEORUSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGLLWTAL2F7ONY5S4QATEORUSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FGLLWTAL2F7ONY5S4QATEORUSU","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":"28caee3c7caf9adfa59718262693ed4113194cb907607d45d24050bb3a1b73f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-27T21:38:11Z","title_canon_sha256":"3da58154732e814d29e86d8f6d9050a6de6923f6e7401137afd509ee1f336d3e"},"schema_version":"1.0","source":{"id":"1310.7255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7255","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7255v1","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7255","created_at":"2026-05-18T03:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"FGLLWTAL2F7O","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FGLLWTAL2F7ONY5S","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FGLLWTAL","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:dd7d3b73dc2048ec63e2347fcff33e5416555212ebf3d7aed03b7cc9677152d0","target":"graph","created_at":"2026-05-18T03:08:45Z","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 show how a recent result of Hrushovsky implies that if an asymptotic cone of a finitely generated group is locally compact, then the group is virtually nilpotent.","authors_text":"Mark Sapir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-27T21:38:11Z","title":"On groups with locally compact asymptotic cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7255","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":"sha256:12a610cc36a98f7b6262b9298f9241587a28b5f3a4c9d8e1af46a57916764647","target":"record","created_at":"2026-05-18T03:08:45Z","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":"28caee3c7caf9adfa59718262693ed4113194cb907607d45d24050bb3a1b73f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-27T21:38:11Z","title_canon_sha256":"3da58154732e814d29e86d8f6d9050a6de6923f6e7401137afd509ee1f336d3e"},"schema_version":"1.0","source":{"id":"1310.7255","kind":"arxiv","version":1}},"canonical_sha256":"2996bb4c0bd17ee6e3b2e401323a3495267fb08bce1f7adc6e5a82a45f4de373","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2996bb4c0bd17ee6e3b2e401323a3495267fb08bce1f7adc6e5a82a45f4de373","first_computed_at":"2026-05-18T03:08:45.828128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:45.828128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MjA7UQIXpWZY6wPh3j5GbFNMtiqNv0F/83aJ3Brjl7dARsPoudgHOMX+tR/FJrIOCWqboaXJVN5H834Fl+F0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:45.828741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12a610cc36a98f7b6262b9298f9241587a28b5f3a4c9d8e1af46a57916764647","sha256:dd7d3b73dc2048ec63e2347fcff33e5416555212ebf3d7aed03b7cc9677152d0"],"state_sha256":"d277381d70653c57e43f9211407556508c44ab319b702844c3c4905e8bb4b47a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bo9nvovVE73/Ffxq8mmkR2vrO3Rtih9hQ61VIJo7lnHbIOCiNuLdrIkTpMYxcLT4Y/r4CHAu9fJ5gtSCvVTCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:11:43.622967Z","bundle_sha256":"25ec3bafe6716a0f254777c839a26a667da18a0b344f9e722738dd90257c3fba"}}