{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7LSHXZUE55YKRYDE5RI5AJEP7A","short_pith_number":"pith:7LSHXZUE","canonical_record":{"source":{"id":"1209.5804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-26T01:15:24Z","cross_cats_sorted":[],"title_canon_sha256":"863fae818e8c9cabd0e5d7c02046c4e45ef2cdb3a5da075d65cea35d377b2a0e","abstract_canon_sha256":"0a3c1e83424eabf21e91fd269e6c15d62bf17d670d4a8fb2adbd85b15aad2280"},"schema_version":"1.0"},"canonical_sha256":"fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3","source":{"kind":"arxiv","id":"1209.5804","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5804","created_at":"2026-05-18T03:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5804v2","created_at":"2026-05-18T03:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5804","created_at":"2026-05-18T03:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"7LSHXZUE55YK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7LSHXZUE55YKRYDE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7LSHXZUE","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7LSHXZUE55YKRYDE5RI5AJEP7A","target":"record","payload":{"canonical_record":{"source":{"id":"1209.5804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-26T01:15:24Z","cross_cats_sorted":[],"title_canon_sha256":"863fae818e8c9cabd0e5d7c02046c4e45ef2cdb3a5da075d65cea35d377b2a0e","abstract_canon_sha256":"0a3c1e83424eabf21e91fd269e6c15d62bf17d670d4a8fb2adbd85b15aad2280"},"schema_version":"1.0"},"canonical_sha256":"fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:23.547295Z","signature_b64":"lS3uANsAaTL2VMYb7akOSO6FzjCpWddhxwmiK9gezonLcOD4Am5JBIFRRXd45/bwLmCYzNC1A8Q8GxEdoK1BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3","last_reissued_at":"2026-05-18T03:44:23.546613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:23.546613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.5804","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":"2026-05-18T03:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLvoUkK8KaNGCwNk0KOeufNIs85uQuFYrCr2mxbYMHBBDGdBY6p0vkNtW/ca9al9HvghT+ai33mIWyVlMep9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:49:52.988231Z"},"content_sha256":"41c3720f2d0a26d3307be1894d335b7b120ca2844602b9349e62ab24b14b90a7","schema_version":"1.0","event_id":"sha256:41c3720f2d0a26d3307be1894d335b7b120ca2844602b9349e62ab24b14b90a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7LSHXZUE55YKRYDE5RI5AJEP7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A parabolic action on a proper, CAT(0) cube complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bronislaw Wajnryb, Pawel Witowicz, Yael Algom-Kfir","submitted_at":"2012-09-26T01:15:24Z","abstract_excerpt":"We consider diagram groups as defined by V. Guba and M. Sapir. A diagram group G acts on the associated cube complex K by isometries. It is known that if a cube complex L is of a finite dimension then every isometry g of L is semi-simple, i.e. its translation length is realized. It was conjectured by D. S. Farley that in the case of a diagram group G the action of G on the associated cube complex K is by semisimple isometries even when K has an infinite dimension. In this paper we give a counterexample to Farley Conjecture and we show that R. Thompson's group F, considered as a diagram group, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5804","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":"2026-05-18T03:44:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zFhYIoSdUtdcLqz00KS8mpDOra/6e9PW4dHbs2a1bgLZt1G2pDQ0h/ep7Bi/UqT+elqLZAdAo+lhho7BfTOpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:49:52.988600Z"},"content_sha256":"c36694e472fc4a2f67c2b3ffd10ca5d53c5a67d557e562bc7eee36e86b4482e7","schema_version":"1.0","event_id":"sha256:c36694e472fc4a2f67c2b3ffd10ca5d53c5a67d557e562bc7eee36e86b4482e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LSHXZUE55YKRYDE5RI5AJEP7A/bundle.json","state_url":"https://pith.science/pith/7LSHXZUE55YKRYDE5RI5AJEP7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LSHXZUE55YKRYDE5RI5AJEP7A/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":"2026-06-23T16:49:52Z","links":{"resolver":"https://pith.science/pith/7LSHXZUE55YKRYDE5RI5AJEP7A","bundle":"https://pith.science/pith/7LSHXZUE55YKRYDE5RI5AJEP7A/bundle.json","state":"https://pith.science/pith/7LSHXZUE55YKRYDE5RI5AJEP7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LSHXZUE55YKRYDE5RI5AJEP7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7LSHXZUE55YKRYDE5RI5AJEP7A","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":"0a3c1e83424eabf21e91fd269e6c15d62bf17d670d4a8fb2adbd85b15aad2280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-26T01:15:24Z","title_canon_sha256":"863fae818e8c9cabd0e5d7c02046c4e45ef2cdb3a5da075d65cea35d377b2a0e"},"schema_version":"1.0","source":{"id":"1209.5804","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5804","created_at":"2026-05-18T03:44:23Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5804v2","created_at":"2026-05-18T03:44:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5804","created_at":"2026-05-18T03:44:23Z"},{"alias_kind":"pith_short_12","alias_value":"7LSHXZUE55YK","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7LSHXZUE55YKRYDE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7LSHXZUE","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:c36694e472fc4a2f67c2b3ffd10ca5d53c5a67d557e562bc7eee36e86b4482e7","target":"graph","created_at":"2026-05-18T03:44:23Z","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 consider diagram groups as defined by V. Guba and M. Sapir. A diagram group G acts on the associated cube complex K by isometries. It is known that if a cube complex L is of a finite dimension then every isometry g of L is semi-simple, i.e. its translation length is realized. It was conjectured by D. S. Farley that in the case of a diagram group G the action of G on the associated cube complex K is by semisimple isometries even when K has an infinite dimension. In this paper we give a counterexample to Farley Conjecture and we show that R. Thompson's group F, considered as a diagram group, ","authors_text":"Bronislaw Wajnryb, Pawel Witowicz, Yael Algom-Kfir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-26T01:15:24Z","title":"A parabolic action on a proper, CAT(0) cube complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5804","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":"sha256:41c3720f2d0a26d3307be1894d335b7b120ca2844602b9349e62ab24b14b90a7","target":"record","created_at":"2026-05-18T03:44:23Z","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":"0a3c1e83424eabf21e91fd269e6c15d62bf17d670d4a8fb2adbd85b15aad2280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-26T01:15:24Z","title_canon_sha256":"863fae818e8c9cabd0e5d7c02046c4e45ef2cdb3a5da075d65cea35d377b2a0e"},"schema_version":"1.0","source":{"id":"1209.5804","kind":"arxiv","version":2}},"canonical_sha256":"fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fae47be684ef70a8e064ec51d0248ff83eeb6c3be60f6b29ad88b8c2d96774f3","first_computed_at":"2026-05-18T03:44:23.546613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:23.546613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lS3uANsAaTL2VMYb7akOSO6FzjCpWddhxwmiK9gezonLcOD4Am5JBIFRRXd45/bwLmCYzNC1A8Q8GxEdoK1BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:23.547295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5804","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41c3720f2d0a26d3307be1894d335b7b120ca2844602b9349e62ab24b14b90a7","sha256:c36694e472fc4a2f67c2b3ffd10ca5d53c5a67d557e562bc7eee36e86b4482e7"],"state_sha256":"4be310be73c54f79981902d3e55bce863944b063684882439d29bf6ec79a7742"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKHirmjyiTF2rx6waJ72YwA8hgXp+Vqn3jHaWWiQnTSiSIuvK5aHT6m3oNXqoMCkiCxraQN7dFTzYYT+ecAsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:49:52.990524Z","bundle_sha256":"f8b71b17cd9bef442958b1ea8adf8cca8fd73eb7f3c4721013277c716ef7066e"}}