{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BD4ZMOXZ2N7WUV73CKMU2ENIW2","short_pith_number":"pith:BD4ZMOXZ","canonical_record":{"source":{"id":"1710.10670","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-29T18:54:51Z","cross_cats_sorted":[],"title_canon_sha256":"74d4c3f60f7b12c96c87a85a731fe66330a23730c98ac9bf7963ec3f13edb600","abstract_canon_sha256":"179a7dc6ba7278fac9e555716aba742be6a9c342ba3e2cb27dd81290a947d3ce"},"schema_version":"1.0"},"canonical_sha256":"08f9963af9d37f6a57fb12994d11a8b6947e851ad72df40fd016631ec062ff6e","source":{"kind":"arxiv","id":"1710.10670","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10670","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10670v3","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10670","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"BD4ZMOXZ2N7W","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BD4ZMOXZ2N7WUV73","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BD4ZMOXZ","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BD4ZMOXZ2N7WUV73CKMU2ENIW2","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10670","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-29T18:54:51Z","cross_cats_sorted":[],"title_canon_sha256":"74d4c3f60f7b12c96c87a85a731fe66330a23730c98ac9bf7963ec3f13edb600","abstract_canon_sha256":"179a7dc6ba7278fac9e555716aba742be6a9c342ba3e2cb27dd81290a947d3ce"},"schema_version":"1.0"},"canonical_sha256":"08f9963af9d37f6a57fb12994d11a8b6947e851ad72df40fd016631ec062ff6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:29.788877Z","signature_b64":"GjLzFm3zbfssWAmRRA4JzsCDlU3hJxpsNQ4o2uSvH6fIYzfJLZxCWB/SS0QV4SIo+pVpafrM3TX+mujGXkPNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08f9963af9d37f6a57fb12994d11a8b6947e851ad72df40fd016631ec062ff6e","last_reissued_at":"2026-05-17T23:55:29.788271Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:29.788271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10670","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aAmiNAs+yUsgLVp98IDyCV/R+1luqpoTnId81BNRTo8/vFT0pUlf/TEhJEwzjp6w3mqwauu5gPx1nc6QiKGqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:37:12.227446Z"},"content_sha256":"d36b2e339d9ce0592e5d72f94e58687ee3c2f9448aacc9aa20863b296c78ad6f","schema_version":"1.0","event_id":"sha256:d36b2e339d9ce0592e5d72f94e58687ee3c2f9448aacc9aa20863b296c78ad6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BD4ZMOXZ2N7WUV73CKMU2ENIW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Tits alternative for $PD(3)$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Michel Boileau, Steven Boyer","submitted_at":"2017-10-29T18:54:51Z","abstract_excerpt":"We prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always contains a rank 2 free group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10670","kind":"arxiv","version":3},"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":"2026-05-17T23:55:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/41QRKfpVEn+8109J7AqyZOhWdvB0v5D/NtX2WhRF3L6n6Kh+MXT7DnfXHScVfTU5di7BXlVVVb7BpcXsoX7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:37:12.228094Z"},"content_sha256":"fae8d2b26ad4774d428c6b9f2fc5c8e51e86bdb14cc81ce67e440dd32c657999","schema_version":"1.0","event_id":"sha256:fae8d2b26ad4774d428c6b9f2fc5c8e51e86bdb14cc81ce67e440dd32c657999"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2/bundle.json","state_url":"https://pith.science/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2/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":"2026-05-29T20:37:12Z","links":{"resolver":"https://pith.science/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2","bundle":"https://pith.science/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2/bundle.json","state":"https://pith.science/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BD4ZMOXZ2N7WUV73CKMU2ENIW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BD4ZMOXZ2N7WUV73CKMU2ENIW2","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":"179a7dc6ba7278fac9e555716aba742be6a9c342ba3e2cb27dd81290a947d3ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-29T18:54:51Z","title_canon_sha256":"74d4c3f60f7b12c96c87a85a731fe66330a23730c98ac9bf7963ec3f13edb600"},"schema_version":"1.0","source":{"id":"1710.10670","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10670","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10670v3","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10670","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"BD4ZMOXZ2N7W","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BD4ZMOXZ2N7WUV73","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BD4ZMOXZ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:fae8d2b26ad4774d428c6b9f2fc5c8e51e86bdb14cc81ce67e440dd32c657999","target":"graph","created_at":"2026-05-17T23:55:29Z","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 prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always contains a rank 2 free group.","authors_text":"Michel Boileau, Steven Boyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-29T18:54:51Z","title":"On the Tits alternative for $PD(3)$ groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10670","kind":"arxiv","version":3},"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:d36b2e339d9ce0592e5d72f94e58687ee3c2f9448aacc9aa20863b296c78ad6f","target":"record","created_at":"2026-05-17T23:55:29Z","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":"179a7dc6ba7278fac9e555716aba742be6a9c342ba3e2cb27dd81290a947d3ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-10-29T18:54:51Z","title_canon_sha256":"74d4c3f60f7b12c96c87a85a731fe66330a23730c98ac9bf7963ec3f13edb600"},"schema_version":"1.0","source":{"id":"1710.10670","kind":"arxiv","version":3}},"canonical_sha256":"08f9963af9d37f6a57fb12994d11a8b6947e851ad72df40fd016631ec062ff6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08f9963af9d37f6a57fb12994d11a8b6947e851ad72df40fd016631ec062ff6e","first_computed_at":"2026-05-17T23:55:29.788271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:29.788271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GjLzFm3zbfssWAmRRA4JzsCDlU3hJxpsNQ4o2uSvH6fIYzfJLZxCWB/SS0QV4SIo+pVpafrM3TX+mujGXkPNDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:29.788877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10670","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d36b2e339d9ce0592e5d72f94e58687ee3c2f9448aacc9aa20863b296c78ad6f","sha256:fae8d2b26ad4774d428c6b9f2fc5c8e51e86bdb14cc81ce67e440dd32c657999"],"state_sha256":"5caa8e2648a460e9f644e905323c37fd2d1701181ceda8216adc21d59f6ba54d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1cwe92xWyfedWA5qSOnO0DNVGJkKJlUwF8d9DSq5AmIr6OaOc57dg2XorZbmzHkxINyGAUkDzeOoL1sBs7zEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:37:12.231791Z","bundle_sha256":"353f6de3d7a975f359301d4e75b6a6e783df35aaac4f68f4d6493c977453802f"}}