{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZLGKYTC5IG76C54UP6XNAMJOKF","short_pith_number":"pith:ZLGKYTC5","canonical_record":{"source":{"id":"1008.3766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-23T07:48:04Z","cross_cats_sorted":[],"title_canon_sha256":"7e7f6b42566a71fb8db4ab2f11ee7b43f568658d09e2615e049e8804b800c868","abstract_canon_sha256":"5fe4b0d8f4618c02b50407bf2a50a607b4ac0b2ed2c6cd7ed6543cd29b70ea27"},"schema_version":"1.0"},"canonical_sha256":"caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397","source":{"kind":"arxiv","id":"1008.3766","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3766","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3766v2","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3766","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZLGKYTC5IG76","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZLGKYTC5IG76C54U","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZLGKYTC5","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZLGKYTC5IG76C54UP6XNAMJOKF","target":"record","payload":{"canonical_record":{"source":{"id":"1008.3766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-23T07:48:04Z","cross_cats_sorted":[],"title_canon_sha256":"7e7f6b42566a71fb8db4ab2f11ee7b43f568658d09e2615e049e8804b800c868","abstract_canon_sha256":"5fe4b0d8f4618c02b50407bf2a50a607b4ac0b2ed2c6cd7ed6543cd29b70ea27"},"schema_version":"1.0"},"canonical_sha256":"caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:02.332978Z","signature_b64":"y/Dz8oY/19yq48DRD3jOkvPO/5YDypNk0QxEUyXgl9m4RbZr/l0cpPFx4Q6R6yPjs1HihD96IC5kckRUsVRqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397","last_reissued_at":"2026-05-18T04:22:02.332573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:02.332573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.3766","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:22:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t14AXdA6uNeY2vjYG8kNKS3joxkzS5pzt5guAqt513DKfeNO38S9saIbcVO8LKQWr7GTBVMxESnFjHRXOqThBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:50:12.559683Z"},"content_sha256":"99e0f2d502cd4a850cffe98a5eb17159d6d46e0f67e91476d91553ccfb62e092","schema_version":"1.0","event_id":"sha256:99e0f2d502cd4a850cffe98a5eb17159d6d46e0f67e91476d91553ccfb62e092"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZLGKYTC5IG76C54UP6XNAMJOKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A non-trivial example of a free-by-free group with the Haagerup property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Fran\\c{c}ois Gautero","submitted_at":"2010-08-23T07:48:04Z","abstract_excerpt":"The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies the Haagerup property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3766","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:22:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fVpiXvmYuL5gCnbLeqwH0wiuNHWzU4kIh6cj8UEowVBnd4qsgvJu8BvmPx8cf7gTpnAyZiFj8qW0SpUGa4sCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:50:12.560147Z"},"content_sha256":"e63f7cad34479b933545bc7c2c1fe09de2d17f9d9a799e56e4ca909d511802d8","schema_version":"1.0","event_id":"sha256:e63f7cad34479b933545bc7c2c1fe09de2d17f9d9a799e56e4ca909d511802d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLGKYTC5IG76C54UP6XNAMJOKF/bundle.json","state_url":"https://pith.science/pith/ZLGKYTC5IG76C54UP6XNAMJOKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLGKYTC5IG76C54UP6XNAMJOKF/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":"2026-06-23T18:50:12Z","links":{"resolver":"https://pith.science/pith/ZLGKYTC5IG76C54UP6XNAMJOKF","bundle":"https://pith.science/pith/ZLGKYTC5IG76C54UP6XNAMJOKF/bundle.json","state":"https://pith.science/pith/ZLGKYTC5IG76C54UP6XNAMJOKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLGKYTC5IG76C54UP6XNAMJOKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZLGKYTC5IG76C54UP6XNAMJOKF","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":"5fe4b0d8f4618c02b50407bf2a50a607b4ac0b2ed2c6cd7ed6543cd29b70ea27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-23T07:48:04Z","title_canon_sha256":"7e7f6b42566a71fb8db4ab2f11ee7b43f568658d09e2615e049e8804b800c868"},"schema_version":"1.0","source":{"id":"1008.3766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3766","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3766v2","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3766","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"ZLGKYTC5IG76","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZLGKYTC5IG76C54U","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZLGKYTC5","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:e63f7cad34479b933545bc7c2c1fe09de2d17f9d9a799e56e4ca909d511802d8","target":"graph","created_at":"2026-05-18T04:22:02Z","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":"The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies the Haagerup property.","authors_text":"Fran\\c{c}ois Gautero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-23T07:48:04Z","title":"A non-trivial example of a free-by-free group with the Haagerup property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3766","kind":"arxiv","version":2},"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":"sha256:99e0f2d502cd4a850cffe98a5eb17159d6d46e0f67e91476d91553ccfb62e092","target":"record","created_at":"2026-05-18T04:22:02Z","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":"5fe4b0d8f4618c02b50407bf2a50a607b4ac0b2ed2c6cd7ed6543cd29b70ea27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-08-23T07:48:04Z","title_canon_sha256":"7e7f6b42566a71fb8db4ab2f11ee7b43f568658d09e2615e049e8804b800c868"},"schema_version":"1.0","source":{"id":"1008.3766","kind":"arxiv","version":2}},"canonical_sha256":"caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397","first_computed_at":"2026-05-18T04:22:02.332573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:02.332573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y/Dz8oY/19yq48DRD3jOkvPO/5YDypNk0QxEUyXgl9m4RbZr/l0cpPFx4Q6R6yPjs1HihD96IC5kckRUsVRqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:02.332978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99e0f2d502cd4a850cffe98a5eb17159d6d46e0f67e91476d91553ccfb62e092","sha256:e63f7cad34479b933545bc7c2c1fe09de2d17f9d9a799e56e4ca909d511802d8"],"state_sha256":"9f02e044ee26840ace141a6e73a9f5a3d1c041d05151e5b772720b1fbac6bc8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GcTeBE9oUWBXM6SWmjCPgvG0NzwHD5RJBXhxZZuJOpSbYinp4vnrzuhCsfB3oq2fO7p5uc/ct8a2T373/zNiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:50:12.562857Z","bundle_sha256":"ab4699403cae83fa0fd00cc9c80bdef04b1c5979551565e99baf0e10cadb8255"}}