{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BLENB36CJ4CB456LNUJQVZIRR2","short_pith_number":"pith:BLENB36C","canonical_record":{"source":{"id":"0904.2624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T03:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"709f14a2532947f58f2c8cc841926ad727091e03d0c0b2388efacced9f9d1168","abstract_canon_sha256":"80c9f4ae124c41040cafdec723067eb7e79430b5f95d143fc4ed1292c15c91ee"},"schema_version":"1.0"},"canonical_sha256":"0ac8d0efc24f041e77cb6d130ae5118eb11ea804f51962f1c7d84f7fe40afbce","source":{"kind":"arxiv","id":"0904.2624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2624","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2624v1","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2624","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"BLENB36CJ4CB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BLENB36CJ4CB456L","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BLENB36C","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BLENB36CJ4CB456LNUJQVZIRR2","target":"record","payload":{"canonical_record":{"source":{"id":"0904.2624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T03:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"709f14a2532947f58f2c8cc841926ad727091e03d0c0b2388efacced9f9d1168","abstract_canon_sha256":"80c9f4ae124c41040cafdec723067eb7e79430b5f95d143fc4ed1292c15c91ee"},"schema_version":"1.0"},"canonical_sha256":"0ac8d0efc24f041e77cb6d130ae5118eb11ea804f51962f1c7d84f7fe40afbce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:27.134885Z","signature_b64":"CEKMc3cMACzWnK4q16UfcV8TVJTFTjGxu78EBvhsB5OtD6WJFpH6cHhERvLS1aZnGiaLCStd667m65hi679BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ac8d0efc24f041e77cb6d130ae5118eb11ea804f51962f1c7d84f7fe40afbce","last_reissued_at":"2026-05-18T03:14:27.134444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:27.134444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.2624","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":"2026-05-18T03:14:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eisPaqo3MN71UM4/5Vrb5FW8lJ/SzNfohwg/t3CZMuJ0khsNiCDc+pl20O+4ltL3JJWCWxDnEepu1Z/xrk5EDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:14:11.512747Z"},"content_sha256":"d7d5773de7e9b55cdc8ad65747618c9891132b60c37032168fbe1a6643c46910","schema_version":"1.0","event_id":"sha256:d7d5773de7e9b55cdc8ad65747618c9891132b60c37032168fbe1a6643c46910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BLENB36CJ4CB456LNUJQVZIRR2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Baker's map and the Simplicity of the Higher Dimensional Thompson Groups nV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Matthew G. Brin","submitted_at":"2009-04-17T03:54:01Z","abstract_excerpt":"We show that the baker's map is a product of transpositions (particularly pleasant involutions), and conclude from this that an existing very short proof of the simplicity of Thompson's group V applies with equal brevity to the higher dimensional Thompson groups nV."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2624","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":"2026-05-18T03:14:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NAc3TIEpw/z2nc5WWMlU+zsFwuD/78/Mj8FKWMJ6TT6YhGN8VqzJGJ0Z6QkmCjAUb/se4ZAQNP5j+cFVUbx3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:14:11.513438Z"},"content_sha256":"38bace3da11af9fa74dc18d90e3b72af4fc5afed426c9c7f3ca123ef41b2a37e","schema_version":"1.0","event_id":"sha256:38bace3da11af9fa74dc18d90e3b72af4fc5afed426c9c7f3ca123ef41b2a37e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BLENB36CJ4CB456LNUJQVZIRR2/bundle.json","state_url":"https://pith.science/pith/BLENB36CJ4CB456LNUJQVZIRR2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BLENB36CJ4CB456LNUJQVZIRR2/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":"2026-06-07T06:14:11Z","links":{"resolver":"https://pith.science/pith/BLENB36CJ4CB456LNUJQVZIRR2","bundle":"https://pith.science/pith/BLENB36CJ4CB456LNUJQVZIRR2/bundle.json","state":"https://pith.science/pith/BLENB36CJ4CB456LNUJQVZIRR2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BLENB36CJ4CB456LNUJQVZIRR2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BLENB36CJ4CB456LNUJQVZIRR2","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":"80c9f4ae124c41040cafdec723067eb7e79430b5f95d143fc4ed1292c15c91ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T03:54:01Z","title_canon_sha256":"709f14a2532947f58f2c8cc841926ad727091e03d0c0b2388efacced9f9d1168"},"schema_version":"1.0","source":{"id":"0904.2624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2624","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2624v1","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2624","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"BLENB36CJ4CB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BLENB36CJ4CB456L","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BLENB36C","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:38bace3da11af9fa74dc18d90e3b72af4fc5afed426c9c7f3ca123ef41b2a37e","target":"graph","created_at":"2026-05-18T03:14:27Z","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 that the baker's map is a product of transpositions (particularly pleasant involutions), and conclude from this that an existing very short proof of the simplicity of Thompson's group V applies with equal brevity to the higher dimensional Thompson groups nV.","authors_text":"Matthew G. Brin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T03:54:01Z","title":"On the Baker's map and the Simplicity of the Higher Dimensional Thompson Groups nV"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2624","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:d7d5773de7e9b55cdc8ad65747618c9891132b60c37032168fbe1a6643c46910","target":"record","created_at":"2026-05-18T03:14:27Z","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":"80c9f4ae124c41040cafdec723067eb7e79430b5f95d143fc4ed1292c15c91ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T03:54:01Z","title_canon_sha256":"709f14a2532947f58f2c8cc841926ad727091e03d0c0b2388efacced9f9d1168"},"schema_version":"1.0","source":{"id":"0904.2624","kind":"arxiv","version":1}},"canonical_sha256":"0ac8d0efc24f041e77cb6d130ae5118eb11ea804f51962f1c7d84f7fe40afbce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ac8d0efc24f041e77cb6d130ae5118eb11ea804f51962f1c7d84f7fe40afbce","first_computed_at":"2026-05-18T03:14:27.134444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:27.134444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CEKMc3cMACzWnK4q16UfcV8TVJTFTjGxu78EBvhsB5OtD6WJFpH6cHhERvLS1aZnGiaLCStd667m65hi679BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:27.134885Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7d5773de7e9b55cdc8ad65747618c9891132b60c37032168fbe1a6643c46910","sha256:38bace3da11af9fa74dc18d90e3b72af4fc5afed426c9c7f3ca123ef41b2a37e"],"state_sha256":"5e62268a71e1509ace7b6a8cddbe3e514da1e842341bc7984f9ff6d791ad5845"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ntKBgBCUEhPkq6C7x2rTRQUxmAQVNHxN82/mLtl+PM6GlTZ0axBFK08mOVMiqyVJYPgB3IjmQzEc0S1VbMFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:14:11.517046Z","bundle_sha256":"2c40abf381203bccfc864dd54998d8740a7b21f339440c3266d287f3acdaa6b8"}}